Bed Shear Stress Under Wave Runup on Steep Slopes

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BEDSHEARSTRESSUNDERWAVE RUNUPONSTEEPSLOPES

DANIELHOWE

a thesis in fulfilment of the requirements for the degree of

DOCTOROFPHILOSOPHY

School of Civil and Environmental Engineering

Faculty of Engineering

UNSW Australia

March 2016 Thesis/Dissertation Sheet

Surname/Family Name Howe : Given Name/s Daniel : Abbreviation for degree as give in the University calendar : PhD Faculty Engineering : School School of Civil and Environmental Engineering : Thesis Title Bed shear stress under wave runup on steep : slopes

Abstract 350 words maximum:

Extensive measurements of swash hydrodynamics and bed shear stress were obtained for surging, collapsing, plunging and spilling swashes, in both medium and prototype scale fixed-bed laboratory wave flumes with steep slopes (1:3 and 1:6, respectively). The hydrodynamics of swash flows were found to adhere surprisingly well to principles from classical fluid mechanics, considering they are far from the uniform, steady conditions for which the principles were originally intended. The quadratic stress law was observed to provide accurate estimates of bed shear stress, based on depth-averaged velocity. This was evidenced by back-calculated friction factors, which remained constant during uprush and backwash (except around flow reversal). Friction factors remained consistent for many different wave cases, and appeared to be only affected by bed roughness. These results show much more consistency than previous studies, because of the quality of the prototype scale measurements. Furthermore, the Colebrook-White equation was shown to provide reasonable estimates of friction factors, given a representative bed roughness and Reynolds number. The leading edge of the shoreline during wave runup was found to follow a parabolic trajectory, but only complete collapse of the incident wave. This suggests that the Shen and Meyer (1963) model is valid for all swash types, and not just for well-developed bores. Collapsing and surging swashes tended to collapse slowly on the beachface, with the instantaneous shoreline accelerating in the landward direction during most of the uprush cycle. This extended period of landward acceleration for collapsing and surging waves is not described well in existing swash zone definitions, which assume the bore collapse process is almost instantaneous. A new generalised definition of the swash zone is proposed to clarify this situation, and allow direct comparison between different swash types. Presently the most robust estimates of swash zone bed shear stress can only be obtained from direct measurements, where the active face of the instrument is mounted flush with the bed and fully exposed to the moving fluid, so that no assumptions about boundary layer structure are required. Existing instruments with this capability are hot film anemometers and mechanical shear plates.

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I have been blessed to work under the supervision of Dr Chris Blen- kinsopp and Professor Ian Turner, both of whom are completely un- afraid to get their feet wet (and more) in the name of coastal research, whether on the French Atlantic coast in near-zero conditions, or in the 39 ◦C heat of a shed in the middle of Germany. To Chris, thank you for your constant enthusiasm, and creative ideas. To Ian, thank you for sharing your vast experimental knowledge, and for helping me focus on the bigger picture. I am also grateful to Associate Professor William Peirson, for as- sisting with the derivation of the momentum equation in Chapter 6. Bill, thank you for taking such a keen interest in my research, and encouraging me to pursue ideas that I believed were dead ends. I was fortunate to work with Dr Michael Allis and Assistant Pro- fessor Jack Puleo during the gwk experiments. Mike, thank you for your eagerness in everything you do, and for your organisation skills in compiling the masses of data we collected. Jack, thank you for making experimental work such fun, all day long. Thank you to the technical staff at gwk, for helping us make the most of our time in the ﬂume. In particular thank you to Stefan Schim- mels, for making us feel so welcome, and for going beyond the call of duty to help us complete our experiments. Thank you to Rob Jenkins, Larry Paice, and Mark Whelan, for your assistance with all things mechanical and electrical, for inspiring me with your elegant craftsmanship, and for always making me feel welcome in the workshop. Thank you to my parents Peter and Janet, for always showing interest in my work. To my wife Vicky, thank you for your love and support, and for waiting patiently for me whenever I stand on the beach to watch the waves. Lastly, I thank the Lord for giving me an eagerness to solve prob- lems and a curiosity to learn more about the processes of the natural world. It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.

Albert Einstein (1879–1955) CONTENTS

1 introduction1 1.1 Wave runup 1 1.2 Sediment transport 4 1.3 Motivations 7 2 review9 2.1 Bed level and hydrodynamics 9 2.2 Bed shear stress 14 2.3 Conclusion 20 3 methodology 23 3.1 Instrumentation 23 3.2 Experimental design 28 3.3 Conclusion 34 4 data processing 35 4.1 Definitions 35 4.2 Depth measurements 35 4.3 Leading edge trajectories 40 4.4 Depth-averaged velocity 43 4.5 Shear plate processing 46 4.6 Conclusion 53 5 anatomy of wave runup 55 5.1 Classical models for wave runup 55 5.2 Different modes of runup 57 5.3 Swash zone definitions 58 5.4 Experimental observations 61 5.5 General definition of swash 67 5.6 Discussion 68 5.7 Conclusion 70 6 bed shear stress and fluid momentum 71 6.1 Motivations for indirect measurement 71 6.2 Derivation of momentum equation 72 6.3 Application of momentum equation 74 6.4 Discussion of results 78 6.5 Alternative methods 83 6.6 Conclusion 86 7 comprehensive bed shear measurements 89 7.1 Variation with hydrodynamic conditions 89 7.2 Quadratic stress law and friction factors 95 7.3 Friction factors for numerical modelling 101 7.4 Estimating f from runup trajectories 106 7.5 Conclusion 109 8 conclusion 111 bibliography 115

xiii LISTOFFIGURES

Figure 1.1 Nearshore wave transformation 1 Figure 1.2 Different phases of swash cycle 4 Figure 1.3 Modes of sediment transport 5 Figure 2.1 Typical bed shear stress time series 15 Figure 2.2 Turbulent boundary layer structure 16 Figure 2.3 Momentum integral method 17 Figure 2.4 Previous measurements of τ0 19 Figure 2.5 Comparison of different studies 19 Figure 3.1 Photographs of ultrasonic sensors 23 Figure 3.2 Detecting water with laser light 25 Figure 3.3 Photographs of laser scanners 26 Figure 3.4 Photographs of shear plates 27 Figure 3.5 Acoustic Doppler profiler 28 Figure 3.6 Experimental setup at wrl 29 Figure 3.7 Experimental setup at gwk 31 Figure 3.8 Experimental setup at gwk (detail) 32 Figure 3.9 Shear plate with rough moulded surface 33 Figure 3.10 Water surface profiles from XBeach model 34 Figure 4.1 Definition sketch of experimental variables 35 Figure 4.2 Ultrasonic sensors in wrl experiments 36 Figure 4.3 Ultrasonic sensor and laser scanner heatmaps 37 Figure 4.4 Ultrasonic sensor and laser scanner profiles 37 Figure 4.5 Video timestack and laser scanner heatmaps 39 Figure 4.6 Performance of laser scanners 39 Figure 4.7 Depths and runup trajectories 40 Figure 4.8 Optical flow patterns in swash 41 Figure 4.9 Runup trajectories from video 42 Figure 4.10 Tracking gwk runup trajectories 43 Figure 4.11 Velocity calculation method 44 Figure 4.12 Swash as a rarefaction wave 45 Figure 4.13 wrl depth-averaged velocities 46 Figure 4.14 gwk depth-averaged velocities 47 Figure 4.15 uq shear plate under single swash event 48 Figure 4.16 uq shear plate under multiple swash events 48 Figure 4.17 uq shear plate signal during draining 49 Figure 4.18 Draining process inside uq shear plate 50 Figure 4.19 Filtering signal from gwk shear plate 50 Figure 4.20 Hydrostatic forces on gwk shear plate 51 Figure 4.21 Correcting gwk shear plate signal 51 Figure 4.22 Shear plate results (rough/smooth) 52 Figure 5.1 Classical runup solutions 56

xiv Figure 5.2 Different swash types 57 Figure 5.3 Mean water level variation 58 Figure 5.4 Definition of swash zone 59 Figure 5.5 Process of bore collapse 60 Figure 5.6 Optical flow heatmap 62 Figure 5.7 wrl runup trajectories 63 Figure 5.8 Normalised runup trajectories 63 Figure 5.9 Spilling and surging swashes 64 Figure 5.10 Depth heatmaps for contrasting T 65 Figure 5.11 Measured gwk runup trajectories 65 Figure 5.12 Normalised runup trajectories 66 Figure 5.13 Shoreline motion during overrun event 66 Figure 5.14 Proposed new swash zone definition 68 Figure 5.15 Flow chart of different nearshore regions 69 Figure 5.16 Swash zone location for irregular waves 69 Figure 6.1 Depth-averaged unsteady free-surface flow 72 Figure 6.2 Spatial and temporal variation in depth 76 Figure 6.3 Spatial and temporal variation in velocity 76 Figure 6.4 Stationary terms of momentum equation 77 Figure 6.5 Convective terms of momentum equation 77 Figure 6.6 Sum of all terms of momentum equation 78 Figure 6.7 Validation of depth-averaged velocities 80 Figure 6.8 Results using acoustic Doppler profilers 80 Figure 6.9 Sensitivity of cross-shore spacing 81 Figure 6.10 Variation in free-surface profile 82 Figure 6.11 Measured velocity profiles 82 Figure 6.12 Application of log law method 84 Figure 6.13 Velocities from acoustic Doppler profiler 85 Figure 6.14 Application of momentum integral method 85 Figure 6.15 Sensitivity of boundary layer thickness 86 Figure 7.1 Peak bed shear stress for different depths 90 Figure 7.2 Measured τ0 on rough and smooth surfaces 90 Figure 7.3 Scale comparison between experiments 91 Figure 7.4 Measured τ0 for different experimental scales 92 ∂h Figure 7.5 Relationship between τ0, U, and ∂t 93 Figure 7.6 Cross-shore variation in τ0 (wrl) 94 Figure 7.7 Cross-shore variation in τ0 (other studies) 94 Figure 7.8 f values for contrasting wave periods (wrl) 96 Figure 7.9 f values for contrasting roughness (wrl) 97 Figure 7.10 Cross-shore variation in f values (wrl) 97 Figure 7.11 f values for contrasting roughness (gwk) 98 Figure 7.12 f values for contrasting wave heights (gwk) 98 Figure 7.13 f values for contrasting wave periods (gwk) 99 Figure 7.14 f values for irregular waves (gwk) 99 Figure 7.15 Cross-shore variation in f values (gwk) 100 Figure 7.16 Boundary layers during flow reversal 100 Figure 7.17 f values from previous and current studies 102 Figure 7.18 f values from Colebrook-White equation (wrl) 104 Figure 7.19 f values from Colebrook-White equation (gwk) 104 Figure 7.20 f values from Colebrook-White equation (gwk) 105 Figure 7.21 Summary of Colebrook-White results 105 Figure 7.22 Runup trajectories on smooth/rough surfaces 107 Figure 7.23 Runup limits on smooth/rough surfaces 107 Figure 7.24 Runup trajectories for non-breaking waves 108 Figure 7.25 Evaluation of Puleo and Holland( 2001) model 109

LISTOFTABLES

Table 2.1 Previous ﬁeld studies 13 Table 2.2 Previous laboratory studies 14 Table 2.3 Previous measurements of τ0 20 Table 3.1 Ultrasonic sensor comparison 24 Table 3.2 Laser scanner comparison 26 Table 3.3 Wave conditions for wrl experiments 30 Table 3.4 Wave conditions for gwk experiments 32

xvi LISTOFSYMBOLS

symbol description units

D Hydraulic diameter m f Fanning friction factor - F Force N g Gravitational acceleration m/s2 h Water depth m H Offshore wave height m

ks Roughness height m

L0 Deep-water wavelength m m Mass kg p Momentum kg.m/s P Pressure N/m2

Rx Runup length m Re Reynolds number - t Time s T Offshore wave period s u Fluid velocity m/s

u0 Free-stream velocity m/s

us Shoreline velocity m/s U Depth-averaged velocity m/s x Bed-parallel co-ordinate m

x0 Horizontal co-ordinate m

xs Shoreline position m z Bed-normal co-ordinate m

z0 Vertical co-ordinate m β Beach slope - δ Boundary layer thickness m θ Shields parameter - κ von Kármán constant - λ Darcy friction factor - ν Kinematic viscosity m2/s

ξ0 Surf similarity parameter - ρ Water density kg/m3 2 τ0 Bed shear stress N/m

xvii

1 INTRODUCTION

1.1 wave runup

Wind waves are the result of the balance between wind stresses acting on the surface of the ocean and the gravitational force trying to restore the equilibrium water surface. When waves approach the coastline they begin to transform as they enter shallow water. As each wave begins to ‘feel’ the seabed, its celerity reduces and face steepens, until it eventually breaks and rolls in through the surf zone towards the shore. The last of the wave’s energy is dissipated as it reaches the land and rushes up the beachface. This region where the water meets the land is the swash zone (Figure 1.1). The swash zone is a focus of active research for several reasons. Most importantly, the shape of the exposed beach proﬁle is governed by swash zone sediment transport. Sediment concentrations in the swash zone are far higher than in the surf zone (e.g. Osborne and Rooker, 1999; Masselink et al., 2005). This drives sediment transport in the cross-shore direction, as sediment in the swash zone is ex- changed between marine processes in the inner surf zone and terrestrial processes on the beachface and dune system. In this way swash mechanisms determine the rate of beach erosion and recovery during and after storms. Accurate estimates of shoreline positions are essential when plan- ning effective measures to accommodate future changes in sea level. Unfortunately it is generally acknowledged that swash zone hydrodynamics and sediment transport are not presently well understood, and this limits our ability to predict the evolution of shorelines into the future.

Figure 1.1: Wave transformation and runup in the nearshore environment. After Svendsen( 2006).

1 2 introduction

The swash zone is a particularly challenging environment to measure, because the flow is shallow, turbulent, aerated and rapidly varying. Placing a recording instrument in the swash zone of a sandy beach is difficult. If it is too high above the bed it may not become submerged in the swash at all; if it is too close to the bed it may become buried in the sand after a small number of swash events. The instrument must also be robust enough to survive (and make observations) in rugged conditions, but it must not be so large that it causes a significant disturbance to the flow. This is further complicated by migration of the swash zone throughout tidal cycles, and infiltration and exfiltration between the swash and the beach water table.

1.1.1 Recent progress

The swash zone has historically received less attention than the inner surf zone, but advances in instrumentation have lead to a surge of endeavours in the past two decades (see reviews by Butt and Rus- sell, 2000; Elfrink and Baldock, 2002; and Masselink and Puleo, 2006). Since the first international workshop on swash zone processes (Puleo and Butt, 2006) many efforts have been made to develop novel measurement techniques to make more extensive swash zone measurements in the laboratory and the field. Some highlights of the new instrumentation and experimental methods developed since the 2006 swash workshop are described below. Barnes and Baldock( 2007) used a flush-mounted shear plate to directly measure the bed shear stress under swash events in a laboratory. Masselink et al.( 2009) used an array of ultrasonic sensors to measure changes in the bed level of a sandy beach on a wave by wave basis. Blenkinsopp et al.( 2010a) used a laser scanner to record high resolution measurements of the time-varying water surface elevations in the swash zone of a sandy beach. Puleo et al.( 2010) developed a conductivity concentration profiler to measure near-bed suspended sediment concentrations in the swash zone in a laboratory, and also in the field (Lanckriet et al., 2013). Puleo and Lanckriet( 2011) deployed an acoustic Doppler profiler in the field to measure high resolution velocity profiles close to the bed. Baldock et al.( 2014) generated swashes in a laboratory using viscous detergents (instead of water), to observe the behaviour of the landward tip of the swash in greater detail. This progress has also been assisted by a number of international collaborative experiments that have taken place in recent years, where 1.1 waverunup 3 dozens of instruments on time-synchronised data acquisition systems have been deployed on a high energy beach at Truc Vert, France (Mas- selink et al., 2009), a macrotidal beach at Perranporth, UK for the Beach Sediment Transport experiment (BeST; Puleo et al., 2014) and on steep gravel and sand beaches in the prototype scale Delta flume in the Netherlands for the BARrier Dynamics EXperiment (BARDEX; Williams et al., 2012, and BARDEX II; Masselink et al., 2013).

1.1.2 Swash zone hydrodynamics

A useful place to begin an examination of swash zone hydrodynamics is with Waddell( 1976), who stated that ‘the backwash ﬂow is deﬁnitely not the reverse of the uprush’. Let us consider swash from a fully-developed bore on a sandy beach during a rising tide. The complete swash cycle can be divided into four phases (Figure 1.2):

1. A bore approaches the dry sand. The top of the water column has high a onshore velocity, while the ﬂow at the bottom of the water column is directed offshore from the preceding backwash. This rotational ﬂow is highly turbulent, and is responsible for mobilising sand grains from the bed and mixing them through the water column (Kraus, 1985; Butt and Russell, 1999).

2. The swash may accelerate briefly as it runs up the beachface, due to the energy released during bore collapse (Puleo et al., 2003; Baldock and Hughes, 2006). If the tide and beach ground water levels permit, some fluid may infiltrate into the beach during this uprush phase (Turner and Masselink, 1998).

3. The swash reaches its maximum runup limit. Flow reversal has already began in the lower regions of the uprush (Masselink and Hughes, 1998; Power et al., 2011), causing thinning of the swash lens.

4. The fluid accelerates in the seaward direction during backwash until it collides with the next incident wave, and the cycle begins again. This final phase is potentially accompanied by fluid exfiltration from the bed (Baird et al., 1996).

The landward edge of the swash zone is easily identified as the maximum runup excursion on the beachface. The seaward edge of the swash zone is more difficult to define, but is generally adopted to be the point of bore collapse (Hughes and Turner, 1999), which is 4 introduction

1. 2.

3. 4.

Figure 1.2: The four phases of a swash cycle on a sandy beach. The water table is shown in dotted lines. After Osborne and Rooker( 1997).

described as the fluid acceleration caused by a rapid conversion of potential to kinetic energy at the shoreline (Yeh and Ghazali, 1988). The peak uprush and backwash velocities are often comparable, but the duration of the backwash can be significantly longer than that of the uprush (Masselink and Hughes, 1998). This velocity skewness has important implications for swash zone sediment transport. A bore on a natural beach will often reach the shoreline before the backwash phase of the preceding swash is complete. This backwash flow will have a retarding effect on the uprush, sometimes stopping it completely. These swash-swash interactions have the effect of removing high-frequency motions from the inner surf zone, and as a result, the duration of swash oscillations will always be longer than the period of the incident waves (Emery and Gale, 1951). The duration of swash oscillations will only ever be equal to the offshore wave period in the case of monochromatic waves, which are only possible in a laboratory (Mase, 1995).

1.2 sediment transport

There are three generally accepted modes of sediment transport underneath a moving fluid; bed load, sheet flow and suspended load (Figure 1.3). Bed load consists of individual grains rolling or sliding along the bed; sheet flow is an extension of bed load, where a number 1.2 sedimenttransport 5

A. B. C.

Figure 1.3: Modes of sediment transport: (A) bed load, (B) sheet flow, and (C) suspended sediment. After Fredsøe and Deigaard( 1992). of layers of sediment are mobilised at once but stay in contact with each other; and suspended load consists of sediment grains that are carried up within the water column and are supported by turbulent currents (Reeve et al., 2004). In the swash zone, the nature of sediment transport differs greatly between uprush and backwash. At the beginning of the uprush, there is a high sediment concentration in the water column (suspended load) from the turbulent bore churning at the bed before its collapse (Osborne and Rooker, 1999). At the top of the uprush however, the fluid velocity reduces to zero and most of the suspended sediment has settled out of the water column. During the backwash phase the fluid slowly accelerates due to gravity, resulting in an increasing level of bed load and sheet flow (Masselink and Hughes, 1998). The equilibrium shoreline of a beach migrates back and forth over time. High steepness wave conditions will typically cause the beachface to retreat landward as sediment is stripped from the beach and deposited offshore, whereas low steepness wave conditions will typically cause the beachface to advance seaward, as sediment from the surf zone is transported back towards the land. The rate of change at the beachface is highest during storms. In fact, years of beach growth driven by low energy waves can be removed by a single storm in just a few hours (Kamphuis, 2010). Sediment transport across the swash zone plays a significant role in shoreline evolution. Field studies have shown that suspended sediment transport rates in the swash zone are much higher than those in the surf zone (Osborne and Rooker, 1999; Masselink et al., 2005). The uprush and backwash motions of every swash have a destabilising effect on sand grains. The volume of sand transported in a single swash may be small (Blenkinsopp et al., 2011), but the action of repeated swashes drives erosion and accretion on the beachface. In this way the beach shoreline is constantly migrating back and forth. Labor- 6 introduction

atory tests have shown that even when the incident waves are kept constant, the beach does not develop a stable form, but instead continues to oscillate and evolve in a state of constant dynamic equilibrium (Swart, 1974).

1.2.1 Sediment transport modelling

Much of our current understanding of sediment transport began with the work of Shields( 1936), which lead to the deﬁnition of the Shields parameter, a dimensionless number used to describe the relationship between the mobilising and stabilising forces acting on sediment grains. The mobilising forces are bed shear stress (for bed load and sheet ﬂow), and turbulence (for suspended load), while the stabilising force is gravity (Fredsøe and Deigaard, 1992). The Shields parameter, θ is given by:

τ θ = 0 (1.1) (ρ ρ)gd s −

where τ0 is bed shear stress, ρs and ρ are the densities of sediment and ﬂuid, respectively, g is gravitational acceleration, and d is a representative sediment grain size. For steady ﬂows in deep channels (such as rivers) bed shear stress is often given by:

τ0 = ρgh sin(β) (1.2)

where h is ﬂuid depth, and β is bed slope. In the swash zone however, the ﬂow is shallow, so bed shear stress is generally assumed to follow the quadratic stress law, adapted from the Rayleigh( 1876) drag equation:

1 τ = ρ f U U (1.3) 0 2 | |

where f is the Fanning( 1893) friction factor, and U is depth-averaged ﬂow velocity. Many modern swash zone sediment transport models are based on formulations derived from the work of Meyer-Peter and Müller (1948) and Bagnold( 1966), which both use bed shear stress as the driving force for sediment mobilisation. These models therefore re-

quire accurate estimates of τ0 and f . Unfortunately there are very few measurements of bed shear stress available, and results vary widely between studies. 1.3 motivations 7

1.3 motivations

For coastal engineers to be able to accurately predict the position of coastlines into the future, an improved understanding of swash zone hydrodynamics is required. Our current understanding of nearshore sediment transport is dependent on bed shear stress, a parameter which has not yet been comprehensively measured, due to the difﬁ- culty of deploying instruments in the swash zone. In this study a number of different instruments are used to record new experimental measurements of swash zone hydrodynamic processes, with a particular focus on bed shear stress. The trajectories of swash motions under different wave conditions are considered, and the applicability of the quadratic stress law in the swash zone is examined. The experiments in this study are performed on steep, impermeable slopes, and therefore the results are especially relevant to engineered coastal structures.

2 REVIEW

Chapter 1 identified the challenges of deploying instruments inside the swash zone. Swash zone flows are intermittent, shallow, turbulent, aerated, rapidly varying and Lagrangian in nature. This means an instrument making Eulerian measurements at a fixed location on the beachface will have a discontinuous time series as the instrument is alternately submerged and exposed by passing swashes (Puleo et al., 2000). This chapter will review previous investigations into wave runup, with a focus on the development of instrumentation over time.

2.1 bed level and hydrodynamics

Many different instruments have been deployed in ﬁeld experiments to measure the hydrodynamic processes inside the swash zone both on natural beaches and under laboratory conditions (see reviews by Butt and Russell, 2000; Elfrink and Baldock, 2002; and Masselink and Puleo, 2006).

2.1.1 Bed level and ﬂow depths

Early investigations in the swash zone were based on observations with the naked eye or measuring tape, to record the size of morphological features (e.g. Branner, 1900). Later investigators buried stakes in the swash zone and used these as benchmarks to manually measure changes in bed level (Sallenger, 1979; Sallenger and Richmond, 1984; Masselink et al., 1997). Because of the manual nature of these measurements, it is difficult to measure changes between individual swash events using this technique. The first high-frequency field measurements of bed levels in the swash zone were reported by Waddell( 1973) who observed swash- swash interactions and bed level changes between swash events with two capacitance wave gauges installed vertically in the upper swash zone. Hughes( 1992) took a similar approach with an array of six capacitance wave gauges distributed evenly across the swash zone of a

9 10 review

natural beach, and made precise measurements of bed levels, instantaneous water depths, and runup trajectories. These measurements were found to be of smaller magnitude than expected, compared with predictions from the shallow water equations. Swash depths have also been measured in the field using buried or flush-mounted pressure transducers. (Baldock et al., 2001) buried pressure measurement probes slightly underneath the bed of a natural beach and found that pressure gradients induced from swash events were much higher than those induced from tidal groundwater flows. Butt and Russell( 2005) used flush-mounted pressure transducers on a natural beach to observe high levels of sediment mobilisation caused by hydraulic jumps in backwash flows. Buried pressure transducers have the advantage of being able to tolerate small changes in bed level without requiring adjustment, but large bed level changes could lead to incorrect measurements if there is vertical flow through the bed beneath the sensor (Turner, 1998). The first remote measurements of bed level on a natural beach were recorded by Masselink et al.( 2009), who mounted an array of 45 ultrasonic altimeters above the beachface. This configuration allowed instantaneous measurements of bed level or fluid depth (if a swash was present) without interfering with the flow, unlike previous measurement techniques. Sediment fluxes of over 100 kg per unit meter beach width were regularly observed for individual swash events during this experiment. Blenkinsopp et al.( 2010a) was first to report the deployment of a two-dimensional laser scanner above the swash zone of a sandy beach, where it made non-intrusive measurements of bed level and swash depth at a significantly higher spatial and temporal resolution than had been possible using previous instruments.

2.1.2 Runup excursion

Emery and Gale( 1951) used video records to make observations on the oscillatory motion of the shoreline in the swash zone, and found that the duration of runup on gently sloping beaches is longer than on steep beaches. Since this pioneering study, optical remote sensing of the nearshore environment has developed into much more sophisticated video capturing systems. The most notable of these is the Argus system, which can provide continuous recordings of geo-referenced images from an array of synchronised video cameras (Holman and 2.1 bed level and hydrodynamics 11

Stanley, 2007). By taking cross-shore transects of contiguous pixels across the beachface and inner surf zone for each video frame, a dataset in space and time (a timestack) can be produced. Holland and Holman( 1993) used video timestacks to track swash trajectories on a natural beach and examine the statistical distribution of the maximum runup excursions. (Holland et al., 2001) applied particle image velocimetry techniques to measure flow patterns across the entire width of the swash zone, and validated their measurements with an in-situ ducted impeller current meter. Many field studies have used resistance wave gauges (runup wires) suspended just above and parallel to the bed to measure the spatial extent of individual swash excursions. Perhaps the most sophisticated these studies was that of Raubenheimer et al.( 1995), in which five parallel runup wires were stacked at different heights above the bed of a gently sloping beach. This study found that swash motions were well-predicted by the shallow water equations, based on wave forcing from a point 50 m offshore. Runup wires are effective instruments, but they tend to be difficult to install, require regular readjustment, and are easily fouled with seaweed and other foreign objects (Guza and Thornton, 1982). Laser scanners have also been used to provide non-intrusive observations of runup excursions. Almeida et al.( 2013) installed a two- dimensional laser scanner on a tower above a gravel beach and extrac- ted runup trajectories during storm conditions. Observations were also collected at night, an operation not possible with traditional optical sensors.

2.1.3 Velocity and ﬂow structure

Early field measurements of fluid velocities in the swash zone were recorded with ducted impeller flow meters, e.g. Sonu et al.( 1974), who observed the velocity power spectrum and found that swash oscillations were of greater duration than incident waves on a natural beach. Niemeyer and Barker( 1990) installed an electromagnetic flow meters close to the bed on a natural beach, and made observations of sediment layers in sheet flow conditions. Ducted impeller flow meters can operate even when they are not completely submerged (unlike electromagnetic current meters), but they cannot record rapid changes in velocity (particularly during uprush) because of the inertia of the impeller itself (Masselink and Hughes, 1998). 12 review

Holland et al.( 1998) was one of the first to deploy an acoustic Doppler velocimeter in the field to measure swash zone flow velocities at a single point close to the bed. This study identified velocity as an important (but not exclusive) parameter in estimating sediment transport. Continued development of acoustic velocity sensors allowed Puleo et al.( 2012) to install an acoustic Doppler profiler in the field and simultaneously measure swash velocity profiles in three dimensions at 1 mm intervals in the lower 20 mm of the water column, and then inferring bed shear stress from these velocity profiles. Acoustic Doppler profilers are capable of measuring flow velocity profiles at a very high spatial and temporal resolution, but their performance can be degraded if the water is too clear for a detectable backscatter signal to be produced, if acoustic beam is blocked by seaweed or other objects, or if the concentration of bubbles or suspended sediment is too high (Elgar et al., 2005). Larson and Sunamura( 1993) used particle image velocimetry to examine flow structure and sediment movement in the swash zone of a small sandy beach in a laboratory, with a particular focus on a beach step just below the still water level. Advances in high-speed camera technology and image processing have allowed this technique to develop to the stage where the structure of swash flows can be measured in great detail (Pedrozo-Acuña et al., 2011). The precise geometry and lighting requirements of particle image velocimetry and related techniques (e.g. laser Doppler velocimetry, laser induced fluorescence, and bubble image velocimetry) make field installations very difficult, so most studies to date have been conducted in a laboratory setting. Depth-averaged velocities in swash flows have also been calculated using volume continuity, based on measured flow depths across the beachface. Blenkinsopp et al.( 2010b) calculated velocities from measured fluid depths provided by an array of 45 ultrasonic sensors, and found a high level of velocity skewness in the offshore direction. This technique was found to perform well when validated against measurements from co-located electromagnetic current meters. It also has the advantage of being non-intrusive, and not requiring constant adjustment after minor changes in bed level.

2.1.4 Development of instrumentation

One challenge with ﬁeld deployments of in-situ instruments is that they often need to be installed just above (or buried just beneath) the 2.1 bed level and hydrodynamics 13

Table 2.1: Selection of previous ﬁeld studies on natural beaches showing the development and adoption of different instrumentation over time. Studies with a focus on bed shear stress are shaded in grey.

study instrumentation areaofinterest

Emery and Gale( 1951) 10 Runup excursions Waddell( 1973) 2 Swash-swash interactions Sonu et al.( 1974) 2 5 Internal fluid velocities Sallenger( 1979) 1 Cusp formation Guza and Thornton( 1982) 3 Runup energy spectra Holman and Guza( 1984) 3 10 Runup excursions Hughes( 1992) 2 Shallow water equations Holland and Holman( 1993) 3 10 Runup statistics Baird et al.( 1996) 4 Groundwater interactions Hughes et al.( 1997) 2 5 Sediment transport Masselink et al.( 1997) 1 3 Beach cusps after storms Holland et al.( 1998) 5 7 10 Cross shore sediment flux Masselink and Hughes( 1998) 3 5 Sediment transport Turner and Masselink( 1998) 1 3 4 Infiltration and exfiltration Butt and Russell( 1999) 6 Suspended sediment Osborne and Rooker( 1999) 2 7 Suspended sediment Puleo et al.( 2000) 4 5 Bore-generated turbulence Holland et al.( 2001) 5 10 Horizontal flow structure Puleo and Holland( 2001) 10 Friction factor estimation Raubenheimer( 2002) 1 4 7 Swash velocities Conley and Griffin( 2004) 1 10 Bed shear stress Butt and Russell( 2005) 4 6 10 Hydraulic jumps in swash Elgar et al.( 2005) 6 7 Swash velocities Masselink et al.( 2005) 4 6 7 Suspended sediment Baldock and Hughes( 2006) 1 10 Swash pressure gradients Austin and Buscombe( 2008) 1 3 4 6 7 10 Gravel beach evolution Masselink et al.( 2009) 4 6 7 8 Transport over tidal cycles Masselink et al.( 2010) 1 4 6 7 8 10 Transport on gravel beach Blenkinsopp et al.( 2010a) 6 8 9 Free surface elevation Puleo et al.( 2012) 4 6 7 8 9 10 Sheet flow transport Almeida et al.( 2013) 8 9 10 Gravel beach during storm 1. Buried stakes 5. Ducted impeller current meter 9. Laser scanner 2. Capacitance gauges 6. Electromagnetic current meter 10. Video camera 3. Runup wire 7. Acoustic Doppler velocimeter 4. Pressure transducers 8. Ultrasonic sensors 14 review

Table 2.2: Selection of previous studies on laboratory beaches showing the development and adoption of different instrumentation over time. Studies with a focus on bed shear stress are shaded in grey.

study instrumentation areaofinterest

Miller( 1968) 1 2 Runup on rough surfaces Synolakis( 1987) 1 3 Non-breaking waves Yeh and Ghazali( 1988) 1 5 Bore collapse Larson and Sunamura( 1993) 7 Phases in swash cycle Baldock and Holmes( 1996) 2 4 Pressure gradients Baldock et al.( 1997) 2 8 Low frequency waves Cox et al.( 2000) 6 Bed shear stress Petti and Longo( 2001) 2 4 6 Turbulence Cowen et al.( 2003) 3 7 Bed shear stress Barnes and Baldock( 2007) 8 9 Bed shear stress O’Donoghue et al.( 2010) 2 3 7 Swash hydrodynamics Alsina and Cáceres( 2011) 8 9 Suspended sediment Sumer et al.( 2011) 5 6 Bed shear stress Pedrozo-Acuña et al.( 2011) 5 7 8 Presure gradients Masselink et al.( 2013) 1 5 8 9 Barrier dynamics 1. Video 4. Capacitance gauges 7. Particle image veloc. 2. Runup wire 5. Pressure transducers 8. Acoustic Doppler veloc. 3. Resistance gauges 6. Laser Doppler veloc. 9. Ultrasonic sensor

bed. These instruments require constant height adjustment to ensure their correct operation every time the bed moves up or down. This has lead to the increased adoption of optical and acoustic remote sensors, which require minimal adjustment (Table 2.1). In contrast to field studies, laboratory experiments are performed in controlled conditions (often on fixed beds). This allows for the use of additional measurement techniques such as laser Doppler velocimetry and particle image velocimetry to make precise cross-sectional measurements of swash flows (Table 2.2).

2.2 bed shear stress

Many investigators have attempted to measure bed shear stress in the laboratory and the field using a variety of different direct and indirect techniques. For the purpose of comparison, the studies herein are considered to be direct only if they were recorded using instruments with a flat transducer surface mounted flush with the bed. Time-varying measurements of bed shear stress under swash flows are characterised by three distinct phases (Figure 2.1): 2.2 bed shear stress 15

0.4 (m)

h 0.2 Uprush Backwash 0 0 2 4 6 8 10

(m/s) 0 U 5 − 0 2 4 6 8 10

50 ) 2

0 (N/m 0 τ 50 − 0 2 4 6 8 10 t (s)

Figure 2.1: Typical depth (top), depth-averaged velocity (middle), and bed shear stress (bottom) time series, for a single swash event.

1. Uprush: a sharp transition from zero to a maximum in onshore-

directed τ0, as the leading edge of the runup passes.

2. Flow reversal: a gradual reduction of τ0 to zero, as the ﬂuid slows and begins to reverse.

3. Backwash: a gradual increase in offshore-directed τ0, as the ﬂow accelerates back down the beachface.

2.2.1 Indirect measurements

Most indirect measurements of swash zone bed shear stress involve fitting measured near-bed velocities to a logarithmic boundary layer velocity profile (Figure 2.2) according to the law of the wall (or log law), after von Kármán( 1930): u? z u = ln (2.1) κ z0 where u is the velocity profile, κ is the von Kármán constant (κ 0.4), ≈ z is height above the bed, z0 is the height above the bed where the idealised velocity is zero (z0 = ks/30 for hydraulically rough flow, 16 review

Free stream ﬂow region

Log law z region

z0 Laminar sublayer

Figure 2.2: Actual velocity proﬁle ( ) and log law approximation ( ), inside a turbulent boundary layer (not to scale).

where ks is Nikuradse( 1933) sand grain roughness), and u? is shear velocity, given by:

p u? = τ0/ρ (2.2)

where τ0 is bed shear stress, and ρ is fluid density. The law of the wall is not valid in the laminar sublayer, but for swash flows the laminar sublayer is so small (typically less than a millimetre), so this simpli- fication is justified. Accurate measurements of velocity and boundary layer thickness are required when using this method to estimate bed shear stress. This is particularly challenging because boundary layers in swash flows are small and vary rapidly (Barnes and Baldock, 2010). Cox et al.( 2000) measured swash velocities in a laboratory at four vertical locations within 3 mm of the bed using laser Doppler velocimetry (LDV), and estimated the bed shear stress from these profiles at a point in the middle of the swash zone using the log law. They found the maximum bed shear stress occurred just below still water level, and that the quadratic stress law, (1.3), provided good estimates of calculated bed shear stress (although f did not remain constant across the swash zone). Several studies have attempted to fit the log law to observations on natural beaches, including Masselink et al.( 2005), who measured swash zone flow velocities with two electromagnetic current meters (EMCMs) installed at heights of 0.03 m and 0.06 m above the bed, and Puleo et al.( 2012), who measured velocity profiles of swash flows in a region 20 mm from the bed with a 2 mm vertical resolution, using a 2.2 bed shear stress 17 acoustic Doppler profiler (ADP). In these two studies 30 and 22 individual swash events were selected, normalised in time and combined into ensemble-average events. The log law was used to calculate the instantaneous bed shear stress from these velocity profiles. The challenge with the log law technique is that swash boundary layers are thin (typically a few centimetres on natural beaches, and often smaller in the laboratory). Obtaining flow velocity profiles in this region is difficult, and there is uncertainty associated with the actual log law fitting, due to the sensitivity of the technique to the choice of z0. An alternative technique for estimating bed shear stress from velocity profiles (originally formulated for steady flows in open channels) is the momentum integral approach described by Fredsøe and Deigaard( 1992):

Z z0+δ ∂ τ0 = ρ (u0 u) dz ,(2.3) z0 ∂t − where τ0 is bed shear stress, ρ is ﬂuid density, δ is boundary layer thickness, u0 is free stream velocity, u is the velocity inside the boundary layer, t is time, and z0 is the height above the bed where the velocity is zero. The momentum integral method relates bed shear stress to the shape of the boundary layer as it changes through time (Figure 2.3). This technique has been applied by Ruju et al.( 2015), who estimated bed shear stress from acoustic Doppler proﬁler measurements on a sandy beach in a prototype scale laboratory.

z u0

u u 0 − z0 u

Figure 2.3: Idealised boundary layer structure used in the momentum integral method (not to scale). 18 review

Another technique used for estimating swash zone bed shear stress is to relate it to the turbulent kinetic energy (TKE) in the ﬂuid using

τ0 = C1 ,(2.4)

where C1 is an empirical constant (C1 = 0.2, according to Soulsby, 1983), and k is the turbulent kinetic energy, deﬁned as

1 2 2 2 k = ρ u0 + v0 + w0 ,(2.5) 2

where u0, v0, and w0 are the turbulent velocity fluctuations in the x, y and z directions, respectively. The turbulent fluctuations are small deviations between the instantaneous velocity, u, and the mean or ensemble-average velocity, u¯, such that u = u u¯. 0 − Kikkert et al.( 2012) used particle image velocimetry (PIV) to measure the structure of swash flows in a laboratory at a high resolution. The measured instantaneous horizontal and vertical fluid velocities for each event were used to calculate the turbulent velocity fluctuations, based on the ensemble-average velocities, and then bed shear stress was calculated using the turbulent kinetic energy method.

2.2.2 Direct measurements

Instead of estimating bed shear stress from velocities above the bed, a more limited number of investigators have mounted sensors flush with the bed to measure bed shear stress more directly. Conley and Griffin( 2004) deployed a hot film anemometer under swash flows in the field and measured the instantaneous bed shear stress for 100 swash events. These events were normalised in time, aligned at the time of peak uprush, and combined into an ensemble event, from which the average bed shear stress was determined. Sumer et al.( 2011) installed a hot film anemometer flush with the bed in a laboratory flume to measure the bed shear stress under an ensemble average of 40 identical plunging solitary waves, at multiple cross-shore locations. Barnes et al.( 2009) used a flush-mounted aluminium shear plate in two different laboratory flumes and made measurements of swash zone bed shear stress under an ensemble average of five solitary bores, at multiple cross-shore locations. Pujara and Liu( 2014) used a similar instrument to measure bed shear stress under breaking and non-breaking waves in a large scale laboratory flume. 2.2 bed shear stress 19

15 4

) Cox et al.( 2000) Conley and Grifﬁn( 2004) 2 10 2 5

(N/m 0 0 0 τ 5 2 − 0 0.2 0.4 0.6 0.8 1 − 0 0.2 0.4 0.6 0.8 1

) Masselink et al.( 2005) 20 Barnes et al.( 2009) 2 20 10

(N/m 0

0 0 τ 20 10 − 0 0.2 0.4 0.6 0.8 1 − 0 0.2 0.4 0.6 0.8 1

5 ) 10 Kikkert et al.( 2012) Sumer et al.( 2011) 2

0 0 (N/m 0

τ 10 − 5 − 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1

) Puleo et al.( 2012) Pujara and Liu( 2014) 2 0 20

(N/m 0 0 5 τ − 20 0 0.2 0.4 0.6 0.8 1 − 0 0.2 0.4 0.6 0.8 1 t (-) t (-)

Figure 2.4: Previous measurements of bed shear stress through a swash cycle using indirect (left) and direct (right) techniques.

40 Pujara and Liu( 2014) Masselink et al.( 2005) 30 ) 2

20 Barnes et al.( 2009) (N/m 0

τ Cox et al.( 2000) 10 Kikkert et al.( 2012) Sumer et al.( 2011) Conley and Grifﬁn( 2004) Puleo et al.( 2012) 0 0 0.5 1 1.5 2 2.5 U (m/s)

Figure 2.5: Relationship between representative swash velocity and peak uprush bed shear stress for previous studies using indirect (◦) and direct ( ) measurement techniques. • 20 review

Table 2.3: Previous measurements of bed shear stress through a swash cycle using indirect and direct techniques.

τ0,max hmax Umax study method bed type (N/m2) (m) (m/s)

Cox et al.( 2000) LDV Fixed Log law 14 0.04 0.5 Masselink et al.( 2005) EMCM Mobile Log law 35 0.15 1.8 Puleo et al.( 2012) ADP Mobile Log law 4 0.05 0.8 Kikkert et al.( 2012) PIV Fixed TKE 10 0.08 1.3 Conley and Griffin( 2004) Hot film Mobile Direct 3 0.141 1.2 Sumer et al.( 2011) Hot film Fixed Direct 6 0.05 0.7 Barnes et al.( 2009) Shear plate Fixed Direct 22 0.08 1.4 Pujara and Liu( 2014) Shear plate Fixed Direct 38 0.08 1.8 1. Significant wave height from 10 m offshore; not swash depth.

While the variation of bed shear stress through time is not identical between studies, it does follow the same general trend (Figure 2.4). The beginning of the uprush phase is characterised by a sharp spike followed by a rapid decay. The bed shear returns to zero in the middle of the swash cycle (around ﬂow reversal), before reaching a negative peak in the middle of the backwash phase. The peak bed shear stress is typically higher during uprush than backwash. The peak bed shear stress values in the studies above differ by an order of magnitude, but this is likely because of different experimental conditions (Table 2.3). When representative swash velocities for each study are considered, a more sensible trend is visible (Figure 2.5). Measurements of swash zone bed shear stress are usually accompanied with estimates of friction factors, which tend to vary widely between studies (Puleo et al., 2012) and indeed within individual swash events (Cowen et al., 2003; Barnes et al., 2009). This is discussed further in Chapter 7.

2.3 conclusion

This review has explored the development of instrumentation used to measure swash zone processes, particularly bed shear stress. Other investigators (e.g. Cowen et al., 2003; Jiang and Baldock, 2015; Inch et al., 2015) have also attempted to quantify swash zone bed shear stress; this review has focussed on the studies that have presented results showing the variation of bed shear stress during a swash cycle (including uprush and backwash) using novel measurements. 2.3 conclusion 21

Chapter 3 provides details of the experimental design of the present study, and the instrumentation used to make new observations of bed shear stress under wave runup on steep slopes.

3 METHODOLOGY

Chapter 2 reviewed previous studies of wave runup, and the instruments used to measure hydrodynamic processes in swash ﬂows. This chapter describes the instrumentation used in the present study, and the experiments undertaken to measure bed shear stress under wave runup on steep slopes.

3.1 instrumentation

3.1.1 Ultrasonic sensors

Ultrasonic sensors employ a piezoelectric crystal to convert electrical energy into high-frequency (> 20 kHz) sound waves. These waves propagate through air and return to the sensor after they are reflected back from a target. The distance to the target is calculated using the time-of-flight principle, and an internal thermometer is used to com- pensate for ambient temperature fluctuations, which alter the speed of sound. The high frequency and low wavelength of the acoustic signal allows sub-millimetre measurement resolutions to be achieved. Ultrasonic sensors have been widely used for industrial applications including remote measurement of levels in water tanks (Sinclair, 2000). Two different models of ultrasonic sensors were used in the present study: Massa M-300/95, and Microsonic mic+35 (Figure 3.1; Table 3.1).

Figure 3.1: Massa M-300/95 (left) and Microsonic mic+35 (right) ultrasonic sensors (from Massa, 2006 and Microsonic, 2005).

23 24 methodology

Table 3.1: Comparison of Massa and Microsonic ultrasonic sensors, as they were conﬁgured in the present study. parameter massa microsonic

Ultrasonic frequency (kHz) 95 400 Sampling frequency (Hz) 4 45 Minimum range (m) 0.3 0.06 Maximum range (m) 4.0 0.6 Resolution (mm) 0.25 0.18

The Massa M-300/95 is a rugged low cost sensor, making it suitable for use in large arrays in harsh field conditions. This sensor was first used to measure fluid depths and bed levels in the swash zone by Turner et al.( 2008), and has since been successfully deployed in several field experiments (Masselink et al., 2009; Puleo et al., 2014) and prototype scale laboratory experiments (Williams et al., 2012; Mas- selink et al., 2013; Vousdoukas et al., 2014). The maximum sampling rate of the Massa sensor is 20 Hz, but this was reduced to 4 Hz for the present study because of limitations in the data acquisition network. The Microsonic mic+35 has a higher cost than the Massa sensor, but it supports analogue signal output and a higher sampling rate. It also has a smaller acoustic footprint, which allows an array of sensors to be placed close together with a low risk of interference from cross talk between sensors. These characteristics make the family of Microsonic mic sensors well suited for laboratory conditions, where they have been used to measure swash depths in small and medium scale experiments (e.g. Barnes and Baldock, 2006; Khezri and Chanson, 2012; Cáceres and Alsina, 2012).

3.1.2 Laser scanners

Laser scanners use a rotating mirror to direct a laser beam outwards radially in a fixed plane. If the laser beam strikes a target as it sweeps along its path, some of the incoming light will be reflected back towards its source. If this diffuse reflection (or backscatter) is detectable by the scanner, then the distance to the target can be calculated using the time-of-flight principle. Airborne laser scanner (or lidar) systems are commonly used for to- pographic and bathymetric surveys. The bathymetric surveying plat- forms are equipped with two laser transmitters operating at different 3.1 instrumentation 25

reﬂection transmission foam ripple turbid absorption scattering scattering scattering

Figure 3.2: Interaction of laser light with water surfaces at oblique incident angles (adapted from Tamari et al., 2011; Allis et al., 2011). wavelengths: infrared light for detecting the water surface, and blue- green light for detecting the seabed (Irish and Lillycrop, 1999). Laser scanners are not ideal for detecting water surfaces, because the reﬂections are usually specular (mirror-like), rather than diffuse. Still water will only be visible to a laser scanner if the incident angle of the laser beam is close to perpendicular; otherwise the light will be perfectly reﬂected away from the scanner or simply absorbed by, or transmitted through the water (Figure 3.2). A laser scanner will only detect water at oblique incident angles if the following features are present (Tamari et al., 2011):

• ripples on the water surface;

• white water or foam on the water surface; or

• sediment suspended high in the water column.

Despite these challenges laser scanners have successfully been used to measure the water surface in rivers (Large and Heritage, 2007; Brodu and Lague, 2012) and marine environments (Belmont et al., 2008; Park et al., 2011). The first measurements of swash flows with a laser scanner were reported by Blenkinsopp et al.( 2010a), with a sick lms200 unit mounted 5 m above a sandy beach. Swash flows on natural beaches are com- paratively well suited to measurement with laser scanners because of the high levels of white water and suspended sediment, especially during the uprush phase. Two different models of laser scanner were used in the present study: sick lms511, and faro focus 3d 120s (Fig- ure 3.3; Table 3.2). 26 methodology

Figure 3.3: sick lms511 (left) and faro focus 3d 120s (right) laser scanners (from sick, 2011 and faro, 2010).

The sick lms511 a relatively low cost laser scanner designed for industrial applications. It is capable of providing two-dimensional line scans in real time via an Ethernet connection, and its robust enclosure makes it well suited for field use. Several other studies have deployed laser scanners from the same product family to measure swash flows on natural beaches (Puleo et al., 2012; Almeida et al., 2013, 2014) and in prototype scale laboratory settings (Masselink et al., 2013; Vous- doukas et al., 2014). The faro focus 3d 120s is a three-dimensional scanner designed for architectural and engineering surveys. It can also be configured to record two-dimensional line scans when operating in its helical mode. Scans are stored on an internal memory card, which can be accessed over Ethernet or a wireless local area network (measurements are not available in real time). The laser beam in the faro scanner has a lower divergence angle than the sick scanner. This enables the faro scanner to make measurements of a longer range and a higher resolution. The rotating mirror in the faro scanner is not enclosed, so the instrument

Table 3.2: Comparison of sick and faro laser scanners, as they were con- ﬁgured in the present study. parameter sick faro

Laser class 1 3R

Angular point spacing (◦) 0.25 0.28 Beam divergence (◦) 0.63 0.01 Laser wavelength (nm) 905 905 Maximum range (m) 65 120

Field of view (◦) 190 305 Points per line 761 1066 Sampling frequency (Hz) 35 24 3.1 instrumentation 27 is not suited to harsh environments where it could be exposed to rain or dust, or other objects that may interfere with the moving parts. The sick scanner uses a class 1 laser, while the faro scanner uses a class 3r laser. Class 1 lasers are considered safe in all conditions, while class 3r lasers are potentially hazardous if the beam is viewed directly, according to iec 60825 (2001). The manufacturer of the faro scanner recommends the nominal ocular hazard area (noha) around the scanner should be kept clear of bystanders, and that the operator should wear safety glasses when working inside this area. Depending on the scanner conﬁguration, the noha ranges from 0.4–24 m. These safety considerations make the faro scanner more challenging to deploy, particularly in the ﬁeld.

3.1.3 Shear plates

Local shear stress transducers are used to measure wall effects in fluids via an active face (typically a flat metal plate) mounted parallel to the flow field and flush with the wall (see review by Kolitawong et al., 2010). Two different shear plates were used in the present study (Figure 3.4): one built at the University of Queensland (uq), and one built for the Große Wellenkanal (gwk). The uq shear plate is the same instrument described in Barnes and Baldock( 2007). The active face consists of a thin aluminium plate with dimensions 100 mm 250 mm where the shorter dimension is × aligned parallel to the flow. The plate is suspended on four flexible stainless steel legs, creating a parallel linkage. A 1 mm gap around the edge of the instrument enclosure allows the plate to deflect back and forth when exposed to shear stresses, and the plate displacement is measured with an eddy current proximity probe. The active face of the gwk shear plate consists of an aluminium disc with a diameter of 150 mm. A flexible rubber gasket sits between the active face and the housing to ensure the shear plate is hermetically

Figure 3.4: uq (left) and gwk (right) shear plates. 28 methodology

40 mm

30 mm

Figure 3.5: Vectrino II acoustic Doppler proﬁler installed above a rough bed (adapted from Nortek, 2011).

sealed (in contrast to the uq plate). Two dual-beam load cells provide bed shear stress measurements in the x and y directions (Pero, 2007).

3.1.4 Acoustic Doppler proﬁler

An acoustic Doppler profiler uses high-frequency sound to measure current velocities over a finite depth range. The unit used in the present study was the Nortek Vectrino II. The transmitter emits a series of 10 MHz pulses from a central acoustic transmitter and a portion of this acoustic energy is scattered back from a 30 mm thick sample volume inside the fluid, where it is detected by one of the four receiver probes (Figure 3.5). The receivers measure the Doppler shift of the acoustic returns and the instantaneous three-dimensional flow components are calculated at a frequency of 100 Hz. The Vectrino II acoustic Doppler profiler has been used to measure velocity profiles in swash flows in several experiments in the field (Puleo et al., 2012; Almar et al., 2014) and the laboratory (Masselink et al., 2013; Yagci et al., 2014).

3.2 experimental design

The present study consisted of two laboratory experiments using medium scale and prototype scale facilities. Both experiments were performed on steep, impermeable slopes. 3.2 experimental design 29

3.2.1 Water Research Laboratory (wrl)

The first set of experiments were performed inside the 3 m flume at the Water Research Laboratory (wrl) in Sydney, Australia. This flume is 30 m long, 3 m wide, and 1.5 m deep. For these experiments a 1:3 plywood slope was constructed approximately 8 m from the wave paddle above an existing bathymetry that had been used for a previous experiment (Figure 3.6). Wave heights were measured with three capacitance wave gauges. Swash depths were measured using an array of eight Microsonic mic+35 ultrasonic sensors spaced at approximately 0.25 m intervals. Bed shear stress was measured with the uq shear plate. All of the instruments were connected to a data acquisition PC sampling at 200 Hz. Each wave run was also recorded with a digital video camera mounted on a tripod beside the flume. Attempts to measure flow depths with laser scanners in this set of experiments were unsuccessful, as the waves were too small to generate bubbly flows through the entire swash zone. The laser scanners could only accurately detect a very small portion of the water surface, where the incident wave first impacted on the beachface. Protracted efforts were made to measure swash velocities using an electromagnetic current meter mounted close to the bed, but the instrument did not perform well with the shallow flows and suffered from electrical interference, so it was abandoned. In the absence of the current meter, depth-averaged fluid velocities were calculated using the volume continuity method (Blenkinsopp et al., 2010b) based on depths derived from the ultrasonic sensors. A test program consisting of monochromatic, bichromatic and irregular waves was developed, attempting to maximise the range of

2 Wave 1.5 Ultrasonic paddle Wave gauges sensors 1 swl d b c 0.5 1:3 a Shear plate Elevation (m) 1:10 locations 0

0 2 4 6 8 10 12 Distance from paddle (m)

Figure 3.6: Experimental setup at wrl. 30 methodology

wave steepness values. Breaker type is generally related to wave steep-

ness using the surf similarity parameter, ξ0 (Battjes, 1974):

tan β ξ0 = ,(3.1) √H/L0

where β is beach slope, H is wave height, and L0 is deep water wavelength, with

gT2 L = ,(3.2) 0 2π

where g is gravitational acceleration and T is period. Because of the small waves and steep slopes used in the wrl experiments, it was more practical to determine the breaker types visually from video

records, instead of directly calculating ξ0. The test program (Table 3.3) was repeated four times. The conditions were identical, except that the shear plate was installed in a different cross-shore position for each case to measure the spatial variation in bed shear stress at points A, B, C, and D (Figure 3.6). The position of the ultrasonic sensors was modiﬁed slightly between each test series, so that two sensors were always located directly above the landward and seaward edge of the shear plate. The most seaward

Table 3.3: Wave conditions for wrl experiments.

id wave type T (s) H (m) breaker type

1 Monochromatic 2.2 0.11 Plunging 2 Monochromatic 2.2 0.08 Collapsing 3 Monochromatic 3.2 0.22 Plunging 4 Monochromatic 3.2 0.16 Collapsing 5 Monochromatic 5.0 0.16 Collapsing 6 Monochromatic 5.0 0.08 Surging 7 Monochromatic 7.0 0.11 Spilling 8 Monochromatic 7.0 0.09 Collapsing 9 Bichromatic 2.2 0.14 Plunging 10 Bichromatic 3.2 0.17 Collapsing 11 Bichromatic 5.0 0.14 Collapsing 12 Bichromatic 7.0 0.22 Spilling 13 Irregular 2.2 0.11 Plunging 14 Irregular 3.2 0.10 Collapsing 15 Irregular 5.0 0.09 Collapsing 16 Irregular 7.0 0.07 Surging 3.2 experimental design 31 sensor was kept in the same position for all tests to provide a constant reference. One additional test program was performed to assess the impact of contrasting roughness, with a sheet of geotextile fabric (Texcel; Geo- fabrics Australasia, 2008) attached to the beach surface surrounding the shear plate. A separate section of fabric was glued to the surface of the shear plate, leaving a small gap for the plate to move back and forth under waves.

3.2.2 Große Wellenkanal (gwk)

The second set of experiments were performed in the Große Wellen- kanal at prototype scale. The Großer Wellenkanal (large wave flume; gwk) is 310 m long, 5 m wide, 7 m deep, and is part of the Forschung- zentrum Küste (Coastal Research Centre; fzk) in Hanover, Germany. For this experiment the instruments were installed on a 1:6 slope, approximately 280 m from the wave paddle (Figure 3.7). Wave heights were measured with resistance-type wave gauges sampling at 120 Hz, and instantaneous water depths in the swash zone were provided by an array of 41 Massa m300/95 ultrasonic sensors sampling at 4 Hz, and mounted to a scaffolding rig at 0.4 m cross-shore intervals, and a height of approximately 1 m. The ultrasonic sensors were supplemented by four laser scanners mounted on two separate crane trolleys suspended above the centre of the flume at distances of 270.0 m and 278.1 m from the wave paddle. One sick lms511 and one faro focus 3d 120s laser scanner were mounted on each trolley, and these instruments were sampling at 35 Hz and 24 Hz, respectively. A video camera with a wide angle lens was mounted on the seaward trolley to visually record the swash flows. Two shear plates were installed flush with the bed at different cross-shore positions, both sampling at 120 Hz. The gwk shear plate (plate A) and the uq shear plate (plate B) were located at distances of

10 Wave Laser scanners paddle Wave gauges Swash 5 swl rig b a Elevation (m) 1:6 0

0 50 100 150 200 250 300 Distance from paddle (m)

Figure 3.7: Experimental setup at gwk. 32 methodology

10 Laser scanners 9

Elevation (m) 5 Ultrasonic b sensors swl a 4 Shear plates and 3 acoustic Doppler 1:6 proﬁlers 2

265 270 275 280 285 290 Distance from paddle (m)

Figure 3.8: Experimental setup at gwk (detail of swash rig).

277.9 m and 281.8 m from the wave paddle, respectively (Figure 3.8). Near-bed velocity proﬁles were measured using two Nortek Vectrino II acoustic Doppler proﬁlers sampling 100 Hz, and installed directly above each shear plate. A total of 60 wave runs were recorded (monochromatic, bichromatic, irregular, and solitary) with wave heights between 0.6 m and

Table 3.4: Wave conditions for gwk experiments.

1 id wave type T (s) H (m) ξ 0 16, 63, 65 Monochromatic 8 0.6 2.1 8, 54 Monochromatic 8 0.8 1.9 30, 57, 74 Monochromatic 8 0.9 1.8 11, 58 Monochromatic 8 1.0 1.7 1, 50 Monochromatic 10 0.6 2.7 3, 4, 14, 15, 21, 51 Monochromatic 10 0.8 2.3 12, 62, 76 Monochromatic 10 1.0 2.1 2, 17, 59, 60 Monochromatic 12 0.6 3.2 5, 64 Monochromatic 12 0.7 3.0 7, 9, 22, 23, 52, 53 Monochromatic 12 0.8 2.8 31, 56, 75 Monochromatic 12 0.9 2.6 10, 61 Monochromatic 14 0.6 3.8 13, 29, 55, 73 Monochromatic 14 0.8 3.3 14, 77 Irregular 10 0.8 2.3 24, 78 Irregular 12 0.8 2.8 6 Solitary - 0.7 - 18 Solitary - 0.8 - 19, 20, 25 28, 66 72 Solitary - 0.9 - − − 1. Rough surface runs: 1-31; smooth surface runs: 50-78 3.2 experimental design 33

50 mm

Figure 3.9: uq shear plate with moulded roughness element attached.

1.0 m, and wave periods ranging from 8 s to 14 s (Table 3.4). The experiments were performed on two different surfaces of contrasting roughness: a ‘rough’ asphalt surface (runs 1-31) and a ‘smooth’ polyethylene surface (runs 50-78). Run numbers 32-49 were not used. The surface of each shear plate was carefully prepared to closely match the roughness of the surrounding slope. Polyurethane moulds of the asphalt surface were glued to the shear plates during the rough surface experiments (Figure 3.9). The moulds were then removed, and the active face of each plate was cleaned for the smooth surface experiments. Fresh water was used in the flume, and this was pumped in directly from the Mittellandkanal (Midland Canal). The water was mostly clear, but there were some fine particles that were easily suspended in the flow. There was also a small amount of sand in the flume, left over from previous experiments. This sand caused some operational prob- lems with the uq shear plate, as it gradually filled up the inside of the instrument over successive swash events, and eventually preven- ted free movement of the support legs. This plate had to be cleaned regularly to ensure it was operating correctly.

3.2.3 XBeach numerical model

A numerical model (XBeach; Roelvink et al., 2009) was used to calculate idealised results of swash hydrodynamics, for comparison with observations from the physical experiments. The XBeach model was one dimensional, with a beach slope of slope 1:10 exposed to monochromatic waves with T = 10 s, and H = 0.5 m. These conditions provided collapsing swash events similar to those typical to the wrl and gwk experiments (Figure 3.10). 34 methodology

0.4 t = 42.7 s 0 0.4 − 4 6 8 10 12 14 0.4 t = 43.3 s 0 0.4 − 4 6 8 10 12 14 0.4 t = 44.5 s

(m) 0 0 z 0.4 − 4 6 8 10 12 14 0.4 t = 46.0 s 0 0.4 − 4 6 8 10 12 14 0.4 t = 47.8 s 0 0.4 − 4 6 8 10 12 14

x0 (m)

Figure 3.10: Water surface proﬁles ( ) for a single collapsing swash event from the XBeach model.

A simpliﬁed version of XBeach was implemented, with many features disabled (e.g. wave energy dissipation, wind effects, sediment transport, and groundwater ﬂows); it was essentially used as a shallow water equation solver. This meant that the exact experimental conditions could not be replicated, because the offshore water depths in the gwk and wrl experiments were transitional (not shallow) for most wave cases.

3.3 conclusion

This chapter has described the experimental design and instrumentation used in the present study. Chapter 4 will examine the data collected during these experiments, and describe the processing techniques used to extract features of interest. 4 DATAPROCESSING

Chapter 3 provided details of instruments and experimental design of the present study. This chapter will examine the data collected during these experiments, and describe the processing techniques used to extract features of interest.

4.1 definitions

At this point it is useful to explicitly deﬁne the variables used to describe swash ﬂows in the present study (Figure 4.1). The x z axes − originate where the still water level intersects the beach slope, h is water depth, U is depth-averaged velocity, and τ0 is bed shear stress. The y axis (not shown) acts in the alongshore direction. Horizontal and vertical co-ordinates (i.e. not oriented with the beach slope) are represented by x0 and z0, respectively.

4.2 depth measurements

4.2.1 wrl: ultrasonic sensors

Ultrasonic sensors measure a distance to a target. The distance from each sensor to the bed was found by identifying stable regions in the signal between swash events, representing areas when the bed was not submerged. The average distance to these ‘dry’ regions was calculated, and the distance observations were subtracted from this value, to give a time series of ﬂow depth, h. The data acquisition rate for the wrl experiments was 200 Hz, however the ultrasonic sensors were observed to have a natural frequency

x z U h swl τ0

Figure 4.1: Deﬁnition sketch of variables.

35 36 data processing

0.03 0.03

0.02 0.02 (m) h 0.01 0.01

0 0 0 0.5 1 1.5 2 0 0.5 1 1.5 2 t (s) t (s)

Figure 4.2: Raw signal (left) and processed signal (right) from ultrasonic sensors showing the depth variation during a single swash event during the wrl experiments.

of approximate 45 Hz, resulting in regular steps in the raw signal. Spikes were removed from the raw signal with a three-point median ﬁlter, then a zero-phase low-pass ﬁlter was applied to this new signal to remove the steps (Figure 4.2).

4.2.2 gwk: ultrasonic sensors and laser scanners

Depth measurements for the gwk experiments were provided simultaneously by time-synchronised ultrasonic sensors and laser scanners. A survey of the experimental setup was performed to determine the x and z co-ordinates of each instrument. The depths from the ultrasonic sensors were calculated in the same way as in the wrl experiments. The laser scanners provided measurements in terms of elevation, relative to the position where they were mounted above the ﬂume. These elevation measurements were converted to relative depths by sub- tracting them from a surveyed cross section of the beachface. Both the sick and faro laser scanners are capable of operating at much higher spatial and temporal resolutions than the Massa ultrasonic sensors (Figure 4.3). This enables the laser scanners to capture features of the uprush in more detail than the ultrasonic sensors, including detection of the steep pressure gradients at the swash front, resolving secondary ripples on the water surface, and tracking the leading edge of the swash as it moves quickly up the beachface. During the backwash however, there is less white water present and the laser scanners are not capable of accurately detecting the water surface. In this case the scanners either return no signal at all, or the laser beam penetrates the water surface and detects sediment 4.2 depth measurements 37

10 10 0.2

8 8 h (m)

(m) 0.1 x 6 6

4 4 0 0 2 4 6 0 2 4 6 t (s) t (s)

Figure 4.3: Depth measurements from ultrasonic sensors (left) and faro laser scanner (right) for a single swash event. Black patches indicate areas of missing data. suspended somewhere in the water column (Figure 3.2). When the depths are small, the laser penetrates all the way to the bed, and a depth of zero will be recorded (Figure 4.4).

4.2.3 gwk: performance of different laser scanners

The faro laser scanner generally performed better than the sick scanner. The ranging noise was much lower (approximately 1 mm for ± the faro scanner compared with 10 mm for the sick scanner), and ± it also had a higher rate of target detection (approximately 85 % compared with 50 % during a single swash cycle). Indeed, during the smooth bed experiments where the polyethylene surface was more likely to give specular reﬂections, the sick scanner could rarely even detect the bed.

t = 0.5s t = 4.5s 4.5 4.5 (m) 0 z 4 4

0 2 4 0 2 4

x0 (m) x0 (m)

Figure 4.4: Depth proﬁles measured with ultrasonic sensors ( ) and faro laser scanner ( ) during uprush (left) and (backwash)◦ phases from the swash• event shown in Figure 4.3. 38 data processing

Signals from the seaward sick and faro laser scanners were compared with a swash timestack (Holland and Holman, 1993) from the beginning of a wave run, generated using geo-rectified frames from the overhead video camera (Figure 4.5). The white water in the swash is clearly visible in the video timestack, but in the first swash much less white water is present. This was because the first swash to arrive in each wave run was a surging wave, as there was no backwash from a proceeding swash to make it break. The sick scanner was observed to only return a signal when white water was present, while the faro scanner returned a signal for most of the temporal and spatial extent of each swash event. At first glance it appears that the faro scanner was accurately recording depths through the entire swash cycle, but in fact it consistently underestimated the depths in the backwash phase. This was caused by the laser beam penetrating through the water surface and detecting sediment suspended in the water column (Figure 4.6). The faro scanner does not detect most of the initial swash event. This is probably because the levels of suspended sediment were much lower for this event. For the subsequent events, the backwash from the proceeding swash causes the incident wave to break before it reaches the shore, and this increased turbulence leads to higher levels of aeration and suspended sediment in the swash zone.

4.2.4 Discussion on depth measurement

In the gwk experiments laser scanners and ultrasonic sensors were used to make simultaneous measurements of free-surface proﬁles in the swash zone. Where there were discrepancies between instruments, it was assumed that the ultrasonic sensors were the most accurate. Both models of laser scanner were capable of reliably detecting uprush events when foam was present on the surface of the water. Typic- ally the sick scanner could not detect anything during the backwash phase. In contrast the faro scanner typically recorded measurements through the entire swash cycle, but the depths in the backwash were underestimated because the scanner was detecting sediment suspended in the water column, rather than the water surface. In these experiments these spurious measurements were easily identiﬁed when compared to the ultrasonic sensors. This suggests that laser scanners are most appropriate as supplementary instruments, with an alternative instrument used to obtain primary depth measurements. 4.2 depth measurements 39

5 (m) x 0 0 5 10 15 20 25 30 35 10

5 (m) x 0 0 5 10 15 20 25 30 35 t (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 h (m)

Figure 4.5: Timestack image from video camera (top), and swash depth measurements from sick (middle) and faro (bottom) laser scanners. Missing data shown in black. The ﬁrst swash is the initial event for the wave run.

4.6

4.4

(m) 4.2 z

4 0 5 10 15 20 25 30 35

4.6

4.4

(m) 4.2 z

4 0 5 10 15 20 25 30 35 t (s)

Figure 4.6: Instantaneous surface elevation measurements from sick (top) and faro (bottom) laser scanners ( ) compared with measurements from a single ultrasonic sensor• ( ) at a cross-shore position of x = 0.85 m, for the same three swash events shown in Figure 4.5. 40 data processing

If no other instruments are available, the sick scanner has advant- ages over the faro scanner, because it only seems to detect the water surface when there is white water present. If there is no white water present, it will simply return no signal, which is preferable to a potentially spurious depth measurement. Laser scanners appear to perform best when deployed on natural beaches in the ﬁeld. This is largely due to longer bubble residence times in salt water (Chanson et al., 2006; Blenkinsopp and Chaplin, 2007), leading to increased persistence of white water in the swash zone. The gwk experiments were performed at prototype scale, but the timestack in Figure 4.5 shows reduced levels of white water, compared with timestacks from previous ﬁeld experiments in the swash zone (e.g. Puleo and Holland, 2001; Power et al., 2011).

4.3 leading edge trajectories

4.3.1 wrl: tracking with ultrasonic sensors

The points at the wet/dry interface for each swash event were identi- ﬁed by locating the intervals where the bed was submerged, based on the depths provided by each ultrasonic sensor. The depth threshold for bed submergence was 5 mm. These points were plotted in time and space, and approximate runup trajectories were obtained using a quadratic ﬁt (Figure 4.7), based on the Shen and Meyer( 1963) ballistics model (see Chapter 5).

1.5 0.1

0.08 1 0.06 h (m) (m) x 0.04 0.5

0.02

0 0 1 2 3 4 5 6 7 t (s)

Figure 4.7: Swash depths from the wrl experiments, with ultrasonic sensor positions ( ), points detected at the wet/dry interface ( ), and estimated runup trajectories ( ). • 4.3 leading edge trajectories 41

4.3.2 wrl: tracking with video

Previous studies using cameras to measure wave runup on beaches have typically used pixel intensities to locate the leading edge of the swash (e.g. Holland and Holman, 1993; Puleo and Holland, 2001; Stockdon et al., 2006) but in this case the pixel intensity technique was not appropriate, because there was very little white water present for the surging swashes, and also because of interference from bright solar reflections on the smooth plywood surface. The frames from the digital video camera were geo-rectified and resampled to give new pixel dimensions of 10 mm 10 mm. The ori- × ginal video frame rate of 30 frames per second was preserved. The video frames were then analysed using optical flow techniques. Op- tical flow is the distribution of apparent velocities arising from the movement of brightness patterns in a series of images (Horn and Schunck, 1981). The leading edge of the swash was detected by find- ing the interface between the region of low optical velocities on the stationary bed and high optical velocities in uprush fluid (Figure 4.8). The leading edge trajectories derived from video records provided much more detail than those derived from the wet/dry interface under the ultrasonic sensor array (Figure 4.9). The camera was not always able to capture the very shallow flows at the peak of the uprush however, because there was no white water present and therefore no contrast against the bed. Any other discrepancies between the ultrasonic sensors and video camera are most likely due to slight alongshore variations in the swash leading edge. The video camera records

1 1

1.5

(m) 1.2 y

2 1.4

2.5 1.6 0.5 0 0.5 1 1.5 0.2 0.4 0.6 0.8 1 − x (m) x (m)

Figure 4.8: Optical ﬂow patterns from apparent pixel velocities ( ) at the leading edge of an uprush event (moving from left to right up the beachface) in the wrl experiments. 42 data processing

1.5

1 (m)

x 0.5

0 1 2 3 4 5 6 7 t (s)

Figure 4.9: Leading edge of the swash detected using video records ( ), and ultrasonic sensors ( ), and parabolic runup trajectories ( • ) for the same swash events◦ shown in Figure 4.7.

do not agree with the estimated parabolic runup trajectories (ﬁtted to the wet/dry interface calculated from ultrasonic sensors) close to the equilibrium shoreline (x = 0). This will be discussed in Chapter 5.

4.3.3 gwk: tracking with laser scanners and ultrasonic sensors

The runup trajectories in the gwk experiments were calculated by plotting heatmaps of the depth measurements from the ultrasonic sensor array and tracing the 10 mm contour level. Runup trajectories were also calculated using observations from the seaward mounted faro laser scanner (Figure 4.10). The laser scanner was able to capture more detail on the runup trajectory during uprush, because of its higher spatial resolution and superior ﬁeld of view (the most seaward ultrasonic sensor was located at x = 1.9 m, while the faro scanner − could detect points offshore as far as x = 10 m). This allowed detec- − tion of additional features, including the breaking of incoming waves as they met the backwash from the preceding runup event. Because of its tendency to underestimate backwash depths, the faro scanner could not accurately detect the landward edge of the swash during backwash (although the ultrasonic sensors performed well in this situation). Less importance was placed on the estimated backwash trajectories because they were subjective, and highly dependent on the threshold depth. Theoretically, the backwash phase ends when the beachface becomes dry, but this is more complex in practice. Visual observations suggest the duration of the beach draining process after individual waves could exceed 30 s in the lower parts of the swash zone. Even then, a thin ﬁlm of water remained on the beachface, dominated by the effects of surface tension. 4.4 depth-averaged velocity 43

15 10 (m)

x 5 0 0 2 4 6 8 10 12 14 16 18 20 22

10 5 (m)

x 0 5 − 0 2 4 6 8 10 12 14 16 18 20 22 t (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 h (m)

Figure 4.10: Depth contours from ultrasonic sensors (top), and runup trajectories (bottom) detected using ultrasonic sensors ( ), and faro scanner ( ) during the gwk experiments on the rough◦ surface. •

4.4 depth-averaged velocity

For both the wrl and gwk experiments the depth-averaged fluid velocities were calculated at every ultrasonic sensor location using the volume continuity method (Blenkinsopp et al., 2010b). This method relies on accurate knowledge of fluid depths across the swash zone, and is based on incremental changes in fluid volume, V, per unit beach width:

Z ∞ V(x, t) = h(x, t) dx ,(4.1) x where dx is the spacing between sensors (Figure 4.11). The ﬂow rate per unit width, q, is calculated from changes in ﬂuid volume in time:

V(x, t + dt) V(x, t) q(x, t) = − ,(4.2) dt where dt is the duration between observations. This ﬂow rate can be converted to depth-averaged velocity by dividing by ﬂuid depth:

q(x, t) U(x, t) = .(4.3) h(x, t)

This method has the advantage of not interfering with the ﬂow, and is able to provide velocity measurements when the depths are too 44 data processing

x5 x4 x3 x2 x1

Uprush V h

Backwash

Figure 4.11: Calculating depth-averaged velocities with the volume continuity method, based on approximate water surface proﬁles ( ) from measured depths at different cross-shore locations ( ). ◦

shallow for other instruments to operate, provided these conditions are met:

1. The water surface proﬁle does not vary rapidly between measurement locations.

2. The entire swash zone is conﬁned within the extents of the instrument array.

3. The ﬂow is two dimensional.

When applying the volume continuity method, a trapezoidal approximation was used to calculate the volume of each segment. A sensitivity analysis was performed on the shape of the uppermost trapezoid

during uprush (between x3 and x4 in Figure 4.11). This included the use of a variable width (based on the swash leading edge position), and a curved water surface proﬁle (rather than triangular). Both of these methods tended to add artefacts to the velocity signal, so a simple ﬁxed-width triangular shape was retained for the uppermost segment for each timestep.

4.4.1 Velocities in wrl experiments

A simple swash event according to the Peregrine and Williams( 2001) solution to the shallow water equations is shown in Figure 4.12. Dur- ing uprush the ﬂuid is constantly thinning, as it spreads out across 4.4 depth-averaged velocity 45

2 0.001

1.5

0.001

(m) 1 0.001 0.1 x 0.2 0.5 0.1 0.3 0 0 1 0.4 2 3 4 t (s)

Figure 4.12: Fluid depths from Peregrine and Williams( 2001) swash solution of the shallow water equations. the beachface. Consequently Freeman and Le Méhauté( 1964) referred to runup as a rarefaction wave, where the leading element is moving faster than all of the elements in the ﬂuid behind it. The trajectory of the leading edge of the swash therefore gives us information about the velocities inside the bulk of the ﬂow. For example, the initial (depth-averaged) uprush velocity at any point in the cross-shore direction must be the same as the velocity of the leading edge of the swash as it passes the same point. Other investigators (Hughes and Baldock, 2004; Jiang and Baldock, 2015) have used this principle to estimate initial uprush velocities when instantaneous velocity measurements were not available. Two criteria were used to validate the depth-averaged velocities in the wrl experiments (Fig- ure 4.13):

1. Depth-averaged velocity must not exceed the leading edge velocity by more than 0.5 m/s during uprush.

2. Depth must be greater then 4 mm.

Calculated velocities that did not fulﬁl these criteria were discarded. This process also ensured the removal of erroneous velocity spikes at the beginning and end of the swash cycle, when depths are small. It was not possible to validate these calculated velocities against other instruments, because of the failure of the electromagnetic current meter.

4.4.2 Velocities in gwk experiments

Velocity profiles for the gwk experiments were measured at two fixed points with two acoustic Doppler profilers, one above each shear 46 data processing

0.03

0.02 (m)

h 0.01

0 0 0.5 1 1.5 2

(m/s) 0 u

2 − 0 0.5 1 1.5 2 t (s)

Figure 4.13: Depth-averaged ﬂow velocities calculated using the continuity method ( ), and estimated velocity of swash leading edge ( ), based on a parabolic trajectory.

plate. Observations were discarded where the correlation of the acoustic beams fell below 60 %. This cutoff threshold is comparable to those use in previous studies (Raubenheimer, 2002; Aagaard and Hughes, 2006). The acoustic Doppler proﬁlers only provided measurements when the sensing head was completely submerged. This left regions at the beginning and end of the swash cycle where no observations were recorded. Depth-averaged velocities were also calculated at 41 additional locations spanning the entire swash zone, using measurements from the array of ultrasonic sensors. These calculated velocities showed good agreement with measured values from the acoustic Doppler proﬁlers (Figure 4.14).

4.5 shear plate processing

The uq and gwk shear plates were used to measure shear stress at the bed. Neither of the shear plates are capable of measuring any other parameters of the ﬂow; indeed they can not detect whether or not they are submerged. This presented challenges when interpret- ing their output, because the shear plates behaved slightly differently depending on whether they were operating in wet or dry conditions. The ﬁrst step for processing the shear plate measurements was to establish a baseline for each instrument corresponding to a bed shear 4.5 shear plate processing 47

0.3

0.2 (m) h 0.1

0 0 5 10 15 20

4 2 0 (m/s)

u 2 − 4 − 0 5 10 15 20 t (s)

Figure 4.14: Depth-averaged flow velocities calculated using the volume continuity method ( ) and measured velocities from the uppermost bin from the acoustic Doppler profiler ( ), approximately 20 mm above the bed. ◦ of zero. Basic fluid mechanics tells us there are two conditions under which bed shear stress will be zero: when the fluid is stationary (u = 0), and more trivially, when there is no flow over the bed (h = 0).

4.5.1 uq plate

The signal from the uq plate tended to drift over time. This was most likely caused by very minor adjustments in the position of the plate, under the force of larger waves. This apparent drift did not signiﬁc- antly affect the measurements of individual swash events. The shear plate drift was corrected for each swash event by shift- ing the signal vertically so that it passed through zero at the time of depth-averaged ﬂow reversal. It was expected that the plate would then also give a reading of zero before and after each swash event (when the depth was zero) but this was often not the case. At this point it is helpful to remember that the shear plate does not directly measure bed shear stress; it simply measures displacement. There are two things that will cause displacement of a shear plate mounted on a slope:

1. Bed shear stress under wave runup.

2. The bed-parallel component of the weight of the plate. 48 data processing

0 (m/s) u 2 − 0 1 2 3 4

) 20 2 10 (N/m

0 0 τ 10 − 0 1 2 3 4 t (s)

Figure 4.15: Depth-averaged velocity (top), and measurements from uq shear plate (bottom) for a single swash event. Bed shear signal is set to pass through zero at the time of ﬂow reversal.

The weight of the plate is 94 g . When the plate is submerged, buoyant forces will alter the weight force acting on the plate. The volume of the aluminium surface of the plate, plus the leg attachment lugs is roughly 23 cm3 (Barnes, 2009, Figure 3.2). On a 1:3 slope, this equates to an effective positive bed shear stress of 3.1 N/m2 when the plate is submerged. This means the plate would give a higher reading when it was under water than when it was dry. This concept is demonstrated in Figure 4.15. Things become slightly more complicated when the shear plate is exposed to multiple swash events, where the bed does not have time to completely drain between events (Figure 4.16). In these cases, the backwash from the previous swash applies a continuous load on the

20 ) 2

(N/m 0 0 τ

20 − 0 2 4 6 8 10 t (s)

Figure 4.16: Shear plate signal for a series of monochromatic waves. The plate does not return to its equilibrium position between swashes, because the bed is still draining. 4.5 shear plate processing 49

0.02 (m)

h 0.01

0 0 1 2 3 4

10 ) 2 5

(N/m 0 0 τ 5 − 0 1 2 3 4 t (s)

Figure 4.17: Depth (top) and shear plate signal (bottom) for a single swash event. The plate does not immediately return to its equilibrium position because the inside of the enclosure takes time to drain. shear plate in the offshore direction, and prevents it from returning completely to its equilibrium position. There is one ﬁnal case in which the shear plate gives a slightly different output. Sometimes the plate returns to zero after each swash event, rather than its equilibrium position (Figure 4.17). This is probably caused by water inside the shear plate enclosure. Barnes et al. (2009) note that surface tension alone is sufﬁcient to maintain water in the gaps, even when mounted on bed slopes up to 1:10. In the present investigation however, the shear plate enclosure was observed to drain between swash events on both the 1:3 and 1:6 slopes in the wrl and gwk experiments, respectively. If the beachface landwards of the shear plate drains more quickly than the plate enclosure itself, then the buoyant forces on the plate may exceed the backwash bed shear (Figure 4.18). In this case, the shear plate signal will increase above the equilibrium position for a short interval. Generally the uq shear plate will give spurious readings between swashes if the bed is dry. Therefore, measurements of bed shear stress from this instrument were discarded when the depths were less than 4 mm and 10 mm for the wrl and gwk experiments, respectively. 50 data processing

Inﬂow from Uplift force beach slope

Outﬂow from plate enclosure

Backwash

Figure 4.18: Cross section of the draining process inside the uq shear plate. If the enclosure has not fully drained before the backwash is complete, the plate will experience a net uplift force.

4.5.2 gwk plate

The gwk shear plate was designed for loads of up to 500 N (Pero, 2007). This is equivalent to a shear stress of approximately 30 kN/m2, well above the maximum bed shear stresses experienced in the swash zone. The gwk shear plate signal therefore required amplification before it could be accurately measured. The added noise from the signal amplification was removed using a low-pass filter (Figure 4.19). The gwk shear plate is fully sealed. When it is submerged in fluid the top of the plate is exposed to hydrostatic pressure, but the bottom

0.2 0.1

(V) 0 0 τ 0.1 − 0.2 − 0 5 10 15 20

40 ) 2 20 0 (N/m

0 20

τ − 40 − 0 5 10 15 20 t (s)

Figure 4.19: Raw shear plate signal (top) and ﬁltered bed shear stress measurements (bottom). 4.5 shear plate processing 51

sin β mg

τ0

mg β

Figure 4.20: Forces experienced by gwk shear plate when submerged. is not. This causes a net force on the plate in the downslope direction.

The signal measured by the plate τtotal, is therefore given by:

τ = τ mg sin β (4.4) total 0 − where τ0 is bed shear stress, and mg sin β is the bed-parallel component of the weight of the fluid above the plate (Figure 4.20). To find the bed shear stress τ0, the mass of the fluid on the plate must be calculated as it varies in time. The mass m is given by:

m = ρhA cos β (4.5) where ρ is ﬂuid density, h is depth and A is the area of the plate. The hydrostatic pressure correction was applied to measurements from the gwk shear plate using depths from the adjacent ultrasonic sensor (Figure 4.21). Importantly, the corrected bed shear stress is close to zero at ﬂow reversal, as expected. Because the gwk plate does not experience buoyant forces when it is submerged, the instrument measures zero bed shear stress when it is dry.

40 )

2 20

0 (N/m 0

τ 20 − 40 − 0 5 10 t (s)

Figure 4.21: Original shear plate signal ( ), apparent shear stress due to hydrostatic pressure on the active face of the plate ( ), and corrected bed shear stress ( ) from a solitary wave. 52 data processing

4.5.3 gwk plate with roughness element attached

Both shear plates were used simultaneously during the gwk experiments. The gwk plate was installed lower on the beachface at instrument position A, and the uq shear plate was installed higher on the beachface at position B (Figure 3.8). Both of the shear plates performed well on the smooth surface, but the gwk plate gave unex- pected results for the rough surface experiments: the peak uprush bed shear stress was barely detected, and the plate had a large offset between wet and dry conditions (Figure 4.22). Because these measurements were taken under solitary waves, the bed was completely dry at the beginning of each runup event. The actual bed shear stress is therefore zero both at the beginning of the record (t = 0 s), and at ﬂow reversal (t 4.5 s). The shear plate signals ≈ were aligned vertically so that the measured bed shear stress was indeed zero at the time of ﬂow reversal. For the rough surface, the uq plate has a small negative offset when the bed is dry, to account for the buoyant forces on the plate (plus the attached roughness mould) when it is submerged. The gwk plate should have no such offset, because it is hermetically sealed and does not experience buoyant forces when submerged. Therefore the rough surface observations from the gwk shear plate were assumed to be spurious, and only the uq shear plate measurements were analysed for the rough surface experiments.

4 4 2 2

(m/s) 0 0

U 2 2 − − 4 4 − 0 5 10 15 − 0 5 10 15

100 100 ) 2 50 50

0 0 (N/m 0 τ 50 50 − − 0 5 10 15 0 5 10 15 t (s) t (s)

Figure 4.22: Ensemble-average bed shear stress measurements under ﬁve solitary waves from gwk shear plate ( ) and uq shear plate ( ) for rough (left) and smooth (right) surfaces. 4.6 conclusion 53

4.6 conclusion

This chapter has outlined the data collected during the present investigation, and has described in detail the processing techniques used to eliminate spurious measurements and extract features of interest. Chapter 5 will now examine classical models for wave runup and assess their validity on steep slopes.

5 ANATOMYOFWAVERUNUP

Chapter 4 explored the processing techniques used to eliminate spurious measurements and extract features of interest from the measured data obtained in the present investigation. This chapter will examine classical models for wave runup and use new observations to assess their validity on steep slopes, resulting in the development of a new, more precise deﬁnition of the swash zone.

5.1 classical models for wave runup

Carrier and Greenspan( 1958) developed a solution to the shallow water equations for standing waves on a sloping bed. Because the waves the describe do not break, their energy is completely reﬂected by the beach, and the leading edge of the shoreline oscillates periodically around the equilibrium shoreline. A solution for broken waves (bores) approaching a beach was subsequently developed by Shen and Meyer (1963). At its simplest level, this model assumes the leading edge of the shoreline, xs, follows a ballistic trajectory:

1 x = u t gt2 sin β (5.1) s s − 2 where us is the initial bore velocity, t is time, g is gravitational acceleration, and β is the beach slope. This rather elegant model has been shown to provide good predictions of runup trajectories during uprush, as observed in several ﬁeld studies (Hughes, 1992; Baldock and Holmes, 1999; Puleo and Holland, 2001), although it does not perform as well during the backwash phase. This is because runup trajectories in nature are typically asymmetrical, with the backwash duration typically longer than uprush (Masselink and Hughes, 1998; Raubenheimer, 2002; Masselink et al., 2005). The solutions for both the non-breaking and breaking waves give similar runup trajectories above the equilibrium shoreline (Figure 5.1). The models differ in the way they treat runup initiation and the interactions between successive swash events. For the purposes of this investigation the Hibberd and Peregrine( 1979) periodic wave imple-

55 56 anatomy of wave runup

1 1

0.5 0.8 0.6 (-)

s 0

x 0.4 0.5 − 0.2 1 0 − 0 1 2 3 4 0 1 2 3 4

1 1

0.5 0.5 (-)

s 0 0 u 0.5 0.5 − − 1 1 − 0 1 2 3 4 − 0 1 2 3 4 t (-) t (-)

Figure 5.1: Predicted dimensionless shoreline position xs (top), and dimensionless shoreline velocity us (bottom), from runup solutions of Hibberd and Peregrine( 1979) for non-breaking waves (left) and Shen and Meyer( 1963) for bores (right).

mentation of the Carrier and Greenspan( 1958) model has been adopted. In this model the runup event is initiated below the equilibrium shoreline. The leading edge of the shoreline accelerates smoothly through the first half of uprush, reaching its maximum velocity near the equilibrium shoreline position. The leading edge velocity reduces to zero at the maximum uprush limit, then continues to accelerate in the seaward direction until it returns to the equilibrium shoreline position. Backwash flows are constantly thinning and accelerating, so they rapidly become supercritical except where the incident waves have very low steepness (e.g. infragravity waves). This supercritical backwash flow will continue to accelerate until it collides with the fluid mass offshore, forming a hydraulic jump. For the Hibberd and Peregrine( 1979) solution it is this hydraulic jump (or backwash bore; Peregrine, 1974) that slows the retreat of the shoreline until the backwash flow thins to nearly zero. The backwash bore then collapses, forming the next uprush event. The Shen and Meyer( 1963) solution does not accommodate interactions between successive runup events, and assumes that each incoming bore travels into water at rest. As the bore progresses into shallow water it becomes fully developed and accelerates until it reaches ter- minal velocity at the equilibrium shoreline, where it encounters the 5.2 differentmodesofrunup 57 beachface. When this solution is applied to periodic waves where swash-swash interactions are present the beginning of uprush will always represent a discontinuity in the shoreline trajectory (Baldock and Holmes, 1999). Importantly, both the Hibberd and Peregrine( 1979) and Shen and Meyer( 1963) solutions predict that the runup trajectory is always accelerating in the offshore direction above the equilibrium shoreline.

5.2 different modes of runup

Wiegel( 1964) classiﬁed surf zone breakers into three types: ‘spilling’, ‘plunging’ and ‘surging’. Galvin( 1968) added a fourth type termed ‘collapsing’, for intermediate breakers between plunging and surging. These different breaker types can also be used to describe wave runup (after Jensen et al., 2003; Figure 5.2):

• Surging: incident wave runs gently up beachface, without sig- niﬁcant steepening of the wave face. On steep slopes the wave may break during backwash.

• Collapsing: incident wave does not break, but the front face becomes very steep before collapsing at the equilibrium shoreline.

• Plunging: incident wave crest plunges violently into shallow water near equilibrium shoreline. Often described as ‘shorebreak’.

• Spilling: incident wave breaks offshore and forms a bore, which disappears at the equilibrium shoreline. The bore can be generated by a plunging or spilling breaker offshore.

Surging Collapsing Plunging Spilling

Figure 5.2: Transformation of surging, collapsing, plunging and spilling swashes. Water surface proﬁles approximately based on the experimental results of Pedersen and Gjevik( 1983), Zelt( 1991), Sumer et al.( 2013), and Yeh et al.( 1989), respectively. 58 anatomy of wave runup

Equilibrium Mean shoreline shoreline

Setup swl Runup

Setdown

Figure 5.3: Variation in mean water level ( ) across the inner surf zone and beachface, including wave induced setdown and setup.

In these descriptions it is assumed the swash zone starts at the equilibrium equilibrium shoreline (the point where the still water level intersects the beachface). This becomes more complicated on natural beaches, because the mean water level rises above the still water level in the inner surf zone as wave momentum is transferred into the water column during the wave breaking process (Bowen et al., 1968). This increase in mean water level (setup) in the inner surf zone is accompanied by a decrease in mean water level (setdown) near the wave breaking point. As a result of this wave induced setup, runup oscillations are centred on the mean water level rather than the still water level (Gourlay, 1992; Figure 5.3).

5.3 swash zone definitions

5.3.1 Seaward boundary of the swash zone

Hughes and Turner( 1999) define the swash zone as the time-varying region extending from the point of bore collapse to the maximum uprush limit. The drawback with this definition is that bore collapse does not occur at a single point, but rather over a finite region in time and space. In laboratory experiments Miller( 1968) showed that the transition from bore mode to runup mode is in fact a gradual process. On steeper slopes bore collapse is particularly difficult to define, as swash events will be formed by collapsing and surging waves, with no bore present. Puleo et al.( 2000) suggested that the seaward limit of the swash zone could be defined as the location where bore turbulence begins to influence local sediment transport. Jackson et al.( 2004) acknowledged this definition, but argued that the ‘true’ swash zone begins where the incident bore ‘intersects the shoreline’ (Figure 5.4). A more 5.3 swash zone definitions 59

x Runup limit

Swash zone

Equilibrium shoreline t

Figure 5.4: Idealised sketch of the swash zone showing the path of incident bores propagating through the inner surf zone, and their runup trajectories on the beachface. general definition was provided by Elfrink and Baldock( 2002), who described the swash zone as the region where the beachface is ‘inter- mittently exposed to the atmosphere’. This definition is intuitive, but is perhaps not useful as a basis for making quantitative observations, because on natural beaches the swash zone is often saturated and may not be exposed to the atmosphere at all between runup events. From observations on natural beaches, Hughes and Moseley( 2007) divided the swash zone into two parts: the outer swash, which is dominated by swash-swash interactions, and the inner swash, where each swash event is completely independent of its neighbours. Puleo and Butt( 2006) identified the lack of a uniform definition for the seaward boundary of the swash zone within the research community.

5.3.2 The process of bore collapse

The term ‘bore collapse’ is used to describe the transformation of the steep front of an incident wave into a thin wedge of fluid as it rushes up the beachface (Figure 5.5). Yeh and Ghazali( 1988) defined bore collapse as the transition between bore and runup, or the ‘rapid conversion of potential to kinetic energy at the shoreline’. Puleo and Holland( 2001) described bore collapse as ‘a rapid decrease in water depth and a rush of water up the beachface’. Hughes( 1992) suggested that bore collapse is complete when there is no water upstream of the incident bore front, and turbulence is no longer being generated on the water surface. Bore collapse has also been likened to the classical dam break problem, where a body of water is released after being retained behind a vertical wall. The dam break problem was first solved by Ritter( 1892), and has since been applied to wave runup flows by many investigat- 60 anatomy of wave runup

5 t = 3.6 s

t = 2.4 s (m) 4 0 z t = 1.2 s 3 t = 0.0 s 2 10 5 0 5 10 − − x0 (m)

Figure 5.5: Detail of the bore collapse process, from laser scanner measurements recorded during the gwk experiments.

ors (e.g. Luccio et al., 1998; Peregrine and Williams, 2001; Pritchard and Hogg, 2005). Solutions to the dam break problem show a rotation of the vertical face of the water body, with a positive wave propagating onto dry ground and a negative wave retreating over the reservoir. The dam break process is continuous, with no obvious end point. This is consistent with the observations of Miller( 1968), who argued that bore collapse is a gradual process where wave runup takes the form of ‘a wedge that progressively elongates until the maximum runup is achieved’.

5.3.3 Acceleration during runup

The bore collapse process is accompanied by a thinning and acceleration of the front of the incident wave as it rushes up the beachface. Most investigators regard the bore collapse process on natural beaches to be practically instantaneous, so this acceleration is not given particular attention. Peregrine and Williams( 2001) extended the solution of Shen and Meyer( 1963) and found that onshore accelerations were only expected to occur for first 10 % of the total duration of the swash cycle (they also note that the shallow water equations are likely to be invalid in this region). The laboratory experiments of Petti and Longo( 2001) also found that onshore accelerations were limited to the first 10 % of the total duration of the swash cycle. Although the duration of this acceleration may be short, it occurs at the beginning of the swash cycle when the velocity of the shoreline leading edge is at a maximum. Adopting the Shen and Meyer( 1963) solution, the initial 10 % of the swash duration is roughly equivalent to 35 % of the total cross-shore 5.4 experimental observations 61 width of the swash zone. This is consistent with the findings of Miller (1968), who observed the spatial extent of the bore collapse process on a variety of different slopes in laboratory conditions. The acceleration during bore collapse is generally considered to be convective, i.e. the velocity of the shoreline leading edge increases as it progresses up the lower portion of the beachface. There is some confusion on whether local accelerations (changes in velocity at a single location) are present during bore collapse. Observations from natural beaches using ducted impeller current meters (e.g. Masselink and Hughes, 1998; Puleo et al., 2003) show a rapid increase in velocity at the beginning of uprush. Puleo et al.( 2003) interpreted this as a large onshore-directed local acceleration, however Baldock and Hughes( 2006) argued that this acceleration was simply an artefact in the signal from the current meter, whose impeller would always be stationary at the beginning of uprush.

5.4 experimental observations

5.4.1 wrl experiments

The shorter period incident waves (T < 4 s) in the wrl experiments generally became collapsing swashes, while the longer period incident waves (T > 4 s) became surging swashes (Table 3.3). In some wave cases the timing of the swash-swash interactions allowed plunging swashes to form. Spilling swashes were observed only in wave case 7, where the incident waves broke offshore, near the transition in the flume bathymetry (Figure 3.6). The instantaneous shoreline position was identified using the optical flow velocities from the video records (see Section 4.3.2). The median velocity variation in the cross-shore direction was calculated for each video frame to create optical flow timestacks for each wave run. In these timestacks the moving fluid appears as a bright area against the stationary bed, which is dark (Figure 5.6). Qualitatively, the shoreline trajectory of the plunging swash case appears to follow the Shen and Meyer( 1963) model, with an abrupt spike at the beginning of every uprush event. This is in contrast to the shoreline trajectory of the surging swash case, which oscillates more gently around the equilibrium shoreline. There is a small oscillation between swash events, where the shoreline attempts to return to its equilibrium position. If the steepness of the incident waves was reduced, the shoreline 62 anatomy of wave runup

1 (m)

x 0

1 − 0 1 2 3 4 5 6 7 8 9 10

0.5 (m)

x 0

0.5 − 0 1 2 3 4 5 6 7 8 9 10 t (s)

Figure 5.6: Heat map of optical ﬂow velocities showing movement of the instantaneous shoreline position relative to the equilibrium shoreline ( ) for plunging swashes (top) and surging swashes with a longer period (bottom).

motion would begin to take the simple periodic form of the Hibberd and Peregrine( 1979) model. Four different monochromatic wave cases were selected from the wrl experiments, representing the four different swash types. Ten swash events were selected for each case, and ensemble averages of the instantaneous shoreline position and velocity were calculated from these events. These ensemble averages were compared with the Shen and Meyer( 1963) model using (5.1), with β = 1/3. The measured shoreline motion showed good agreement with the model for all four swash types in the upper portion of runup (Fig- ure 5.7). As predicted by the model, the plunging and spilling swash types reach their maximum velocity very close to the equilibrium shoreline position. The collapsing and surging swashes do not share this behaviour. Instead they continue to accelerate as they move up the beachface, reaching their maximum velocity above the equilibrium shoreline. This trend is clearer when the runup trajectories from the uprush phase are made dimensionless, from the point where the instantaneous shoreline ﬁrst begins to move landward, to the point of maximum runup (Figure 5.8). The spilling case does not quite ﬁt this trend; this is likely because the spilling bores were not well developed, 5.4 experimental observations 63

1.5 1.5 1.5 1.5 1 1 1 1

(m) 0.5 0.5 0.5 0.5 s x 0 0 0 0

0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5

3 3 3 3 2 2 2 2 (m/s)

s 1 1 1 1 u 0 0 0 0 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 t (s) t (s) t (s) t (s)

Figure 5.7: Observed ( ) and modelled ( ) runup trajectories (top), instantaneous shoreline velocities (bottom), and regions where (5.1) is valid ( ) for surging, collapsing, plunging and spilling swashes (left to right). and were formed because of the irregular bathymetry, rather than from a typical gentle planar slope. Two interesting features are visible when examining the shoreline velocities of the different swash types. First, there is an initial peak in velocity at the beginning of the plunging case. This can be interpreted as the rapid acceleration of the breaker jet as it impacts on the beachface. The following peak shows the location where the bulk of the ﬂuid catches up to the surge from the jet. This phenomenon is visible in the shorebreak of steep beaches, and is illustrated well in Petti and Longo( 2001, Figures 9 and 10). Second, the collapsing and surging cases do not accelerate through uprush as rapidly as the plunging and spilling cases. This is caused by a lag between the arrival of the leading edge of the wave and the wave crest. Orbital ﬂuid motions will dominate the hydrodynamics of a surging wave right up to the shoreline. This will cause landward

1 1 1 1 (-)

s 0.5 0.5 0.5 0.5 x

0 0 0 0 0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1 t (-) t (-) t (-) t (-)

Figure 5.8: Dimensionless observed ( ) and modelled ( ) uprush trajectories, and regions where (5.1) is valid ( ) for surging, collapsing, plunging and spilling swashes (left to right). 64 anatomy of wave runup

Surging Spilling

Figure 5.9: Comparison of the horizontal crest to trough distance for surging and spilling swashes.

movement of the shoreline before the wave crest (and the bulk of water underneath it) actually reaches the beachface. In contrast, a well-developed bore will not cause the shoreline to move landwards until it collapses on the beachface (Figure 5.9).

5.4.2 gwk experiments

The surf similarity parameters for the gwk wave cases ranged from

ξ0 = 1.7 (T = 8 s, H = 1.0 m) to ξ0 = 3.8 (T = 14 s, H = 0.6 m). Most of the swashes would best be described as surging, although the incident waves usually broke offshore of the equilibrium shoreline as they met the backwash from the preceding swash event. The only true surging swashes (from unbroken waves) were observed during the solitary wave cases, and for the initial wave in each monochromatic wave train. The steeper incident waves tended to break more violently, forming plunging swashes. The shoreline motion for the incident waves of high steepness followed a similar pattern to the plunging swashes from the wrl experiments (Figure 5.10). The shoreline motion for the incident waves of low steepness followed a smooth periodic trajectory, resembling the Hibberd and Peregrine( 1979) model. In contrast to this model, the observed instantaneous shoreline oscillation is not centred on the equilibrium shoreline, but is landward of it. This apparent onshore translation is an illustration of wave induced setup. Four monochromatic wave cases were selected for comparison, rep-

resenting a range of incident waves from low steepness (ξ0 = 3.8) to

high steepness (ξ0 = 1.8). The runup trajectories for each wave case were determined using depth measurements from both the ultrasonic sensors and laser scanners. Ensemble averages of shoreline position and velocity were calculated and these were compared with the predictions from (5.1), with β = 1/6. 5.4 experimental observations 65

15 10 5 (m)

x 0 5 − 0 5 10 15 20 25 30 35 40 45 15 10 5 (m)

x 0 5 − 0 5 10 15 20 25 30 35 40 45 t (s)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 h (m)

Figure 5.10: Heat map of measured depths from laser scanner showing the instantaneous shoreline position relative to the equilibrium shoreline ( ) for monochromatic incident waves of high steepness (ξ0 = 1.7; top) and low steepness (ξ0 = 3.3, bottom).

The observed runup trajectories showed good agreement with the model with the two wave cases of higher steepness (ξ0 < 3), but not for the cases with lower steepness (Figure 5.11). For the case with

ξ0 = 3.2 the shoreline velocity had the same double peak structure as the plunging swash from the wrl experiments (Figure 5.7). This case was not actually plunging, but the end of each runup event was characterised by the formation and collapse of a large backwash bore (the

10 10 10 10

(m) 5 5 5 5 s x 0 0 0 0 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 6 6 6 6

4 4 4 4

(m/s) β = 1/11

s 2 2 2 2 u 0 0 0 0 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 t (s) t (s) t (s) t (s)

Figure 5.11: Observed ( ) and modelled runup trajectories (top) and shoreline velocities (bottom), using β = 1/6 ( ), and β < 1/6 ( ), and regions where (5.1) is valid ( ), for incident waves with ξ0 = 3.8, 3.2, 2.8, and 1.8 (left to right). 66 anatomy of wave runup

1 1 1 1 (-)

s 0.5 0.5 0.5 0.5 x

0 0 0 0 0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1 t (-) t (-) t (-) t (-)

Figure 5.12: Dimensionless observed ( ) and modelled uprush trajectories using β = 1/6 ( ), and β < 1/6 ( ), and regions where (5.1) is valid ( ) for ξ0 = 3.8, 3.2, 2.8, and 1.8 (left to right).

ﬁrst peak), before the arrival of the next incident wave (the second peak). As a result, only the very last part of the runup trajectory is described well by (5.1). Generally, the incident waves of lower steepness continued to accelerate landward for a larger portion of the uprush phase, consistent with the results from the wrl experiments. This trend is more evident when the runup trajectories are made dimensionless (Figure 5.12). Interestingly, the runup trajectories for the case of lowest steepness (ξ = 3.8) could still be described well by (5.1) if the beach gradient, β, was reduced. The Shen and Meyer( 1963) model predicts that runup trajectories from well-developed bores are parabolic. This result suggests that the parabolic runup trajectory also provides an appropriate description of collapsing and surging incident waves, even if the actual runup extent is underpredicted. The Shen and Meyer( 1963) model performs worst for swashes that plunge violently onto the beachface, or those that form large backwash bores that collapse shortly before the following incident wave has reached the beachface. These cases both result in an shoreline velocity with two peaks, and an irregular runup trajectory. This is comparable to a swash overrun event, where one large bore catches up to a smaller bore after it has collapsed. This phenomenon is can often be observed on gently sloping natural beaches (Figure 5.13).

t Initial Overrunning swash swash Figure 5.13: Instantaneous shoreline motion during a swash overrun event. 5.5 general definition of swash 67

5.5 a new generalised definition of the swash zone

Most definitions of the swash zone are based on observations from natural beaches where bores are present. As a result, unbroken waves are not well described by these definitions. For example, when defin- ing the seaward boundary of the swash zone, Jackson et al.( 2004) required the shoreline to be sharply intersected by a bore (not gently nudged landward by an unbroken wave). The results from the wrl and gwk experiments show that the four different swash types all vary in the way they begin their climb up the beachface, but at some point during uprush they all begin to follow the Shen and Meyer( 1963) ballistic trajectory (although waves with low steepness may require a reduced beach slope to fit this model). If this transition point is used to divide the swash zone into two regions, then direct comparison of different swash types becomes possible for the first time. This also allows the collapse (and acceleration) of the incident wave at the beginning of the uprush phase to be treated as a separate process, removing some of the present confusion on the existence of local accelerations in swash flows. The stages of wave runup can then be described as follows:

1. The swash event originates at the point where the instantaneous shoreline ﬁrst begins to move in the landward direction.

2. As the instantaneous shoreline begins to move landward, the front of the incident wave collapses by thinning and accelerating up the beachface. The collapse process can occur rapidly (for spilling waves) or gradually (for surging waves).

3. After the collapse is complete, the swash is fully developed. From this point the instantaneous shoreline begins to accelerate in the seaward direction, its trajectory dominated by gravity (as a function of the beach slope) and frictional effects.

4. The swash ends after the instantaneous shoreline stops accelerating in the seaward direction. The next swash event may start instantly (for spilling waves), or there may be a delay before the instantaneous shoreline reverses direction (for surging waves).

The leading edge of the shoreline in the uprush phase is easy to identify both visually, and with a variety of different instruments. Loc- ating the landward edge of the shoreline visually during backwash is more difﬁcult, but an approximate position can be calculated if water 68 anatomy of wave runup

x Runup limit Fully- developed Swash swash zone zone Collapse zone Equlilibrium t shoreline

Figure 5.14: Proposed generalised deﬁnition of the swash zone.

depth measurements are available and a minimum depth threshold is assumed. In this new generalised deﬁnition, the swash zone is the envelope between the extreme landward and seaward position of the instantaneous shoreline. Within this there are two distinct regions: the collapse zone, where incident wave collapses on the beachface, and the fully- developed swash zone, where the shoreline trajectory is dominated by gravity (Figure 5.14). Here the term ‘collapse’ has been adopted instead of the more familiar ‘bore collapse’ to allow the deﬁnition to be more general, extending to include unbroken waves where no bores are present.

5.6 discussion

This new generalised swash zone deﬁnition would only make subtle changes to the way swash ﬂows are viewed on natural beaches dominated by spilling swashes. In this case, the collapse zone would only account for a small portion of the total swash zone width, because the incident wave collapse process is rapid. It is more applicable to situations in which:

• violent plunging swashes cause internal overunning effects;

• the incident waves have very low steepness; or

• the beachface is very steep.

The drawback with this definition is that it is difficult to determine the nature of the shoreline trajectory in the field simply from visual observations. One possible approach to estimating the location of the developed swash zone may be to estimate the point where the instantaneous shoreline appears to stop accelerating in the landward direction (Figure 5.15). 5.6 discussion 69

Has incident No wave reached Surf zone beachface?

Yes Yes Collapse zone Is shoreline accelerating landwards? No Fully- developed swash zone

Figure 5.15: Flow chart to determine the current regime of an incident wave as it transitions from the surf zone into the swash zone.

Attempts were made to relate the width of the fully-developed swash zone to incident wave steepness or swash type, using Figures 5.8 and 5.12. No general trends were apparent, mostly because of the overrunning effect for plunging waves and large backwash bores. The situation becomes more complicated when irregular waves are considered, because the collapse of incident waves is dependent on swash-swash interactions. In this case the fully-developed swash zone appears to progressively shrink when a series of consecutive runup events of increasing magnitude arrive at the beach (Figure 5.16). A greater understanding of swash-swash interactions is required before this new swash zone deﬁnition could be implemented in nu-

15 10 (m)

s 5 x 0

0 20 40 60 80 100 120 140 160

(m/s) 0 s u 5 − 0 20 40 60 80 100 120 140 160 t (s)

Figure 5.16: Shoreline ( ) position (top) and velocity (bottom), runup envelope ( ), transition points ( ), and fully-developed swash zone ( ), from irregular waves in the gwk experiments. 70 anatomy of wave runup

merical models of the nearshore environment. Its advantage however, is that it removes some ambiguity in the present terminology of the nearshore environment.

5.7 conclusion

This chapter has provided an overview of the various existing definitions of the swash zone. The shoreline trajectories during wave runup for both small and large scale experiments have been found to agree well with the ballistics solution of Shen and Meyer( 1963), for all different swash types. The main deviation from the model occurs early in the uprush phase, while the incident wave is collapsing and accelerating in the landward direction as it moves up the beachface. The total width of the collapse process was found to be up to 70 % of the entire runup width in some cases. The largest collapse widths were observed for incident waves of low steepness, or when large backwash bores were present. This chapter proposed that each swash event should be considered as having two distinct phases, representing two separate regions on the beachface: collapse, where landward accelerations of the instantaneous shoreline are present, and fully-developed swash, where the shoreline trajectory is dominated by gravity (as a function of the beach slope). This new generalised definition of the swash zone is particularly applicable to plunging and surging waves on steep slopes, including dykes and other engineered coastal structures. It may also help to bring some clarity to the definition of bore collapse, and the presence of local accelerations in swash flows. In Chapter 6 attempts are made to calculate bed shear stress using fluid momentum principles, and these estimates are compared with experimental observations. 6 BEDSHEARSTRESSANDFLUIDMOMENTUM

Chapter 5 examined the predictions of shoreline motion given by the classical models of wave runup, and expanded the generally accepted definition of the swash zone to make it more applicable to steep slopes. This chapter will use fluid momentum principles to estimate bed shear stress under wave runup, and compare these estimates with experimental observations. Section 6.2 contains a derivation of the depth-averaged momentum equation for unsteady flow, completed by William Peirson.

6.1 motivations for indirect measurement

The most robust measurements of swash zone bed shear stress to date have been recorded using instruments with a transducer mounted flush with interface between the bed and the fluid (see Section 2.2.2). These instruments provide direct measurements of bed shear stress at a single location by determining the forces imparted by the fluid on the bed. Indirect bed shear stress measurement techniques approach the problem from a different perspective, by considering the equal (but opposite) forces imparted by the bed on the fluid. Bed shear stress causes deformation of fluids, especially at shallow depths. External fluid deformations are visible as changes in the fluid free surface (such as a rough bed causing a reduction in the velocity of the fluid and an increase in the steepness of the fluid leading edge during uprush). Internal fluid deformations consist of changes in flow structure, and the development of boundary layers. Previous studies using indirect measurements of bed shear stress under wave runup have attempted to quantify these internal fluid deformations close to the bed (see Section 2.2.1). In this study a new technique was investigated, whereby bed shear stress was estimated by measuring external fluid deformations alone. These estimates were obtained by applying the depth-averaged momentum equation to high resolution measurements of the the spatial and temporal variation of the fluid free surface during wave runup.

71 72 bed shear stress and fluid momentum

z ∂h ∂x

h U

dx β

Figure 6.1: A depth-averaged control volume for unsteady free-surface ﬂow.

Indirect bed shear stress measurement techniques are desirable, because they negate the challenges of installing sensors precisely at the ﬂuid/bed interface, especially if the bed is mobile. This new technique, combined with observations from an array of ultrasonic sensors is a particularly attractive concept, as it would potentially en- able bed shear stress to be estimated at all points in the swash zone, without interfering with the ﬂow.

6.2 derivation of momentum equation1

Wave runup can simplified by considering it as depth-averaged unsteady free-surface flow up a planar surface of slope β (Figure 6.1), where spatial and temporal gradients of depth, velocity, and density exist. Continuity requires that mass be conserved within a small control volume in the fluid. If the control volume has unit width and length dx, then its mass m, is given by

m = ρh dx (6.1)

where ρ is inflow fluid density and h is inflow depth. The temporal rate of change in the mass of the control volume is equal to the mass of the inflow minus the mass of the outflow:

∂(ρh dx) ∂ρ ∂h ∂U = ρhU ρ + dx h + dx U + dx ∂t − ∂x ∂x ∂x (6.2)

1 Section author: W. L. Peirson, Water Research Laboratory, School of Civil and Envir- onmental Engineering, UNSW Australia, Sydney, Australia. [email protected] 6.2 derivation of momentum equation 73 where t is time and U is inﬂow velocity. The control volume momentum, p, can be obtained from the product of mass and velocity:

p = ρhU dx .(6.3)

In steady ﬂow the momentum inside the control volume does not ∂p vary in time ( ∂t = 0). In this case the ﬂow is unsteady so the change in control volume momentum can be calculated by equating it to an applied force, Fp, so (6.2) becomes

∂(ρhU dx) F = ρhU2 p ∂t − ∂ρ ∂h ∂U 2 + ρ + dx h + dx U + dx (6.4) ∂x ∂x ∂x which at ﬁrst order, reduces to   2 ∂(ρhU) ∂ ρhU F = dx  +  .(6.5) p  ∂t ∂x 

The forces on the control volume consist of ﬂuid pressure at the in-

ﬂow and outﬂow (FP), friction from the slope (Ff ), and gravity (FW). Assuming that the pressure distributions normal to the slope are approximately hydrostatic, the net pressure force can be calculated:

1 1 ∂ρ ∂h 2 F = ρh2g cos β ρ + dx h + dx g cos β P 2 − 2 ∂x ∂x ! gh2 ∂ρ ∂h = dx cos β ρgh cos β .(6.6) − 2 ∂x − ∂x

Friction (bed shear stress; τ0) is generally assumed to follow the quadratic stress law, a modiﬁed form of the Reynolds drag equation:

1 τ = ρ f U U (6.7) 0 2 | | where f is the Fanning friction factor. Since τ0 is acting against the direction of ﬂow on the base of a control volume of unit width and length dx, the friction force is given by

1 F = ρ f U U dx .(6.8) f −2 | | 74 bed shear stress and fluid momentum

From the geometry of the control volume, the gravity force parallel to the slope is given by

F = ρgh sin β dx .(6.9) W −

By equating (6.5) with (6.6), (6.8) and (6.9) and removing redundant space increments dx, the complete momentum equation is obtained:

Fp FP z }| { z }| { ∂(ρhU) ∂(ρhU2) gh2 ∂ρ ∂h + = cos β ρgh cos β ∂t ∂x − 2 ∂x − ∂x

Ff FW z }| { z }| { 1 ρ f U U ρgh sin β .(6.10) − 2 | | −

Assuming the ﬂow has is no variation in air entrainment and there- ∂ρ ∂ρ fore no spatial or temporal gradient in ﬂuid density ( ∂t = 0 , ∂x = 0), then (6.10) becomes

∂(hU) ∂(hU2) ∂h 1 ρ + ρ = ρgh cos β ρ f U U ρgh sin β , ∂t ∂x − ∂x − 2 | | − (6.11)

which can be expanded and rearranged in terms of τ0:

∂U ∂h ∂(U2) ∂h τ = ρh ρU ρh ρU2 0 − ∂t − ∂t − ∂x − ∂x ∂h ρgh cos β ρgh sin β .(6.12) − ∂x −

6.3 application of momentum equation

In essence, the momentum equation is composed of these basic elements:

∂h ∂h ∂U ∂U h, U, , , , . ∂t ∂x ∂t ∂x

Precise measurements of temporal and spatial variation in velocity and depth across the swash zone are required to estimate these terms. The observations collected during the gwk experiments represent perhaps the most complete measurements of runup depths and velocities 6.3 application of momentum equation 75 recorded to date. The wrl measurements provide a useful comparison at a smaller experimental scale. One representative monochromatic wave test case from each of the wrl and gwk (smooth bed) experiments was selected, and two different ensemble swash events were calculated to evaluate the accuracy of (6.12) for estimating bed shear stress under wave runup. Direct measurements of τ0 were provided by shear plates, for comparison. The experimental observations were complemented with output from an XBeach numerical model, consisting of a planar beach with a slope of 1:10, exposed to monochromatic waves with T = 10 s and H = 0.5 m (Section 3.2.3). This numerical model provided idealised results of each time varying parameter, as predicted by the shallow water equations, unaffected by experimental noise. The momentum equation was evaluated in three stages. First, the basic elements describing temporal and spatial variation in depth (Figure 6.2) and velocity (Figure 6.3) were calculated. Second, the actual terms of (6.12) were calculated, considering the stationary (Fig- ure 6.4) and convective (Figure 6.5) terms separately. Finally, the sum of all of the terms was calculated and compared with the measured (or modelled) bed shear stress (Figure 6.6).

6.3.1 Results

The basic depth-related terms from the wrl and gwk experiments show good qualitative agreement with the XBeach model results (Fig- ure 6.2). The main difference is that the XBeach model predicts a more rapid increase in depth at the beginning of uprush. Of the three ∂h depth-related terms, only ∂t appears to vary in the same manner as τ0, exhibiting a large positive peak during uprush, and a sustained negative region during backwash (Figure 2.1). The experimental measurements of the basic velocity-related terms are similar to those predicted in the XBeach model, however the wrl results appear to be less stable than the gwk results (Figure 6.3). This may be due to the different experimental scales. Small perturbations on the water surface will have a more signiﬁcant impact on the wrl results because the total depths are small. This is evident in the relative magnitudes of the depth and velocity envelopes for the two different experiments. Of the three velocity-related terms, only the velocity itself appears to vary in the same manner as τ0, during a swash 76 bed shear stress and fluid momentum

0.08 0.06 0.4 0.2

(m) 0.04

h 0.2 0.1 0.02 0 0 0 0 0.5 1 1.5 2 0 2 4 6 8 10 0 2 4 6 8 0.3 0.6 0.3 0.2 0.4 0.2 0.2 (m/s) 0.1 0.1 t h ∂ ∂ 0 0 0 0.1 0.2 0.1 − 0 0.5 1 1.5 2 − 0 2 4 6 8 10 − 0 2 4 6 8 0 0 0

0.05 0.05 0.05

(m/m) − − − x h ∂ ∂ 0.1 0.1 0.1 − − − 0 0.5 1 1.5 2 0 2 4 6 8 10 0 2 4 6 8 t (s) t (s) t (s)

Figure 6.2: Envelope ( ) and ensemble-average ( ) depth (top), temporal rate of change (middle), and spatial rate of change (bottom), for wrl, gwk, and XBeach results (left to right).

2 5 2

(m) 0 0 0 U 2 5 2 − − − 0 0.5 1 1.5 2 0 2 4 6 8 10 0 2 4 6 8

) 4 4 2 2 2 2 0 0 0 (m/s

t 2 2 U ∂

∂ − − 4 4 2 − − − 0 0.5 1 1.5 2 0 2 4 6 8 10 0 2 4 6 8 3 3 1.5 2 2 1 1 1 0.5 (m/s.m)

x 0 0 0 U ∂ ∂ 1 1 0.5 − 0 0.5 1 1.5 2 − 0 2 4 6 8 10 − 0 2 4 6 8 t (s) t (s) t (s)

Figure 6.3: Envelope ( ) and ensemble-average ( ) velocity (top), temporal rate of change (middle), and spatial rate of change (bottom), for wrl, gwk, and XBeach results (left to right). 6.3 application of momentum equation 77

300 600 150 t U ∂ ∂ 200 400 100 h

ρ 100 200 50 − 0 0 0 0 0.5 1 1.5 2 0 2 4 6 8 10 0 2 4 6 8

0 0 0 t h ∂ ∂ 200 500 200

U − − − ρ 400 1,000 400 − − − − 600 1,500 600 − 0 0.5 1 1.5 2 − 0 2 4 6 8 10 − 0 2 4 6 8 0 0 0

β 50 200 50 − − − sin 100 400 100 − − − gh

ρ 150 600 150 − − − − 200 800 200 − − − 0 0.5 1 1.5 2 0 2 4 6 8 10 0 2 4 6 8 t (s) t (s) t (s)

Figure 6.4: Stationary terms of momentum equation for wrl, gwk, and XBeach results (left to right). Units in N/m2.

200 500 50 ) 2 x U ∂ ( ∂ 0 0 0 h ρ

− 200 500 50 − − − 0 0.5 1 1.5 2 0 2 4 6 8 10 0 2 4 6 8 300 1,500 300 x h 200 1,000 200 ∂ ∂

2 100 500 100 U ρ

− 0 0 0 100 500 100 − 0 0.5 1 1.5 2 − 0 2 4 6 8 10 − 0 2 4 6 8 β 60 300 80

cos 60 x h 40 200 ∂ ∂ 40

gh 20 100 20 ρ

− 0 0 0 0 0.5 1 1.5 2 0 2 4 6 8 10 0 2 4 6 8 t (s) t (s) t (s)

Figure 6.5: Convective terms of momentum equation for wrl, gwk, and XBeach results (left to right). Units in N/m2. 78 bed shear stress and fluid momentum

400 1,000 200 ) 2 200 500 100 0 0 0 (N/m

0 200 500 100 τ − − − 400 1,000 200 − 0 0.5 1 1.5 2 − 0 2 4 6 8 10 − 0 2 4 6 8 200 400 20 ) 2 100 200 10 0 0 0 (N/m

0 100 200 10 τ − − − 200 400 20 − 0 0.5 1 1.5 2 − 0 2 4 6 8 10 − 0 2 4 6 8 t (s) t (s) t (s)

Figure 6.6: Stationary ( ) and convective ( ) terms of momentum equation (top), with calculated ( ) and actual ( ) bed shear stress (bottom) for wrl, gwk, and XBeach results (left to right). Line colours correspond to those in Figures 6.4 and 6.5.

cycle. This is unsurprising, as velocity is the primary component of the quadratic stress law, (6.7). When all of the terms of the momentum equation are combined, they prove to estimate bed shear stress poorly for both the wrl and gwk experimental results, with none of the uprush, backwash, or ﬂow reversal phases being accurately represented (Figure 6.6). In contrast, the calculated bed shear stress from the momentum equation shows good agreement with the XBeach model results (with the exception of small numerical errors near the wet/dry interface at the beginning

and end of the swash event). Xbeach calculates τ0 internally using the quadratic stress law—which is on the left hand side of (6.12)—so this provides a useful arithmetic check.

6.4 discussion of results

Estimating bed shear stress from hydrodynamic measurements of the fluid free surface using the momentum equation for depth-averaged flow does not appear to yield accurate results when compared to experimental observations. To explain this discrepancy it is useful to compare the experimental results to the idealised situation in the XBeach model (Figure 6.6). The six terms of the momentum equation are generally one order of magnitude greater than the expected bed shear stress. One small error in any one of these terms will disturb this fine balance, drastically reduce the accuracy of the final result. 6.4 discussionofresults 79

6.4.1 Accuracy of velocities

The experimental observations were of a high quality, but some errors may have arisen when calculating the terms of the momentum equation. The simplest component of the momentum equation, h, can be derived in one step:

1. Calculate h from ultrasonic sensor observations at a single point.

In contrast, the process of deriving the most complex component of ∂u the momentum equation, ∂x , involves several steps:

1. Calculate h from ultrasonic sensor observations at all points across the beachface.

2. Calculate U at all points, using the depth-averaged volume continuity method.

∂U 3. Calculate ∂x by ﬁnding the difference in U at two different points separated by an appropriate distance dx.

Any small errors in the original depth measurements will be retained and potentially magnified during subsequent calculations. This is especially true when calculating derivatives, because the numerical dif- ferentiation process inherently amplifies any noise in a signal. The depth-averaged velocities used in the analysis were all derived using measurements from ultrasonic sensors. These were validated against direct velocity measurements from acoustic Doppler profilers for the gwk experiments. The acoustic Doppler profilers could only provide velocity measurements for a region close to the bed, and only when the instrument was fully submerged. This corresponded to the middle of the runup cycle when velocities were low. It was assumed that the uppermost bin of the acoustic Doppler profiler (z = 0.022 m) gave an approximate representation of the free stream velocity, u0. The approximate free stream velocity from the acoustic Doppler profilers generally showed good agreement with the depth-averaged velocities derived from the ultrasonic sensors (Figure 6.7), but with two exceptions. First, flow reversal appears to occur slightly earlier in the swash cycle according the acoustic Doppler profiler observations (this consistent with boundary layer theory, where flow reversal begins at the bed in the presence of an adverse pressure gradient). Second, the depth-averaged velocities from the ultrasonic sensors appear to be slightly underpredicted during both uprush and backwash. 80 bed shear stress and fluid momentum

0 (m/s) U

2 −

2 0 2 − u0 (m/s)

Figure 6.7: Velocities ( ) derived from acoustic Doppler proﬁler (u ) and ul- • 0 trasonic sensors (U), compared with the line of equality ( ).

The momentum equation was re-calculated using velocity terms derived purely from acoustic Doppler profilers, to investigate the sig- nificance of these slightly differing velocity measurements. The two instruments had cross-shore spacing dx = 4.5 m. The spatial and temporal velocity gradients measured with the acoustic Doppler profilers showed good agreement with those derived from ultrasonic sensors (Figure 6.8). The bed shear stress estimate from the momentum equation was slightly improved using the acoustic Doppler profiler velocities. The result was still an order of magnitude too large, but it matched the direction of flow for both uprush and backwash. Several additional wave cases were examined, with similar results.

6.4.2 Sensitivity

The momentum equation method was tested for additional wave cases from the wrl and gwk experiments, but it failed to provide

0.6 ) ) 200 2 0 2 0.4 0 (m/s (m/s.m)

1 (N/m

t 0.2 U

− 0 x ∂ U ∂ τ ∂ ∂ 200 − 2 0 − 2 4 6 8 2 4 6 8 2 4 6 8 t (s) t (s) t (s)

Figure 6.8: Temporal (left) and spatial (centre) velocity terms, and complete momentum equation (right), calculated using acoustic Doppler profilers ( ) and ultrasonic sensors ( ), compared with shear plate measurements ( ). 6.4 discussionofresults 81 accurate estimates of bed shear stress under any conditions. Smooth- ing techniques were applied to the noisier terms, but this did not significantly improve the results. Particular attention was given to the convective terms in the momentum equation, as these are the most difficult to measure. A range of different values of cross-shore spacing, dx, were tested when calculating these terms. It is tempting to minimise the spacing, to resolve free surface and velocity fluctuations at the maximum possible resolution. Adopting this approach will give a noisy result, however, as any small fluctuations in the free-surface elevation are amplified. If the spacing is larger the resulting signal will be cleaner, but the bed may be dry at the upstream measurement point during the beginning and end of the uprush event, and the true free-surface gradient will not be captured. The values of dx used to calculate the convective terms for the wrl and gwk results were 0.3 m and 1.4 m, respectively. The free-surface ∂h gradient term, ∂x , was found to be relatively insensitive to the choice of horizontal spacing (Figure 6.9). This is because the free-surface profiles did not vary rapidly in space, except for the runup leading edge (Figure 6.10). The values of dx selected for the wrl and gwk experiments were not sufficient to resolve the steep leading edge of the runup fluid during uprush. The free-surface gradients were therefore underestimated in this region. This decision can be justified for two reasons. First, the leading edge travels quickly during uprush, so the initial steep surface gradient is short lived. Second, the assumption of hydrostatic pressure is likely to be invalid if the free-surface gradient is steep, so

0.02 − 0.04 − (m/m) x h ∂ ∂ 0.06 − 0.08 − 0 2 4 6 8 10 t (s)

Figure 6.9: Measured free-surface gradients calculated with cross-shore spa- cings of 0.4 m ( ) and 1.6 m ( ) for gwk data. 82 bed shear stress and fluid momentum

6 t = 3.6 s

5 (m) 0

z t = 1.4 s 4

t = 0.0 s 3 5 0 5 10 15 − x0 (m)

Figure 6.10: Free-surface proﬁles during uprush, derived from laser scanner observations. The free-surface gradient remains fairly constant across the beachface, apart from the blunt leading edge.

it is expected that the momentum equation would not be accurate in these conditions anyway.

6.4.3 Boundary layers and aeration

Two important assumptions about runup flows were made during the derivation of the momentum equation. The first was that the flow is depth averaged, with no boundary layers present. This assumption is non-trivial, because the bottom boundary layer can extend high into the water column during runup, particularly during backwash (O’Donoghue et al., 2010; Lanckriet and Puleo, 2015). The boundary layers measured during the gwk smooth bed experiments did not appear to cover a significant portion of the water column during runup, due to the large flow depths and low bed roughness (Figure 6.11). Boundary layers may have been more important in the wrl experiments, but they were not measured.

6.0 s 5.5 s 5.0 s 4.5 s 4.0 s 3.5 s 3.0 s 2.5 s 0.02 (m)

h 0.01

0 3 2 1 0 1 2 − − − u (m/s)

Figure 6.11: Velocity proﬁles from acoustic Doppler proﬁler ( ), showing boundary layer development during an ensemble runup◦ event. 6.5 alternative methods 83

The second assumption was that the fluid density remains constant. While the density of individual water particles will not change during runup, the total density of the fluid will be affected by changes in aeration. Cox and Shin( 2003) measured aeration (in terms of void fraction) for breaking waves in a laboratory. They observed peak void fractions of 15–20 % immediately after the broken wave passed a fixed point. This was followed by a rapid decay in void fraction. No void fraction measurements were recorded during the gwk and wrl experiments, but it is likely that the effects of aeration would have been confined to the initial stages of uprush. Visual observations suggest that uprush bores are highly aerated, especially near the runup leading edge. Bubbles are generated from waves breaking near the shoreline, and are then advected onshore during uprush, while additional bubbles are generated by turbulence at the runup leading edge. In this investigation bubbles were observed to typically rise out of the water column before flow reversal (Figure 4.5), but video timestacks from previous investigations suggest they may persist further into the backwash phase on natural beaches (e.g. Holland and Holman, 1993; Puleo and Holland, 2001; Power et al., 2011).

6.5 alternative methods

Two additional methods were assessed, to estimate bed shear stress from indirect measurements: the log law method, and the momentum integral method. The turbulent kinetic energy method (Section 2.2.1) was not assessed, as the velocity measurements from the wrl and gwk experiments were of insufﬁcient spatial and temporal resolution (this method requires particle image velocimetry, or other related measurement techniques).

6.5.1 Log law method

The log law method was used to estimate bed shear stress in the gwk experiments, based on measured velocity profiles from the acoustic Doppler profilers. An ensemble-average swash event was calculated from a representative smooth bed wave case, and bed shear stress was estimated by fitting velocity profiles to these observed velocities using (2.1). These estimates were then compared with shear plate measurements. 84 bed shear stress and fluid momentum

t = 3.9 s = 1.6 s t = 3.9 s = 1.6 s

) t t 2 0.02 0.02

(N/m 0.01 0.01 0 τ 0 0 2 1 0 1 2 2 1 0 1 2 − − − − t (s) t (s)

10 10 0

(m) 0 z 10 − 10 20 − − 0 2 4 6 8 0 2 4 6 8 u (m/s) u (m/s)

Figure 6.12: Measured velocities (◦) and ﬁtted velocity proﬁles ( ) calculated with the log law (top), and log law predictions ( ), and observed values ( ) of bed shear stress (bottom), with z0 = 0.04 mm (left) and z0 = 0.004 mm (right).

The challenge with applying the log law is estimating the value

of z0. This quantity is too small to measure experimentally, but it is a highly sensitive parameter in the log law. It was not possible to obtain a satisfactory ﬁt between the log law velocity proﬁles and measured velocities for both uprush and backwash. Instead, two different cases

were considered: z0 = 0.04 mm, which gave a good ﬁt for uprush,

and z0 = 0.004 mm, which gave a good ﬁt for backwash (Figure 6.12). The bed shear stress estimates derived from the log law were more

accurate when z0 was optimised for the backwash velocity proﬁles;

the magnitude of τ0 was overpredicted when z0 was optimised for the uprush velocity profiles. These results confirm that the log law can potentially provide useful estimates of bed shear stress from measured velocity profiles, but

the results are highly sensitive to the value of z0, which is difﬁcult to determine. Further discussion on the speciﬁc application of the log law to the gwk experiments is provided by Allis et al.( 2014).

6.5.2 Momentum integral method

The momentum integral method was applied to the same representative ensemble swash event from Section 6.5.1, again using acoustic Doppler proﬁler measurements of ﬂow velocities close to the bed. The variation in boundary layer thickness, d, was determined by iterat- 6.5 alternative methods 85

0.02 (m)

z 0.01

0 2 1.5 1 0.5 0 0.5 1 1.5 2 − − − − u (m/s)

Figure 6.13: Measured velocities from acoustic Doppler profiler, inside ( ) and outside (◦) the calculated boundary layer, and fitted velo-• city profiles ( ) from the log law. ively fitting logarithmic velocity profiles to acoustic Doppler profiler measurements, starting from the bed and continuing upwards as long as the coefficient of determination was sufficiently high (R2 > 0.9) to obtain a good fit (Figure 6.13). Three different approaches were used to estimate bed shear stress with the momentum integral (Figure 6.14). In the first approach, d was obtained purely from measured velocities. This meant that τ0 could only be calculated in the region close to flow reversal (when depths were large, and the acoustic Doppler profiler was submerged), and that d could not exceed 22 mm, because velocity measurements were only available in this range. This approach provided appropriate estimates of τ0 early in the backwash phase, but not in uprush.

0.1 0.1 0.1 (m)

h 0.05 0.05 0.05

0 0 0 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 20 20 20 ) 2 10 10 10 0 0 0 (N/m

0 10 10 10

τ − − − 20 20 20 − 0 2 4 6 8 − 0 2 4 6 8 − 0 2 4 6 8 t (s) t (s) t (s)

Figure 6.14: Depth ( ) and thickness ( ) of boundary layer (top), and measured ( ) and calculated ( ) bed shear stress (bottom), with d from acoustic Doppler proﬁler• measurements (left), d from uprush depth (centre), and ddeﬁned manually (right). 86 bed shear stress and fluid momentum

δ 0.04 0.04 0.04

(m) δ

z 0.02 0.02 0.02 δ

0 0 0 2 1 0 2 1 0 2 1 0 − − − − − − u (m/s) u (m/s) u (m/s)

Figure 6.15: Identical measured velocities ( ), with logarithmic velocity pro- ◦ ﬁles ( ), and velocity difference (u0 u; ), for boundary layers of different thickness ( ). −

In the second approach, d was assumed to be equal to the swash depth during uprush, and to reach a maximum of 22 mm during backwash (until this was limited by depth). Where measured velocities were unavailable, logarithmic velocity proﬁles were calculated using depth-averaged velocities derived from the ultrasonic sensors

(assuming that the free stream velocity, u0, was approximately equal to the depth-averaged velocity, U). This approach did not improve

the estimates of τ0 in the uprush phase. In the third approach, the value of dwas deﬁned manually. The best

estimates of τ0 were obtained when the boundary layer thickness was constantly increasing in uprush, returning to zero at ﬂow reversal, then increasing again during backwash. Closer examination of (2.3)

explains this behaviour: for τ0 to decrease with time, the velocity difference inside the boundary layer (u u), must be increasing with 0 − time. This behaviour can be easily forced by ensuring the boundary layer is always growing (Figure 6.15). These results suggest that the momentum integral method is not suitable for estimating bed shear stress under wave runup.

6.6 conclusion

In this chapter a new technique for estimating bed shear stress under wave runup was described. The technique uses the momentum equation for depth-averaged ﬂow to relate bed shear stress to time- varying water surface proﬁle measurements. The momentum equation was applied to experimental observations from the small scale wrl experiments and the prototype scale gwk experiments, and the calculated results were compared to direct shear plate measurements. The bed shear stress estimates from the momentum equation did not show good agreement with measured values. Several explana- 6.6 conclusion 87 tions were suggested to account for this result. These were (in order of importance):

1. Magnitude of terms: the ﬁnal result of the momentum equation is much smaller than each of the individual terms. Therefore a small error in one term will disturb this ﬁne balance.

2. Measurement accuracy: the depth-averaged velocities were calculated using measurements from ultrasonic altimeters. These calculated values deviated slightly from direct acoustic Doppler proﬁler measurements when velocities were large.

3. Boundary layers: the momentum equation assumes the ﬂow is depth averaged. This assumption is invalid if the ﬂow structure is dominated by boundary layers.

4. Aeration: variations in ﬂuid density were ignored in the analysis. Uprush ﬂows are often highly aerated, so this may affect bed shear stress close to the runup leading edge.

The instruments used in this investigation represent the state of the art for measurement of swash zone hydrodynamics at prototype scale. However, further advances in instrumentation may allow the momentum equation approach to be applied successfully in the future. In addition to the depth-averaged momentum equation, two alternative methods of estimating bed shear stress were assessed, using measured velocity profiles close to the bed. These methods were capable of providing accurate estimates of bed shear stress, but only when subjective assumptions were made about the top and bottom of the boundary layer. Presently the most robust method for obtaining measurements of bed shear stress under wave runup is with direct measurement techniques, using either a hot film anemometer (Con- ley and Griffin, 2004; Sumer et al., 2011) or flush-mounted shear plate (Barnes and Baldock, 2007; Pujara and Liu, 2014). Chapter 7 will examine in detail the direct measurements of bed shear stress recorded by shear plates during the wrl and gwk experiments. The relationship between bed shear stress and other experimental parameters will be investigated, and the variation of friction factors under runup flows will be discussed.

7 COMPREHENSIVEBEDSHEARMEASUREMENTS

In Chapter 6 attempts were made to indirectly estimate bed shear stress under wave runup by applying principles of ﬂuid continuity and momentum. This chapter will investigate the relationship between direct measurements of bed shear stress and other experimental parameters, and will assess the applicability of the quadratic stress law for runup ﬂows.

7.1 variation with hydrodynamic conditions

A rich dataset of direct bed shear stress measurements was collected during the wrl and gwk experiments. Shear plates were deployed in multiple locations across the beachface under a wide range of incident wave conditions (see Section 3.2). This section examines the relationship between bed shear stress and other hydrodynamic parameters.

7.1.1 Maximum swash depth

Shear stress in river beds is often calculated using the depth-slope product:

τ0 = ρgh sin(β) ,(1.2 revisited) where bed shear stress, τ0, is directly proportional to flow depth, h. Peak bed shear stress in swash flows occurs early in the uprush and late in the backwash (Figure 2.1). In both these cases the depths are small, so clearly bed shear stress in the swash zone is not directly proportional to the instantaneous fluid depth. Intuitively, it might be expected that the maximum depth would correlate with the maximum uprush bed shear stress for each individual swash event. Upon examination of results from the wrl and gwk experiments, however, it is clear that this is not the case. Meas- urements recorded using the uq shear plate, from a single location on the beachface for each experiment, show only a very weak correlation

89 90 comprehensive bed shear measurements

0.2

0.15 (m) 0.1 max h 0.05

0 0 10 20 30 40 50 2 τ0 (N/m )

Figure 7.1: Peak uprush bed shear stress and maximum swash depths for irregular waves from the wrl ( ) and gwk ( ) experiments. ◦ •

between peak bed shear stress and maximum swash height, hmax (Fig- ure 7.1). The wrl results in particular show vastly different values of peak bed shear stress for swashes of similar depths.

7.1.2 Bed roughness

The gwk experiments were performed on contrasting rough asphalt and smooth polyethylene surfaces. The measured bed shear stress for the two different surfaces was compared for identical monochromatic waves (Figure 7.2). As expected, the bed shear stress is signiﬁcantly larger on the rough surface. The peak backwash bed shear also occurs earlier in the swash cycle for the rough case, compared to the smooth case. This is probably

100 )

2 50 (N/m 0

τ 0

50 − 0 5 10 15 20 25 30 35 40 t (s)

Figure 7.2: Measured bed shear stress for identical monochromatic waves from gwk experiments on rough ( ) and smooth ( ) surfaces at position B. 7.1 variation with hydrodynamic conditions 91 caused by the gap (approximately 5 mm wide) between the moulded roughness element attached to the active face and the external housing of each shear plate (Figure 3.9). The gap was kept as small as possible while still allowing free movement of the plate, but the additional form drag of the roughness mould may have caused the shear plate to overestimate the magnitude of bed shear stress. For this reason the results from the smooth surface experiments were deemed to be more reliable, and were given greater attention in the analysis.

7.1.3 Beach slope and experimental scale

The wrl and gwk experiments were performed on slopes of 1:3 and 1:6, respectively. It is difﬁcult to compare the effects of these contrasting slopes directly, because the experimental scales are so different and it was beyond the scope of this investigation to vary the slopes within either experiment. Assuming that the hydrodynamics of runup ﬂows are independent of incident wave height, the effect of contrasting beach slopes was considered by selecting one monochromatic wave case from each of the wrl and gwk (smooth surface) experiments. Measurements were taken from the upper part of the beachface at instrument position B (Figure 3.8) for the gwk experiments. This ensured the depths and velocities were as close as possible to those of the wrl experiments, even though the runup duration was much longer (Figure 7.3).

(m) 6 x

0 0 2 4 6 8 t (s)

Figure 7.3: Runup trajectories ( ), instrument positions ( ) and regions of interest ( ), illustrating the comparative scale of the wrl (lower) and gwk (upper) experiments. 92 comprehensive bed shear measurements

0.1 0.1

(m) 0.05 0.05 h

0 0 0 1 2 3 0 2 4 6

2 2 0 0 (m/s)

U 2 2 − − 0 1 2 3 0 2 4 6 ) 2 20 20

0 0 (N/m 0 τ 20 20 − 0 1 2 3 − 0 2 4 6 t (s) t (s)

Figure 7.4: Ensemble-average measurements ( ), and envelopes ( ) of depth (top), velocity (middle), and bed shear (bottom), for wrl (left) and gwk (right) experiments. Note different time scales.

Ensemble-average swash events were calculated for the two experimental cases, and the bed shear stress measurements were found to be larger for the wrl results (Figure 7.4). This is despite similar flow depths and velocities, similar bed roughness on the surrounding slope, and identical roughness on the shear plate surface (the uq shear plate was used in both cases). Previous experimental studies have shown that rapidly accelerating flows generate stronger bed shear stresses than gradually accelerating flows of a similar velocity (e.g. Nielsen, 2002; van der A et al., 2011). The runup flows in the wrl experiments were indeed accelerating more rapidly than those from the gwk experiments (the velocity gradients in Figure 7.4 appear qualitatively similar, but the time scales differ by a factor of two). Ignoring the obvious differences in experimental scale, this result suggests that an increase in beach slope will lead to larger bed shear stresses in runup flows.

7.1.4 Time-varying parameters

∂h In Section 6.3 two parameters were identiﬁed ( ∂t , and U) which appear to vary proportionally with τ0 through a swash cycle. These parameters were compared with shear plate measurements under monochromatic waves from the wrl and gwk (smooth bed) experiments, 7.1 variation with hydrodynamic conditions 93

0.1 0.1

0 0 (m/s) t h ∂ ∂ 0.1 0.1 − − 20 10 0 10 20 20 10 0 10 20 − − − −

2 2

0 0 (m/s) U 2 2 − − 20 10 0 10 20 20 10 0 10 20 − − − −

) 4 4 2

/s 2 2 2

(m 0 0 U

| 2 2 − − U | 4 4 − − 20 10 0 10 20 20 10 0 10 20 − − − − 2 2 τ0 (N/m ) τ0 (N/m )

Figure 7.5: Variation of different parameters under monochromatic waves compared with measured τ0 for wrl (left) and gwk (right) experiments. at a single cross-shore location (Figure 7.5). The depth-varying term ∂h ∂h ( ∂t ) appears to be proportional to τ0 in uprush only; ∂t is relatively constant during backwash, regardless of τ0, and is not zero at ﬂow reversal (because ﬂow reversal occurs after the maximum swash depth is reached). Depth-averaged velocity (U) shows a better correlation with τ0 in both uprush and backwash, but becomes non-linear when velocities are large. This non-linearity can corrected if the velocity term is squared, while retaining its direction. This result is not un- expected, as U U is the active term in the quadratic stress law (see | | Section 7.2).

7.1.5 Cross-shore location

Cox et al.( 2000), Barnes et al.( 2009), and Sumer et al.( 2011) measured the cross-shore variation in swash zone bed shear stress, and all found τ0 to reach a maximum slightly above still water level, reducing to zero near the maximum uprush limit. Bed shear stress was measured at four different positions on the beachface during the wrl 94 comprehensive bed shear measurements

1 (-) 0, max τ

/ 0 0 τ

1 − 0 0.2 0.4 0.6 0.8 1

Rx (-)

Figure 7.6: Cross-shore variation of normalised peak bed shear stress envelope for monochromatic waves of period T = 5 s ( ), T = 3.2 s ( ), and T = 2.2 s ( ) from wrl experiments.

experiments, and the cross-shore bed shear stress envelope was calculated for three different monochromatic wave cases (Figure 7.6). The envelope was normalised with respect to the peak uprush bed shear,

τ0,max, and the maximum uprush limit, Rx. The wrl bed shear stress measurements showed good agreement with the previous studies for the uprush phase, but were generally larger during backwash (Figure 7.7). The peak uprush bed shear stress also occurred higher up the beachface for the present investigation. This is likely due to the steeper slopes, and the longer collapse time for the incident waves (since maximum velocities are reached further up the slope).

(-) 0.5 0, max τ /

0 0 τ

0.5 − 0.2 0 0.2 0.4 0.6 0.8 1 − Rx (-)

Figure 7.7: Cross-shore variation of normalised peak bed shear stress envelope from wrl experiments ( ) compared with previous studies (Cox et al. 2000; , Barnes et al.• 2009; , Sumer et al. 2011; +). ◦ × 7.2 quadratic stress law and friction factors 95

7.2 quadratic stress law and friction factors

Shear stresses are generated at the interface between the ﬂuid and the bed. For rough turbulent ﬂows, the bed shear stress is commonly related to a friction factor f through the quadratic stress law:

1 τ = ρ f U U .(6.7 revisited) 0 2 | |

This formulation is well established for calculating bed shear stress in steady flows, where f remains constant (e.g. Putnam and Johson, 1949; Jonsson, 1966). It has also been widely adopted for use in runup flows, where unsteady conditions prevail. Many laboratory and field experiments have used (6.7) for calculating friction factors, but the results vary dramatically between studies, with mean values ranging from f = 0.001 (Conley and Griffin, 2004) to f = 0.04 (Cox et al., 2000). Furthermore, many studies have found f to differ between uprush and backwash, and even to vary continuously through the swash cycle (Cowen et al., 2003). The effective friction factor for the wrl and gwk experiments was back calculated from velocity and bed shear stress measurements, using (6.7). Friction factors calculated in this way tend to approach infin- ity close to flow reversal, because the divisor is close to zero. For the purposes of this analysis, friction factors were not calculated when velocities were small ( U < 0.5 m/s), because bed shear stress is at a | | minimum near flow reversal anyway.

7.2.1 Results: wrl

The mean f was found to be approximately 0.01 for a range of wave cases from the wrl experiments (Figure 7.8), and was most consistent during the backwash phase. Estimates of f were also calculated for the single wave case on the rough geotextile surface, and these were found to be slightly higher ( f = 0.015–0.02 ) than those on the smooth plywood surface (Fig- ure 7.9). Again, it is expected that the shear plate was affected by form drag from the geotextile surface, so only the smooth surface results were included in the main analysis. Higher peaks in ﬂuid depth were also observed on the rough surface during uprush. This is caused by the increased friction reducing the maximum runup excursion and 96 comprehensive bed shear measurements

conﬁning the ﬂuid to the lower portion of the swash zone, where it forms a steeper, higher peak. Friction factors were generally highest in the centre of the swash zone (Figure 7.10). There was little variation between uprush and backwash, with the exception of the 5 s period wave case, where f was highest during backwash.

7.2.2 Results: gwk

The mean f for the gwk experiments was found to be approximately 0.005 for the smooth surface, and 0.01 for the rough surface (Figure 7.11). On the smooth surface, f remained fairly consistent for incident waves of varying height (Figure 7.12), and period (Fig- ure 7.13). Friction factors were also calculated for a selection of irregular waves from the smooth surface experiments (Figure 7.14). The friction factors showed more variability within swash cycles than the ensemble-average cases, but the mean value was similar. A mean f value was calculated for each runup event, and these friction factors did not show any signiﬁcant trends across the beachface, or between uprush and backwash phases (Figure 7.15).

0.06 0.06 0.04 0.04 (m)

h 0.02 0.02 0 0 0 1 2 0 1 2 ) 2 20 20

0 0 (N/m 0 τ 20 20 − − 0 1 2 0 1 2 0.02 0.02 0.015 0.015

(-) 0.01 0.01 f 0.005 0.005 0 0 0 1 2 0 1 2 t (s) t (s)

Figure 7.8: Friction factors for wrl wave cases of period 2.2 s (left), and 3.2 s (right), calculated from measurements at position B ( ), C ( ), and D ( ). 7.2 quadratic stress law and friction factors 97

0.06 0.06 0.04 0.04 (m)

h 0.02 0.02 0 0 0 1 2 0 1 2 ) 2 50 50

(N/m 0 0 0 τ

0 1 2 0 1 2 0.03 0.03

0.02 0.02 (-) f 0.01 0.01

0 0 0 1 2 0 1 2 t (s) t (s)

Figure 7.9: Friction factors for wrl wave cases of period 2.2 s (left), and 3.2 s (right) for smooth plywood ( ) and rough geotextile ( ) cases, calculated from measurements at position B.

0.01

0 (-) f 0.01 −

0.02 − 0 0.2 0.4 0.6 0.8 1

Rx (-)

Figure 7.10: Cross-shore variation of friction factors for monochromatic waves of period T = 5 s ( ), T = 3.2 s ( ), and T = 2.2 s ( ) from wrl experiments. Positive and negative values of f indicate uprush and backwash phases, respectively. 98 comprehensive bed shear measurements

0.4 0.4 (m)

h 0.2 0.2

0 0 0 2 4 6 8 10 0 2 4 6 8 10 )

2 50 50

0 0 (N/m 0 τ 50 50 − − 0 2 4 6 8 10 0 2 4 6 8 10

0.015 0.015

(-) 0.01 0.01 f 0.005 0.005 0 0 0 2 4 6 8 10 0 2 4 6 8 10 t (s) t (s)

Figure 7.11: Friction factors for identical gwk ensemble-average monochromatic wave cases on rough ( ) and smooth ( ) beds, calculated from measurements at position A (left) and B (right). Rough bed measurements at A not shown (see Section 4.5.3).

0.4 0.4

(m) 0.2 0.2 h

0 0 0 2 4 6 8 10 0 2 4 6 8 10

) 40 40 2 20 20 0 0 (N/m

0 20 20 τ − − 40 40 − 0 2 4 6 8 10 − 0 2 4 6 8 10

0.015 0.015

(-) 0.01 0.01 f 0.005 0.005 0 0 0 2 4 6 8 10 0 2 4 6 8 10 t (s) t (s)

Figure 7.12: Friction factors for gwk (smooth bed) ensemble-average monochromatic wave cases of period T = 12 s and offshore heights of 0.6 m ( ), 0.7 m ( ), and 0.9 m ( ), from measurements at position A (left) and B (right). 7.2 quadratic stress law and friction factors 99

0.4 0.4

(m) 0.2 0.2 h

0 0 0 2 4 6 8 10 0 2 4 6 8 10

) 40 40 2 20 20 0 0 (N/m

0 20 20 τ − − 40 40 − 0 2 4 6 8 10 − 0 2 4 6 8 10

0.015 0.015

(-) 0.01 0.01 f 0.005 0.005 0 0 0 2 4 6 8 10 0 2 4 6 8 10 t (s) t (s)

Figure 7.13: Friction factors for gwk (smooth bed) ensemble-average monochromatic wave cases of offshore wave height H = 0.9 m and periods of 8 s ( ), and 12 s ( ), calculated from measurements at position A (left) and B (right).

0.4 0.3

(m) 0.2 h 0.1 0 0 5 10 15 20 25 30 35 40 45 40 ) 2 20 0 (N/m

0 20 τ − 40 − 0 5 10 15 20 25 30 35 40 45

0.015

(-) 0.01 f 0.005 0 0 5 10 15 20 25 30 35 40 45 t (s)

Figure 7.14: Friction factors for irregular waves from the gwk (smooth bed) experiments, calculated from measurements at position A ( ) and B ( ). 100 comprehensive bed shear measurements

0.015

0.01 (-) f

0.005

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Rx (-)

Figure 7.15: Normalised cross-shore distribution of average uprush ( / ) and backwash ( / ) friction factors, calculated for individual• irregular waves◦ from the gwk (smooth bed) experiments.

7.2.3 Discussion of shear plate measurements

The calculated friction factors from the gwk and wrl experiments are typically elevated immediately after ﬂow reversal, before stabilising as the backwash develops. This is probably due to adverse pressure gradients causing ﬂow reversal to initially occur at the bed, rather than uniformly through the entire water column (e.g. Figure 6.13). During this time the near-bed velocity will deviate from the depth-

averaged velocity and τ0 will no longer be proportional to U, leading to an overprediction of f (Figure 7.16). Apart from the region around ﬂow reversal, the friction factors presented above appear to be relatively constant during uprush and backwash. The results from the gwk smooth surface experiments in particular (Figure 7.12) show much more consistency than previous studies (e.g. Barnes et al., 2009; Puleo et al., 2012). Indeed, the vari-

f overpredicted in this region

τ0 > 0 τ0 = 0 τ0 < 0 τ0 < 0 τ0 < 0 U > 0 U > 0 U 0 U < 0 U < 0 ≈ Figure 7.16: Boundary layer development during flow reversal, in the presence of an adverse pressure gradient. 7.3 friction factors for numerical modelling 101 ation in f during a swash cycle is often plotted with a logarithmic scale (Cowen et al., 2003; Kikkert et al., 2012). These more consistent results are likely because of the high quality of the measurements obtained during the gwk experiments. The simultaneous operation of the ultrasonic sensor array, shear plates, acoustic Doppler profilers and laser scanners represents the present state of the art for measuring swash hydrodynamics on a large scale. The gwk shear plate had not been deployed in the swash zone prior to this investigation. This is the first time a shear plate with a load cell design has been used to measure swash zone bed shear stress (previous designs have used eddy current displacement sensors). Due to logistical constraints the gwk shear plate was not directly tested alongside the uq shear plate, but simultaneous measurements taken from different cross-shore locations show similar signals between the two instruments (Figure 7.14). Compared with previous designs, the gwk shear plate is rugged and fully sealed, making it particularly suitable for environments with high wave loads, or where suspended sediment is present.

7.3 friction factors for numerical modelling

Many numerical models use friction factors to calculate hydrodynamics and sediment transport in the swash zone (see reviews by Broc- chini and Baldock, 2008, and Bakhtyar et al., 2009), but there is a high level of uncertainty regarding the actual value of f to use. It seems the end user of a numerical model has three choices when choosing an appropriate friction factor: 1. Leave f at the default software setting.

2. Choose f from the results of previous swash studies.

3. Estimate f using steady-state hydraulics, based on site-speciﬁc parameters.

7.3.1 Retaining the default value of f

Retaining the default f in a numerical model is the simplest approach to take, but it is not the most desirable. The model can still be successfully validated and against measured data, simply by altering other calibration constants. But this becomes meaningless if the calibration constants are simply masking errors in the friction factor. 102 comprehensive bed shear measurements

0.1

f 0.01

0.001

) ) ) ) ) ) ) ) ) 2004 2003 2009 2012 2001 2015 1995 2012 2000

Hughes( Inch et al.( Cox et al.( (smooth surface) (smooth surface) Puleo et al.( Cowen et al.( Barnes etKikkert al.( et al.( gwk wrl Conley and Grifﬁn( Puleo and Holland(

Figure 7.17: Estimates of f from current investigation ( ) and selected previous studies of swash flows in fixed-bed laboratory experiments () and mobile bed field experiments (♦), showing variation between uprush (M/N), and backwash (O/H), where reported.

7.3.2 Friction factors from previous studies

In the absence of a suitable field study from the site of interest, a value of f may be taken from existing literature. The problem is that estimates of f vary by more than an order of magnitude between studies (Figure 7.17). Until recently friction factors were typically found to be higher during uprush compared to backwash (Masselink and Puleo, 2006), but some recent results show the opposite behaviour (Kikkert et al., 2012; Puleo et al., 2012). Estimates of f from laboratory experiments are generally lower than those from field experiments, but results from Cox et al.( 2000) and Conley and Griffin( 2004) also contradict this apparent trend.

7.3.3 Application of steady-state hydraulics principles

Methods for calculating friction factors for oscillatory flows in open channels generally relate f to the wave period, orbital velocity amp- litude, and bed roughness (e.g. Swart, 1974; Nielsen, 1992; Soulsby, 1997). Since swash flows are not dominated by the offshore wave period or orbital fluid motions, the only remaining parameter of in-

terest here is bed roughness, ks. 7.3 friction factors for numerical modelling 103

If swash flows are approximated as steady flows in a rectangular channel of infinite width, a friction factor can be calculated with the aid of the Colebrook-White (1939) equation: ! 1 k 2.51 = 2 log s + ,(7.1) √λ − 10 3.7D Re√λ where λ is the Darcy( 1857) friction factor, related to the Fanning (1893) friction factor, f , by

λ = 4 f ,(7.2) while D is hydraulic diameter (D = 2h for wide rectangular channels), and Re is Reynolds( 1883) number, given by

uD Re = ,(7.3) ν

6 2 where u is fluid velocity, and ν is kinematic viscosity (ν = 10− m /s for water). The Colebrook-White equation was originally designed for fully- developed, uniform, steady flows in circular pipes flowing completely full (Knight et al., 2009). The equation is also considered to be applicable to open channel conditions, but swash flows do not represent fully-developed or steady conditions. Nevertheless friction factors were calculated for the wrl and gwk experiments with (7.1), using measured flow depths and velocities. The roughness of the shear plates for the smooth surface experiments was taken as ks = 0.003 mm. The roughness for the asphalt moulded surface from the gwk experiments was taken as ks = 0.6–1.5 mm.

These ks values were based on the recommended values for smooth aluminium and rough concrete, from Barr( 1995). These friction factors were compared with friction factors derived from shear plate measurements using the quadratic stress law in Sec- tion 7.2, for the wrl experiments (Figure 7.18), and the gwk experiments on smooth (Figure 7.19) and rough (Figure 7.20) surfaces. The friction factors calculated using the Colebrook-White equation compared favourably with those from the quadratic stress law, and a particularly good agreement was observed for the gwk smooth surface experiments. Several additional wave cases were examined and similar results were observed. The Colebrook-White method tended to underpredict f for waves of lower steepness (Figure 7.21). 104 comprehensive bed shear measurements

0.06 0.06 0.04 0.04 (m)

h 0.02 0.02 0 0 0 1 2 0 1 2

105 105

4 4

Re (-) 10 10

103 103 0 1 2 0 1 2

0.015 0.015

(-) 0.01 0.01 f 0.005 0.005 0 0 0 1 2 0 1 2 t (s) t (s)

Figure 7.18: Friction factors from the wrl experiments, calculated using (7.1) ( ) and (6.7)( ), from measurements at position B (left) and C (right), from a single ensemble-average monochromatic wave case of period T = 3.2 s.

0.4 0.4

(m) 0.2 0.2 h

0 0 0 2 4 6 8 10 0 2 4 6 8 10

106 106

5 5

Re (-) 10 10

104 104 0 2 4 6 8 10 0 2 4 6 8 10

0.015 0.015

(-) 0.01 0.01 f 0.005 0.005 0 0 0 2 4 6 8 10 0 2 4 6 8 10 t (s) t (s)

Figure 7.19: Friction factors from the gwk smooth surface experiments, calculated using (7.1)( ) and (6.7)( ), at position A (left) and B (right) for a single ensemble-average monochromatic wave case of offshore wave height H = 0.9 m and period of 12 s. 7.3 friction factors for numerical modelling 105

0.3 0.3

0.2 0.2 (m)

h 0.1 0.1

0 0 0 2 4 6 8 0 2 4 6 8

106 106

5 5

Re (-) 10 10

104 104 0 2 4 6 8 0 2 4 6 8 0.03 0.03

0.02 0.02

(-) ks = 1.5 mm f 0.01 ks = 0.6 mm 0.01

0 0 0 2 4 6 8 0 2 4 6 8 t (s) t (s)

Figure 7.20: Friction factors from the gwk rough surface experiments, calculated using (7.1)( ) and (6.7)( ), for ensemble-average monochromatic wave cases of offshore wave height H = 0.9 m and periods of 8 s (left) and 12 s (right), from position B.

Rough Smooth 0.015

AB 0.01 (-)

f AB 0.005

0 1.8 2.6 3.3 1.7 1.8 2.1 2.6 3.0 3.2 3.3 3.8 ξ (-)

Figure 7.21: Mean f values from (7.1)( ) and (6.7)( ), at A and B, for different wave cases from the rough◦ (left) and• smooth (right) surface gwk experiments, with ks = 1.6 mm and ks = 0.003 mm, respectively. Error bars show one standard deviation from the mean. Values of f close to ﬂow reversal U < 1 m/s neglected. | | 106 comprehensive bed shear measurements

This is an encouraging result, suggesting that a reasonable estimate

of f may be obtained using just ks and a representative Reynolds number (based on local ﬂow depths and velocities), without requiring any measurements of bed shear stress at all.

7.4 estimating f from runup trajectories

Puleo and Holland( 2001) adopted the frictionless ballistic model of Shen and Meyer( 1963), and with the addition of a bed shear stress term (6.7), attempted to estimate friction coefﬁcients on a sandy beach based on measured runup trajectories. Their formulation gave the

position of the shoreline leading edge, xs, during uprush 2δhu a xs (t) = ln ,(7.4) f u b

with     p s  1 us f u g f u sin β  a = cos tan−   t  (7.5)   q  −  2gδhu sin β 2δhu

   p  1 us f u  b = cos tan−   ,(7.6)   q  2gδhu sin β

and backwash

  s  2δhb  g f b sin β  xs (t) = ln cosh  t  ,(7.7) − f b − 2δhb

where t is time, δh is the depth of the ﬂuid leading edge, f is the

Fanning friction factor, us is the initial leading edge velocity, g is gravity, and β is beach slope. The u and b subscripts refer to the uprush and backwash phases, respectively.

7.4.1 Beach slope and breaker type

Puleo and Holland( 2001) noted that the effects of varying friction would be much more apparent on gently sloping beaches, because 7.4 estimating f from runup trajectories 107

10 (m) x 5

0 0 10 20 30 40 50 60 70 80 t (s)

Figure 7.22: Runup trajectories from identical irregular waves from the gwk experiments, on the rough ( ) and smooth ( ) surfaces. The signal is clipped below x = 4 m for the smooth surface case, because a portion of the ultrasonic sensor array was ofﬂine. the horizontal runup excursions are longer than on steep beaches, making it easier to identify relative changes. For the gwk experiments, maximum runup excursions were generally larger on the smooth surface than the rough surface, as expected (Figure 7.22). Approximately 300 runup events were compared for identical irregular wave cases, and the runup excursions were found to be of the order of 10 % higher on the smooth surface (Figure 7.23). Interestingly, the runup excursions for the solitary (non-breaking) wave cases were not measurably different between the rough and

10 y = 0.9x + 0.1

(m), smooth surface 8 x R

4 4 6 8 10 12 14 16

Rx (m), rough surface

Figure 7.23: Maximum runup extents ( ) for identical irregular waves from the gwk experiments on rough• and smooth surfaces, with the line of equality ( ) and a linear ﬁt ( ). 108 comprehensive bed shear measurements

15 15 10 10 (m)

x 5 5 0 0 0 5 10 0 5 10

4 4 2 2

(m/s) 0 0

U 2 2 − − 4 4 − 0 5 10 − 0 5 10 )

2 50 50

(N/m 0 0 0 τ 50 50 − 0 5 10 − 0 5 10 t (s) t (s)

Figure 7.24: Runup trajectories for breaking (left) and non-breaking (right) waves from the gwk rough ( ) and smooth ( ) surface experiments, calculated from measurements at position B. Breaking waves are monochromatic; non-breaking waves are solitary.

smooth surface experiments, despite having similar velocity and bed shear stress to the breaking waves (Figure 7.24). This suggests that the maximum runup extent of non-breaking waves is largely independent of bed roughness, which seems reasonable, if two extreme non-breaking wave cases are considered. First: a wave of very low steepness such as a tidal wave, and second: a wave encountering a nearly vertical wall. In both these cases it is expected that the bed roughness would have very little inﬂuence on the runup excursion. Thus Puleo and Holland( 2001) model appears to be invalid for non-breaking waves, because runup extent is not related to bed friction. The model should still be largely applicable to natural beach conditions, however, because individual runup events are generally driven by broken wind waves.

7.4.2 Application of Puleo and Holland (2001) model

Measured runup trajectories from the gwk rough surface experiments

were compared with predictions from (7.4), with δh = 0.05 m, and us 7.5 conclusion 109

15 15 f = 0.000 10 10 f = 0.005 f (m) = 0.020 x 5 5

0 0 0 2 4 6 8 0 2 4 6 8

6 6

4 4 (m/s)

s 2 2 u

0 0 0 2 4 6 8 0 2 4 6 8 t (s) t (s)

Figure 7.25: Measured runup trajectories ( ), and predictions from (7.4) ( ), with f = 0.02, 0.005, and 0, for ensemble-average cases of offshore wave height H = 0.9 m and periods of 8 s (left) and 12 s (right), from the gwk rough surface experiments. was taken from the maximum velocity of the runup leading edge. The Puleo and Holland( 2001) model generally underpredicted the maximum runup excursions, even with f = 0 (Figure 7.25). This meant that it was not possible to assess this method for estimating friction factors. This result suggests that (7.4) is not appropriate for use on steep slopes with surging and collapsing waves (the conditions in Puleo and Holland( 2001) appear to be fully-developed bores on beach slopes with approximately half the steepness of the gwk experiments).

7.5 conclusion

This chapter investigated the relationship between swash zone bed shear stress and other experimental parameters. The variation in τ0 during a swash cycle was found to be proportional to the square of depth-averaged velocity ( U U) which is the driving term in the | | quadratic stress law. Friction factors were back calculated from the quadratic stress law, and were found to remain constant during uprush and backwash (except around ﬂow reversal) for many different wave cases in the gwk experiments, and appeared to be only affected by bed roughness. These results show much more consistency than previous studies, because of the quality of the prototype scale measurements. 110 comprehensive bed shear measurements

This adds further evidence to support the applicability of the quadratic stress law for swash flows. Under this approach, bed shear stress under wave runup can be approximated using depth-averaged velocities (ignoring fluid boundary layers) while retaining a reasonable level of accuracy. This has important (and positive) implications for numerical modelling of hydrodynamics and sediment transport in swash flows. The Colebrook-White equation was used to estimate friction factors for use with the quadratic stress law. Despite being originally intended for steady uniform flows, the equation was found to provide reasonable estimates of f for swash flows, using a representative rough-

ness, ks, and Reynolds number, Re. The runup trajectories of different swash types were examined, on both rough asphalt and smooth polyethylene surfaces. The Puleo and Holland( 2001) model for estimating friction factors from shoreline oscillations was found to be not suitable for collapsing and surging swashes on steep slopes. The maximum runup excursions for breaking waves were typically of the order of 10 % higher on the smooth surface. The runup trajectories of non-breaking waves were found to be largely unaffected by contrasting bed roughness. 8 CONCLUSION

Methodology

Extensive measurements of swash zone hydrodynamics were collected during this investigation, in both medium and prototype scale fixed-bed laboratory wave flumes. Measurements were collected using ultrasonic sensors, from which instantaneous fluid depths and depth-averaged velocities were derived, without interfering with the flow. The volume continuity method (Blenkinsopp et al., 2010b) was found to provide accurate estimates of fluid velocities in the swash zone, compared with direct measurements from acoustic Doppler profilers mounted close to the bed. Direct measurements of swash zone bed shear stress were obtained using two flush-mounted shear plates: one using an eddy current displacement sensor (Barnes and Baldock, 2007), and one with a dual- beam load cell. This investigation has provided the first measurements of swash zone bed shear stress from an instrument using a load cell design. This alternative design uses no moving parts, so the instrument is rugged and fully sealed, making it especially suitable for environments with high wave loads and/or where suspended sediment is present.

Anatomy of wave runup (Chapter 5)

The leading edge of the shoreline during wave runup was found to follow a parabolic trajectory, but only after complete collapse of the incident wave. This suggests that the Shen and Meyer( 1963) model is valid for all swash types, and not just for well-developed bores. The runup trajectories for incident waves that plunged violently onto the beachface resembled swash overrun events, where the white water from the initial plunging jet was overtaken later in the uprush phase, by the collapsing bulk of the ﬂuid in the incident wave. Collapsing and surging swashes were observed to collapse slowly on the beachface, with the instantaneous shoreline accelerating in the landward direction for up to 70 % of the uprush cycle. This extended

111 112 conclusion

period of landward acceleration for collapsing and surging waves is not described well in existing swash zone deﬁnitions, which assume the bore collapse process is almost instantaneous. A new generalised deﬁnition of the dynamic regions within the nearshore environment is proposed, to clarify this situation:

swash zone The region where the instantaneous shoreline oscillates back and forth on the beachface.

collapse zone The region where landward accelerations of the instantaneous shoreline are present.

fully-developed swash zone The region where the shoreline trajectory is dominated by gravity (as a function of beach slope).

This new deﬁnition of the swash zone enables direct comparison between different swash types. It is particularly applicable to beaches or coastal structures with steep slopes, or in conditions where the incident waves are not well-developed bores.

Bed shear stress and ﬂuid momentum (Chapter 6)

In this investigation, attempts were made to estimate bed shear stress based on momentum principles, using just ﬂuid depths (and associated depth-averaged velocities) measured across the entire swash zone. This technique did not yield accurate estimates of bed shear stress, mostly because the technique is sensitive to small measurement errors. Improved instrumentation may allow more satisfactory results to be obtained in future. Previous studies have estimated swash zone bed shear stress indirectly, from measurements of internal ﬂuid velocities. These tech-

niques can provide useful estimates of τ0, but their accuracy is ulti- mately limited by necessary (and sometimes subjective) assumptions on the complex boundary layer development that occurs during uprush and backwash. conclusion 113

Comprehensive bed shear measurements (Chapter 7)

The hydrodynamics of swash flows are often described with principles from classical fluid mechanics. These principles generally describe swash flows surprisingly well, considering they are far they deviate from the uniform, steady conditions for which the principles were originally intended. In the present investigation the quadratic stress law was observed to provide accurate estimates of bed shear stress, based on depth- averaged velocity. This was evidenced by the back calculation of friction factors, which remained constant during uprush and backwash (except around flow reversal). Friction factors remained consistent for many different waves cases, and appeared to be only affected by bed roughness. Furthermore, the Colebrook-White equation was shown to provide reasonable estimates of f , given a representative bed roughness and Reynolds number.

Recommendations

In addition to the ultrasonic sensors, high resolution instantaneous water surface profiles were collected using laser scanners during the prototype scale experiments, but these instruments were found to only provide useful measurements during uprush. Laser scanners appear best suited to field conditions, where runup flows are characterised by high levels of aerated water and suspended sediment. Moulded roughness elements approximately 5 mm thick were attached to each shear plate, to replicate the asphalt surface on the beachface of the prototype scale experiments. These roughness elements caused additional form drag on the surface of each shear plate, reducing the accuracy of bed shear stress measurements. When at- taching roughness elements to shear plates, it is recommended that they be as thin as possible (e.g. sandpaper, Barnes et al., 2009).

Closing remarks

This investigation has provided further evidence to support the applicability of the quadratic stress law for swash ﬂows. Under this approach, bed shear stress under wave runup can be approximated using depth-averaged velocities (ignoring ﬂuid boundary layers), while retaining a reasonable level of accuracy. This has important (and pos- 114 conclusion

itive) implications for numerical modelling of hydrodynamics and sediment transport in swash flows. Presently the most robust estimates of swash zone bed shear stress can only be obtained from direct measurements, where the active face of the instrument is mounted flush with the bed and fully exposed to the moving fluid, so that no assumptions about flow structure are required. Instruments with this capability are hot film anemometers (Conley and Griffin, 2004; Sumer et al., 2011) and mechanical shear plates (Barnes and Baldock, 2007; Pujara and Liu, 2014). BIBLIOGRAPHY

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