ARTICLE IN PRESS
Continental Shelf Research 26 (2006) 574–588 www.elsevier.com/locate/csr
Field observations of instantaneous water slopes and horizontal pressure gradients in the swash-zone
T.E. Baldocka,Ã, M.G. Hughesb
aDivision of Civil Engineering, University of Queensland, St Lucia, Qld, 4072, Australia bSchool of Geosciences, University of Sydney, Sydney, NSW, 2006, Australia
Received 28 January 2005; received in revised form 21 June 2005 Available online 13 March 2006
Abstract
Field observations of instantaneous water surface slopes in the swash zone are presented. For free-surface flows with a hydrostatic pressure distribution the surface slope is equivalent to the horizontal pressure gradient. Observations were made using a novel technique which in its simplest form consists of a horizontal stringline extending seaward from the beach face. Visual observation, still photography or video photography is then sufficient to determine the surface slope where the free-surface cuts the line or between reference points in the image. The method resolves the mean surface gradient over a cross-shore distance of 5 m or more to within 70.001, or 1/20th 1/100th of typical beach gradients. In addition, at selected points and at any instant in time during the swash cycle, the water surface slope can be determined exactly to be dipping either seaward or landward. Close to the location of bore collapse landward dipping water surface slopes of order 0.05–0.1 occur over a very small region (order 0.5 m) at the blunt or convex leading edge of the swash. In the middle and upper swash the water surface slope at this leading edge is usually very close to horizontal or slightly seaward. Behind the leading edge, the water surface slope was observed to be very close to horizontal or dipping seaward at all times throughout the swash uprush. During the backwash the water surface slope was observed to be always dipping seaward, approaching the beach slope, and remained seaward until a new uprush edge or incident bore passed any particular cross-shore location of interest. The observations strongly suggest that the swash boundary layer is subject to an adverse pressure gradient during uprush and a favourable pressure gradient during the backwash. Furthermore, assuming Euler’s equations are a good approximation in the swash, the observations also show that the total fluid acceleration is negative (offshore) for almost the whole of the uprush and for the entire backwash. The observations are contrary to recent work suggesting significant shoreward directed accelerations and pressure gradients occur in the swash (i.e., qu/qt40 qp/qxo0), but consistent with analytical and numerical solutions for swash uprush and backwash. The results have important implications for sediment transport modelling in the swash zone. r 2006 Elsevier Ltd. All rights reserved.
Keywords: Swash; Long wave runup; Pressure gradients; Flow acceleration; Boundary layers; Sediment transport; Bores; Dam break
1. Introduction
The hydrodynamics in the swash zone govern ÃCorresponding author. Tel.: +61 7 33469432; fax: +61 7 336545999. sediment transport mechanisms during wave run-up E-mail addresses: [email protected] (T.E. Baldock), and run-down, which in large part control beach [email protected] (M.G. Hughes). face morphology. The swash zone therefore plays an
0278-4343/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.csr.2006.02.003 ARTICLE IN PRESS T.E. Baldock, M.G. Hughes / Continental Shelf Research 26 (2006) 574–588 575 important role in littoral sediment transport, boundary layer to account for turbulence (Puleo particularly during episodes of beach erosion and and Holland, 2001; Butt et al., 2001), improved recovery (Elfrink and Baldock, 2002). In particular, descriptions of suspended sediment behaviour, the sediment transport in the upper swash zone is particularly sediment advected into the swash from important for both berm building and beach bore collapse (Hughes et al., 1997b; Jackson et al., scarping. Prediction of sediment transport in the 2004; Pritchard and Hogg, 2005) and finally the swash zone is complicated by different transport effects of local (Eulerian) fluid accelerations or modes (Horn and Mason, 1994), high concentra- horizontal pressure gradients (Nielsen, 2002; Puleo tions of sediment (Hughes et al., 1997a; Osborne et al., 2003). The latter may modify the transport and Rooker, 1999) and diverging flow (Hibberd and rates directly (see Nielsen, 1992) or serve as a proxy Peregrine, 1979; Raubenheimer and Guza, 1996; for turbulent effects that are not well understood Baldock and Holmes, 1997). These are combined (Puleo et al., 2003). with high flow velocities and very shallow water Given that the total horizontal force on sediment depths (Hughes and Baldock, 2004). Seaward and particles comprises the sum of a drag force and shoreward boundary conditions may also modify inertial (pressure) forces (Nielsen, 1992), the direc- the net sediment flux in the swash zone. Examples tion of pressure gradient forces in the swash is of include the advection of turbulence and sediment fundamental importance for a correct description of from the surf zone into the swash (Hughes et al., the hydrodynamics and sediment dynamics. While 1997b; Kobayashi and Johnson, 2001; Jackson the free stream pressure gradient in oscillatory flow et al., 2004; Pritchard and Hogg, 2005) or the causes the bed shear stress to lead the free stream overtopping of beach berms (Baldock et al., 2005). flow velocity, classical boundary layer theory Butt and Russell (2000) and Elfrink and Baldock assumes the free stream pressure (and gradient) is (2002) provide extensive reviews of these issues, as imposed onto, and across, the boundary layer well as swash zone hydrodynamics and sediment (Schlichting, 1979). Whether the swash boundary transport in general. layer should be regarded as a variation of an A significant and unresolved issue is the physi- oscillatory boundary layer or as a boundary layer cally inconsistent nature and/or poor performance more equivalent to that in unidirectional flows of sediment transport models for the swash zone, remains to be established (see discussions by Cowen particularly in cases where there is zero net et al., 2003; Masselink et al., 2005). The direction of transport or shoreward net transport (i.e. the case the free stream pressure gradient in the swash is of of an equilibrium or an accreting beach, respec- fundamental importance in this regard. However, tively). To date, most swash sediment transport there are no direct measurements of instantaneous models are based on derivatives of the Energetics horizontal pressure gradients in the swash, although approach (Bagnold, 1966; Bailard, 1981), describing they may be derived from some limited water depth the bed load, suspended load or total load transport measurements (see Section 2 below). as a simple function of velocity, i.e., un or The present paper addresses this point and equilibrium models (Pritchard and Hogg, 2005). If presents field observations of the instantaneous friction factors and/or transport coefficeints are water surface slopes in the swash zone using a held constant for uprush and backwash, this novel technique. For free-surface flows with a invariably results in predictions of net offshore hydrostatic pressure distribution the surface slope transport as a result of the flow asymmetry in the is equivalent to the horizontal pressure gradient. swash (e.g. Masselink and Hughes, 1998; Puleo Furthermore, if shear stresses within the fluid are et al., 2000, 2001). This is not realistic, given the small, Euler’s equations apply and the horizontal stability of most beaches, and provides no mechan- pressure gradient is directly proportional to the ism for net shoreward transport and sediment total fluid acceleration (local plus convective, e.g. accretion on the upper beach. Dean and Dalrymple, 1991; see Section 2.2). The Recent modelling aproaches to address this issue novel measurement technique therefore avoids the have considered modifications to the bed shear significant complication of strong vertical gradients stress or particle stability by accounting for infiltra- in the flow velocity. Field observations are pre- tion and exfiltration effects (Turner and Masselink, sented from four different sites encompassing a 1998; Baldock et al., 2001; Butt et al., 2001), large range of beach slopes and swash conditions. modified descriptions for the friction factor or The results are presented in photographic form, ARTICLE IN PRESS 576 T.E. Baldock, M.G. Hughes / Continental Shelf Research 26 (2006) 574–588 which best illustrate the data, and in graphical form. Raubenheimer, 2002). The Peregrine–Williams so- They include water surface slopes from the inner lution predicts very brief periods of shoreward total surf zone, through bore collapse and uprush, and acceleration as the bore collapses, although they the end of the backwash. Section 2 reviews previous note that strictly the solution is not valid in this work and considers data and numerical model region. Only seaward total acceleration is predicted results relevant to the present study. Simple thereafter. The local acceleration is predicted to be relations are also derived from the swash solution seaward at all times (see Section 2.2 below). The of Peregrine and Williams (2001) to delimit regions numerical calculations of Hibberd and Peregrine of the swash with different flow characteristics and (1979) show similar results; for a uniform bore acceleration. Section 3 describes the methodology collapsing at the shore the local Eulerian velocity and field sites and the observations are presented reduces throughout the uprush, followed by an and discussed in Section 4. Final conclusions follow increasingly negative velocity (negative local accel- in Section 5. eration) throughout the backwash until the forma- tion of a backwash bore. The water surface dips 2. Previous work and governing equation seaward everywhere except during bore collapse and the formation of a backwash bore or shear wave 2.1. Flow characteristics (Peregrine, 1974). These analytical and numerical results are consis- Swash may be forced by non-breaking waves or tent with laboratory data that show a seaward broken waves (bores), with the resulting motion dipping water surface for most of the swash cycle described by two different solutions to the non- (Baldock and Holmes, 1997) and little evidence of linear shallow water equations (NLSWE). For non- positive (shoreward) local fluid accelerations (Petti breaking waves, typically standing long waves, the and Longo, 2001). Concurrently, field data obtained solution of Carrier and Greenspan (1958) predicts a with impellor current meters show a rapid increase to shoreward dipping water surface for short durations a maximum velocity just after inundation during the at the beginning and end of the swash cycle. While uprush, and a slower decrease toward zero velocity at standing long waves may be an energetic part of the the end of the backwash (e.g. Masselink and Hughes, total swash motion, in most practical cases the long 1998; Puleo et al., 2000, 2003). This has been waves co-exist with broken short waves, and interpreted as representing large onshore directed separating the two components in the swash is not accelerations at these phases of the swash cycle, with trivial (Baldock and Huntley, 2002). In any event, the local acceleration a surrogate for a pressure the long waves may themselves be breaking (Battjes gradient (Puleo et al., 2003). However, given that et al., 2004). The broken waves form bores in the impellor current meters must start from a stationary surf zone and collapse upon reaching a location situation, an apparent local acceleration will inher- with zero water depth, carrying turbulence and ently be recorded at the beginning of the uprush. In suspended sediment into the swash (Masselink and contrast, field data obtained by Acoustic Doppler Hughes, 1998). Velocimetry (ADV) show no onshore directed accel- Shen and Meyer (1963) presented an analytical erations in the swash provided that appropriate data solution to the NLSWE describing swash motion quality thresholds are applied and the velocity record following bore collapse. This has been extensively is correctly undefined when the sensor is out of the investigated under laboratory and field conditions water (e.g. Raubenheimer, 2002, Hughes and Bal- (Yeh et al., 1989; Hughes, 1992, 1995; Baldock and dock, 2004). It should be noted that measurements Holmes, 1997, 1999; Holland and Puleo, 2001, just seaward of the inner surf/swash boundary do Hughes and Baldock, 2004). Peregrine and Williams show the accelerations expected under non-breaking (2001) extended this solution to obtain the kine- or broken waves (e.g. Baldock and Holmes, 1997; matics over the full swash zone, with the same Raubenheimer, 2002; Raubenheimer et al., 2004). solution further extended by Pritchard and Hogg (2005) to calculate suspended sediment transport in 2.2. Theoretical description and momentum equation the swash. Numerical solutions of the NLSW equations (Hibberd and Peregrine, 1979; Kobayashi The Peregrine and Williams (2001) analytical et al., 1989) also provide a good description of bore swash solution provides a simple description of the driven swash (Raubenheimer and Guza, 1996; flow characteristics in the x–t plane. Their solution ARTICLE IN PRESS T.E. Baldock, M.G. Hughes / Continental Shelf Research 26 (2006) 574–588 577 gives the non-dimensional bed parallel velocity, prediction of only a small region of subcritical flow u(x,t)as and a predominantly supercritical backwash. In- deed, close to the seaward end of the swash, xE0, 2 ÀÁ uðx; tÞ¼ t t2 þ x , (1) the backwash becomes supercritical prior to the 3t time of maximum run-up. The supercritical nature where x is measured along the slope (we have of the backwash is of fundamental importance in retained their nomenclature despite the conflict with the discussions later. While the largest swash events the usual horizontal coordinate x). They illustrate the are typically forced by transient wave groups and locus of critical flow (u ¼ c,whereu is the flow consist of two or more uprushes in sequence velocity and c is the shallow water wave speed) (Baldock, 2006), the Peregrine and Williams (2001) during the uprush, given by the curve x ¼ 1=2t2,and solution is derived for a single swash event. It is thus where x and t are non-dimensional cross-shore not valid within the backwash bore or next incident distance (positive shoreward) and time, respectively bore, but this is outside the region of interest here, (Fig. 1). Further manipulation of the solution which is the time interval after bore collapse and provides the additional simple relationships for xX0: before the next incident bore passes the point of interest. Friction can be expected to modify 5t2 8t x ¼ for u ¼ c in the backwash; (2a) these results slightly, but the effects appear largely 2 confined to the run-up tip (Packwood and Pere- grine, 1981) and are not expected to significantly x ¼ t2 t for u ¼ 0 ðflow reversalÞ. (2b) alter the flow characteristics indicated in Fig. 1, These curves delimit different characteristic re- merely the exact value of the loci given by Eq. (2a gions of the swash flow, i.e. supercritical or and b). subcritical flow, uprush or backwash (Fig. 1). Shen The dimensional momentum (Navier–Stokes) and Meyer (1963) and Peregrine and Williams equation in the x direction (noting x is now defined (2001) is a particular solution for the swash flow. as horizontal) is While Guard and Baldock (2006) present general DU qp qt qt qt characteristics solutions for swash hydrodynamics, r ¼ rX þ xx þ yx þ zx , (3) Dt qx qx qy qz which show increases in depth and changes in the time of flow reversal compared to the analytical where r is the fluid density, U is the depth averaged solution above, the essential features of the swash horizontal flow velocity, X is the body force, p is the motion remain unchanged. It should be noted that pressure, t is the fluid shear stress, and y and z are the real flow would deviate to some extent from the transverse and vertical directions, respectively. these solutions, due to the singularity at the origin, Neglecting transverse flow, the total acceleration, the neglect of friction, and potential inaccuracies in DU/Dt, is the sum of the local (Eulerian) accelera- the predicted depth. However, it is not expected that tion, qU/qt,andtheconvectiveacceleration,UqU/qx. these differences will change the overall character- The body force, X,iszerointhex direction in this istics of the flow. Of particular interest here is the instance; gravity acts through the pressure gradient, qp/qx. Shear stresses may reduce the acceleration of fluid particles, particularly close to the bed toward the 2 end of the backwash when the flow becomes a fluid–sediment slurry (see Hughes, 1992; Raubenhei- 1.5 mer et al., 2004), i.e., the flow velocity observed at a ) − 1 supercritical point is dependent on the cumulative effects of (
x supercritical friction on the flow further upstream. However, in 0.5 the following, only the relationship between the pressure gradient and the flow acceleration is subcritical 0 considered, i.e. inviscid swash. Euler’s equation thus 0 0.5 1 1.5 2 2.5 3 3.5 4 applies, which for hydrostatic pressure is (c.f. Dean t ( − ) and Dalrymple, 1991): Fig. 1. Flow regions derived from the swash solution of DU qU qU 1 qp qZ Peregrine and Williams (2001). shoreline position, — ¼ þ U ¼ ¼ g (4) — u ¼ c (uprush), — — u ¼ 0, —— u ¼ c (backwash). Dt qt qx r qx qx ARTICLE IN PRESS 578 T.E. Baldock, M.G. Hughes / Continental Shelf Research 26 (2006) 574–588 and where Z is the water surface elevation with steep spillways at very high Reynolds numbers respect to an arbitrary horizontal datum. A positive (4108) or within turbulent boundary layers are pressure gradient, qp/qx or qZ/qx, corresponds to a assumed to still obey the hydrostatic law (e.g. water surface dipping downward in the negative Henderson, 1966; Stansby, 2003), at least over (seaward or offshore) x-direction. The dimensional length scales of order of the flow depth. While the horizontal velocity, U, and bed parallel velocity, u, fluid density may change in regions of high air differ by a constant scaling factor (see Peregrine and concentration, we are unaware of any data that Williams, 2001) and a factor cos y, where y is the indicates that this is likely to change the relationship bed slope. Since 1-cos y is negligible for most between the free surface slope and the pressure natural and artificial beach slopes, u and U are gradient in the fluid. Therefore, in the following, we effectively equivalent and the distance measured assume that the surface slope is a good direct along the slope is equal to that in the horizontal (see measure of the horizontal pressure gradient within Hibberd and Peregrine, 1979). Here Eq. (4) is used the main body of the flow. since it is more transparent than using a bed parallel Some additional relationships describing the flow coordinate system, and obtaining qZ/qx is straight- accelerations can be derived from the Peregrine and forward with the measurement technique described Williams (2001) swash solution, where all variables in Section 3 below. are again non-dimensional as in their paper: A fundamental assumption in this analysis is that qu 2 ÀÁ the pressure within the swash flow is hydrostatic. ¼ t2 þ x , (5) qt 3t2 The assumption of hydrostatic pressure in shallow free surface flows with minimal streamline curvature qu 2 ¼ , (6) has been conventional in the literature for over 100 qx 3t years. Since 1871, the Saint-Venant equations and their derivatives, particularly the non-linear shallow qu 4 u ¼ ðt t2 þ xÞ, (7) water equations, have been shown to accurately qx 9t2 describe the essential properties of a very large qu class of free surface flows with and without friction, x ¼ t2 t for u ¼ 0 (8) ranging from dam break flows (Ritter, 1892; qx Whitham, 1955) to non-breaking wave swash and following Pritchard and Hogg (2005), (Carrier and Greenspan, 1958), the propagation of x ¼ 2t 5t2 for Du=Dt ¼ 0. (9) bores (Stoker, 1957), bore-driven swash (Shen and Meyer, 1963; Peregrine and Williams, 2001), one- Shoreward of the point of bore collapse, x40, dimensional waves in channels (Lighthill, 1978) and Eq. (5) gives a negative (offshore) local acceleration tsunami run-up (Carrier et al., 2003). Similarly, at all times. The horizontal flow is also diverging at numerical models based on the hydrostatic assump- all times (Eq. (6)), leading to rapid thinning of the tion describe the essential features of the flow in swash (Hibberd and Peregrine, 1979; Larson and the surf and swash zones with a good degree Sunamura, 1993; Raubenheimer and Guza, 1996). of accuracy (e.g. Hibberd and Peregrine, 1979; Shoreward directed convective acceleration (Eq. (7)) Kobayashi et al. 1989; Watson and Peregrine, 1992; and total acceleration (Eq. (9)) occur close to the Raubenheimer et al., 1995; Raubenheimer, 2002; time of bore collapse as noted by Yeh et al. (1989) and many others). We are not aware of any data and Hughes and Baldock (2004), although the that directly demonstrates swash flows are hydro- solution may not be valid close to the singularity static or otherwise. However, recent laboratory at x ¼ t ¼ 0(Peregrine and Williams, 2001). Fig. 2 measurements (Petti and Longo, 2001; Cowen et illustrates the regions of shoreward and seaward al., 2003) showing that the velocity field is always accelerations in the x–t plane. It is interesting to primarily parallel to the bed suggests that the note that since qu/qx is always positive, the direction assumption is a practical one. Furthermore, friction of the convective acceleration (Eq. (8)) is always the effects are usually small and expected to predomi- same as the flow direction, in contrast to steady nantly influence the shape of the leading edge (e.g. wave motion. Furthermore, the convective accel- Whitham, 1955; Hogg and Pritchard, 2004). This is eration and local acceleration counterbalance each discussed further below with reference to the field other during the uprush, resulting in negative total observations. Highly turbulent flow flows down acceleration for nearly the whole swash event. ARTICLE IN PRESS T.E. Baldock, M.G. Hughes / Continental Shelf Research 26 (2006) 574–588 579
2 offshore). Furthermore, the backwash is nearly always a supercritical flow (Fig. 1), a condition 1.5 Du/Dt>0 readily determined from the flow depth and flow u∂u/∂x>0 u∂u/∂x<0
) velocity (e.g. Hughes et al., 1997b) or careful visual − 1 ( observation (see Section 4). x A fundamental tenet of ‘‘open channel’’ or free- 0.5 Du/Dt<0 Du/Dt<0 surface hydraulics is that supercritical flow is not 0 influenced by the downstream flow conditions 0 0.5 1 1.5 2 2.5 3 3.5 4 unless those conditions propagate upstream to, or t ( − ) occur at, the point of interest or measurement location (e.g. Daugherty and Franzini, 1965; Chan- Fig. 2. Regions of different flow acceleration derived from the son, 2004). Typical examples are hydraulic jumps swash solution of Peregrine and Williams (2001). The local or Eulerian acceleration, qu/qt is always negative. shoreline and fully developed bores; in neither case does the position, — — uqu=qx ¼ 0, —— Du=Dt ¼ 0. horizontal pressure gradient influence the flow upstream of the leading edge of the jump or bore. From Euler’s equation (Eq. (4)), the horizontal Therefore, deceleration of a supercritical backwash pressure gradient is expected to be negative (giving a by an adverse pressure gradient further downstream landward net pressure force) for only approximately is contrary to basic principles. Furthermore, if an 10% of the swash cycle, and then only in the region incident bore is fully developed, i.e. a positive surge close to the point of bore collapse. This is consistent or shock, then it will have no influence on the with the data of Baldock and Holmes (1997, 1999), upstream flow, even if that flow is subcritical. These Petti and Longo (2001) and the estimates of Hughes conditions are analogous to a tidal bore propagat- and Baldock (2004). Therefore, for most of the run- ing upstream, or a dam break into still water (e.g. up and the entire backwash the Peregrine and Chanson, 2004). Hence, neither subcritical nor Williams solution gives a seaward dipping water supercritical uprush/backwash flows will be influ- surface. These results are in marked contrast with enced by subsequent fully developed incident bores the estimates of local accelerations and horizontal until the bore reaches the measurement location. pressure gradients inferred from Eulerian velocity The horizontal forces on sediment particles arise and depth measurements by Puleo et al. (2003). from pressure gradients and drag forces (Nielsen, Puleo et al. (2003) presented data from the upper 1992, p. 98.). The pressure gradient force may be swash that they interpreted as showing large written in terms of total acceleration as in Eq. (4), shoreward directed local flow accelerations and but the local acceleration is frequently used in horizontal pressure gradients at the start and end of conjunction with an inertia or hydrodynamic mass the swash cycle, an idea originally presented by coefficient instead, since qu/qt is ‘‘easier’’ to measure Puleo and Holland (2001). The horizontal pressure with a current meter. If the particle is also gradient was stated to be onshore (corresponding to accelerating, the inertial force on the particle may a shoreward dipping water surface) during the entire be better described by using the slip velocity swash cycle. Hence, the mean inferred pressure (Nielsen, 1992, p. 167). The pressure force from gradient for that data must also be negative, the body of the flow is unchanged. Hence, in a corresponding to a mean water surface dipping in modified transport model of the form q ¼ unþ the landward direction. This is inconsistent with the f ðDu=DtÞ, the direction of the pressure gradient or widespread observation that the mean water surface flow acceleration is particularly important. For in the inner surf and swash always dips seaward, i.e. example, incorporating a pressure gradient or flow wave setup (Bowen et al., 1968, Longuet-Higgins, acceleration term acting in the wrong direction into 1983; Nielsen, 1988). Puleo and Holland (2001) and a sediment transport model of the form above Puleo et al. (2003) also argued that the backwash potentially leads to large errors, particularly as u-0, was opposed or decelerated by an adverse pressure i.e. transport in the wrong direction. Accounting for gradient arising from the fluid mass on the lower a pressure gradient acting in the wrong direction beach, or the next incident bore further offshore. may also lead to misleading results when con- This is difficult to reconcile with a backwash surface sidering the effects of friction on the shoreline dipping seaward in the same way as the beach motion. Consequently, given the significant differ- slope (as opposed to deeper water depths further ences between the flow accelerations and pressure ARTICLE IN PRESS 580 T.E. Baldock, M.G. Hughes / Continental Shelf Research 26 (2006) 574–588 gradients predicted by the analytical swash solution observation, still photography or video photogra- and previous work and those inferred by Puleo et al. phy is then sufficient to determine the direction of (2003), direct measurements of the water surface the instantaneous water surface slope and direction slopes and pressure gradients in the swash on of the pressure gradient in the swash. The mean natural beaches appear to be beneficial and these slope between two points can also be determined are reported below. from digitised data. In the field a series of 5 horizontal stringlines were 3. Field study stacked vertically at 5 cm intervals, although any number and spacing could be used as required. Each 3.1. Methodology stringline was 3 mm diameter orange cord, easily visualised in photographs or video records under a A novel but simple technique was developed to range of lighting and surf conditions. Thin (5 mm resolve instantaneous and spatial mean water sur- diameter) vertical rods were spaced along the face slopes (Fig. 3). In its simplest form a physical stringlines to provide a horizontal reference scale horizontal datum is set up on the beach by means of in photographs, with the stringline spacing provid- a taught stringline extending seaward from the ing a vertical scale. Image rectification is therefore beach face. The ends of the stringline can be levelled not required and no particular camera orientation is to within 71 mm over a distance of 5–20 m using necessary; best results are obtained looking long- conventional surveying techniques or a manometer shore, but in high energy swash photographs may tube. If the seaward end of the stringline is exposed be taken at an angle from further shoreward. There but covered further landward, then the water is no requirement to maintain the camera axis surface is dipping seaward, and vice versa. Visual horizontal unless horizontal lines are desired in the image. The vertical rods assist in defining the water surface at locations where the surface is below or Possible water surface between the stringlines. The rods also enable the Horizontal stringline speed of an incident bore or swash front to be determined from video records. In the present study the stringline spacers were placed at 5 m intervals, Possiblewater surface with vertical rods at 1–2 m intervals. The total Beach surface length of the stringlines varied from 20 m for mild beach gradients to 5 m for steep beach gradients. (a) Fig. 3(b) and photographs in Section 4 illustrate the Incidentbore Water surface Stringline stack complete arrangement. The method enables the instantaneous water surface to be determined to within 73mm at cross-shore locations separated by 5 m or more, resolving the mean gradient to within 70.001, or Beachsurface 1/20th–1/100th of typical beach gradients. In addi- Vertical rod tion, the water surface slope can be determined exactly to be either seaward or landward where the Star post and stringline water surface cuts a stringline—thus at these points spacer (b) no averaging over the horizontal is required. The technique is also applicable in the inner surf zone Fig. 3. (a) Schematic of stringline arrangement. Two possible and provides information on the steepness of the water surfaces are shown. The water surface slope and horizontal pressure gradient can be determined exactly to be either seaward front face of incident bores, together with the water or landward where the water surface cuts the stringline. surface slope either side of the bore. The stringlines (b) Typical stringline arrangement. Star post spacing 5 m, vertical can also be sunk within a trench so that they exit the rod spacing 1–2 m. Horizontal stringline spacing 5 cm. The water beach at different elevations. This enables an surface shown corresponds to a backwash flow and the next accurate assessment of the water surface slope at incident bore. Two or more 5 m sections are usually deployed, depending on the beach gradient and likely swash depths. The the uprush tip, allows for bed level changes, and is mean surface slope between vertical rods or star posts is easily necessary on steep beaches since the stringlines determined from a photograph or video image. rapidly reach a considerable elevation above the ARTICLE IN PRESS T.E. Baldock, M.G. Hughes / Continental Shelf Research 26 (2006) 574–588 581 bed. The lines may also be stepped down the beach indicative of both spilling and plunging breakers. to account for tidal water level variations. Numer- On the steeper beaches shore breaks frequently ical values of the surface elevation relative to any occurred at high tide. stringline and fixed horizontal coordinate are easily The stringlines were deployed on both rising and extracted from the images with standard image falling tides, with observations made from the inner analysis software or from hard copies. Water surf zone, through bore collapse and to the run-up surface elevations can be obtained with an accuracy tip on all beaches. Data are obtained from either better than the stringline thickness (3 mm) where the photographic or video records. The findings dis- surface cuts the line and to with an accuracy of cussed in Section 4 are based on over 1000 digital better than 5 mm where the vertical rods intersect photographs and over 3 h of video record, part of the surface. Horizontal coordinates are accurate to the latter digitised to give individual images at 0.2 s within 1–2 cm. Over shorter distance of order 1 m, intervals. In the upper swash, where the swash front the surface gradient can thus be obtained to within was moving relatively slowly, visual observation 70.01. Bubbles and splashes can obscure the ‘‘true’’ was sufficient to determine a landward or seaward water surface at certain points, but do not hinder dipping water surface slope. determining overall mean surface slopes. Multiple images are available to overcome this if necessary. It 4. Results is not necessary to determine the surface positions at locations other than where the surface intersects a The results are best described by photographs line or vertical rod, but the images show the overall illustrated in Figs. 4 and 5. These photographs were surface slope very clearly, even at the small scale selected on the basis of image quality as much as for presented here. the flow conditions they depict, and therefore are from still photographs. Although space limits the 3.2. Field sites number of images that can be presented here, the images shown are representative of the entire set of Field observations were made at four sites on the observations. Note that in panels 4(a), (b) and 5(a) Australian east coast: Ocean Beach, Umina, New the vertical rods were not equally spaced as they South Wales (NSW); Avoca Beach, NSW; Belongil were placed initially to assist in highlighting the Beach, NSW and Eagers Beach, Moreton Is., water surface, rather than to provide a reference Queensland. The field deployments encompass the scale. All stringlines were horizontal, even if they do period June–December 2004, with the data pre- not appear so in the images. While black and white sented here collected over 9 different days. For these images are shown in the printed version of the beaches, the beach gradient in the swash zone varied journal, colour versions with improved clarity are between 0.028 and 0.11 (Table 1). Surf zone beach given in the electronic version (i.e. ScienceDirect). profile gradients ranged from 0.025 to 0.04. Sedi- Panel 4(a) illustrates the water surface slope at the ment sizes varied between 0.22 and 0.53 mm. Off- commencement of collapse of a fully developed shore significant wave height over the different bore. It is of interest to note that the water surface deployments and measurement times ranged from slope behind the bore is very close to horizontal, 0.98 to 1.9 m, with peak wave periods between 6.2 suggesting that in the inner surf zone significant and 12.2 s. The surf similarity parameter (Battjes, total fluid acceleration is confined to the bore front 1974, based on offshore significant wave height and (see also panels 4(e) and 4(f)). This is important in surf zone gradient) ranged from 0.11 to 0.62, the context of sediment suspension and transport just prior to bore collapse. The red arrows highlight Table 1 short exposed lengths of the same stringline, Beach gradients and surf similarity parameter illustrating that the technique can provide a very accurate measure of the instantaneous free surface Field Site Surf zone Beach face Surf similarity, z gradient gradient profile over large distances. Panels 4(b–e) show backwash flows at the Belongil Beach 0.025 0.028 0.22 seaward end of the swash zone, together with Ocean Beach 0.043 0.068 0.62 the next incident bore. In panels 4(b), (d) and Avoca Beach 0.026 0.08–0.11 0.2–0.4 (e) the backwash is supercritical, whereas in panel Eagers Beach 0.014 0.05 0.11 4(c) it is subcritical. Supercritical flow can be ARTICLE IN PRESS 582 T.E. Baldock, M.G. Hughes / Continental Shelf Research 26 (2006) 574–588
Fig. 4. Instantaneous water surface slopes in the inner surf zone and lower swash zone. Arrows highlight short exposed lengths of the same horizontal stringline. (a) Inner surf zone and commencement of bore collapse, Belongil beach. (b) Incident bore and supercritical backwash flow, Belongil beach. (c) Incident bore and subcritical backwash flow, Ocean Beach. (d) Incident bore and supercritical backwash flow, Avoca Beach. (e) Incident bore and supercritical backwash flow, Eagers Beach. (f) Inner surf zone and bore collapse, Avoca Beach. identified by the fact that the vertical rods and star In all cases, including the subcritical backwash, the posts do not cause an upstream flow disturbance, water surface clearly dips seaward to the leading i.e. small disturbances cannot propagate upstream. edge of the next incident bore, i.e. the pressure ARTICLE IN PRESS T.E. Baldock, M.G. Hughes / Continental Shelf Research 26 (2006) 574–588 583
Fig. 5. Instantaneous water surface slopes in the swash zone. Arrows highlight short exposed lengths of the same horizontal stringline. (a) Uprush, lower swash, Belongil Beach. (b) Uprush, lower swash, Belongil Beach. (c) Uprush, mid-upper swash, Ocean Beach. (d) Uprush, lower swash, Avoca Beach. (e) Uprush, mid-lower swash, Eagers Beach. (f) Uprush, mid-lower swash, Eagers Beach. gradient is positive and the total acceleration results are consistent with the analytical swash negative. Observations at times of flow reversal solution and the basic characteristics of supercritical show that the incident bore similarly has no flow and shocks as discussed previously. At the end influence on almost stationary upstream flow. These of the backwash the water surface slope approaches ARTICLE IN PRESS 584 T.E. Baldock, M.G. Hughes / Continental Shelf Research 26 (2006) 574–588 the beach slope and remains seaward dipping until turbulence and secondary waves on the surface the water drains away or the arrival of the next (Fig. 6(b and d)). The leading edge dips shoreward incident bore. Panel 4(f) shows more detail during over a distance of about 0.5 m with a gradient of bore collapse; the water surface behind the bore front about 0.15. Friction leads to a convex or rounded is again close to horizontal, with the shoreward front, and from Whitham (1955), infinite negative dipping water surface limited to the leading edge (first gradients could occur at the intersection of the 0.5–1 m). It is also clear from this image that pressure water and beach face. In this region the pressure sensors are unlikely to give an accurate measure of gradient balances friction. For the dam break the surface gradient as a result of the intense solutions, the maximum velocity occurs at the tip turbulence and air entrainment. While the assump- and qu/qt and DU/Dt are zero or negative to leading tion of hydrostatic pressure may be violated in order behind the front (Whitham, 1955; Hogg and the bore front, in large part due to air entrainment, Pritchard, 2004). On steeper beaches, or in the mid- Figs. 4 (a and f) suggest the pressure gradient behind upper swash on milder slope beaches, the surface the bore front is very small. Strong surface gradients may dip seaward even at the leading edge (Fig. 6(c)). occur across the bore front as expected, but these The different shape of the swash tip during uprush have no influence on the backwash further up slope. and backwash may be relevant to improving The water surface slopes and pressure gradients ballistic swash models that incorporate friction at during uprush are illustrated in panels 5(a–f). The the tip (e.g. Hughes, 1995; Puleo and Holland, leading edge of the uprush is convex as noted by 2001). Baldock and Holmes (1997), rather than concave as Recent analytical solutions, as well as equilibrium given by the inviscid swash solution. This results in type sediment transport models, suggest that sus- a very small region of order 0.5 m behind the leading pended sediment concentrations (SSC) for fine- edge where shoreward slopes occur, and this is medium sands are maximum very close to the swash discussed in more detail below. In this region of the tipduringuprush(e.g.Pritchard and Hogg, 2005), flow the depth is typically less than 5–10 cm and the since that is where the flow velocity is greatest. flow exhibits the usual ‘‘frothy’’ nature at the tip. However, the predicted sediment flux peaks some way Close to the point of bore collapse, the shoreward behind the front as a result of limited flow depths in dipping slopes at the leading edge correspond to the tip region. Field data suggests the SSC peaks maximum negative pressure gradients of order further somewhat further behind the tip, of order 0.05–0.1 (Fig. 6). In contrast, in the middle and 0.5–2 s (e.g. Osborne and Rooker, 1999; Puleo et al., upper swash zone the water surface slope even at the 2003), but this may be partly related to instrument leading edge is frequently horizontal or seaward elevation and OBS response in the ‘‘frothy’’ tip. dipping (panels 5 (c and f)). Seaward of the leading Hence, the importance of the convex front in terms of edge the water surface oscillates about the horizon- sediment transport remains to be assessed, particu- tal due to small irregularities (see Fig. 6) or dips larly relative to the contribution from pre-suspended seaward for the remainder of the swash event. This sediment in the bore (Jackson et al., 2004; Pritchard is also the case in the lower swash. and Hogg, 2005; Alsina et al., 2005). Fig. 6 shows the above results in graphical form, Behind the leading edge, the instantaneous sur- where both the surface elevation and surface face gradient oscillates around zero in the lower-mid gradient have been derived directly from the images. swash, increasing to order b/2 near the run-up tip Positive gradients correspond to a seaward dipping on the steeper beaches. Indeed, of interest is how surface. The data are shown at points where the frequently the surface is nearly horizontal over surface intersects a stringline or vertical rod. While distances of up to 5 m, both behind the bore front resolution could clearly be improved with more lines (Fig. 4(a)), and in the swash (Fig. 5(a)), and and/or rods, it is more than adequate for the particularly on the milder sloping beaches. The purpose of determining the surface slopes. During surface gradient in the backwash ranges from order backwash, (Fig. 6(a)), the surface slope increases b/2 to b. These limits are physically sensible and seaward, approaching the beach gradient toward consistent with previous analytical and numerical the latter stages. The slope is positive until the toe of results (Hibberd and Peregrine, 1979; Peregrine and the incident bore. After bore collapse, in the lower Williams, 2001) and small-scale experimental data swash the surface slope behind the leading edge is (Baldock and Holmes, 1997). In the backwash, we almost zero, with small deviations due to residual have never observed the exact surface slope where ARTICLE IN PRESS T.E. Baldock, M.G. Hughes / Continental Shelf Research 26 (2006) 574–588 585
0 0.03
-0.02 0.025
-0.04 ) -
0.02 ( -0.06 0.015 -0.08
0.01 Gradient
Elevation (m) -0.1 -0.12 0.005 -0.14 0 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 (a) x (m)
0 0.15
-0.02 0.1 0.05 -0.04 0 -0.06 -0.05
-0.08 Gradient (-)
Elevation (m) -0.1 -0.1 -0.15 -0.12 -0.2 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 (b) x (m)
0 0.08 -0.02 -0.04 0.06 -0.06 0.04 -0.08 Gradient (-) Elevation (m) -0.1 0.02 -0.12 -0.14 0 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00 (c) x (m)
0 0.1
-0.01 0.05 -0.02 0 -0.03 -0.05 Gradient (-)
Elevation (m) -0.04
-0.05 -0.1
-0.06 -0.15 -2.00 -1.50 -1.00 -0.50 0.00 (d) x (m)
Fig. 6. Cross-shore variation in instantaneous free surface elevation and free surface gradient. —B—, surface elevation; & , surface gradient (rhs). (a) Supercritical backwash flow, Belongil beach (panel 4(b)). Most negative location corresponds to the toe of the incident bore. (b) Uprush, lower swash, Belongil Beach (panel 5(a)) (c) Uprush, mid-upper swash, Ocean Beach (panel 5(c)). (d) Uprush, mid-lower swash, Eagers Beach (panel 5(e)). ARTICLE IN PRESS 586 T.E. Baldock, M.G. Hughes / Continental Shelf Research 26 (2006) 574–588 the line cuts the surface to be negative, except Close to the location of bore collapse, shoreward during the formation of backwash shear waves (e.g. dipping water surface slopes (typically 0.05–0.1) Peregrine, 1974). occur over a small region (order 1–0.5 m) at the With the exception of the blunt or convex leading convex leading edge. In the middle and upper edge, the present observations clearly show the swash, the water surface slope at even the leading near-surface horizontal pressure gradient within the edge is frequently horizontal or seaward dipping. swash to be zero or positive everywhere at all times. Behind the leading edge region the water surface Hence, noting the caveats discussed above, from slope was observed to be horizontal or seaward Eq. (4), for all practical purposes, the total dipping at all times throughout the swash uprush. acceleration in the swash zone is therefore negative The water surface slope during the backwash was or offshore at all times. Again assuming hydrostatic observed to be always dipping seaward, approach- pressure, the observations show that at any fixed ing the beach slope, and remained seaward dipping point the boundary layer is predominantly subjected until a new uprush edge or incident bore passed any to an adverse pressure gradient during the uprush. particular cross-shore location of interest. In contrast, during the backwash the boundary The analytical swash solution is further illustrated layer is always subjected to a favourable pressure by some simple relationships describing the different gradient until the water drains away or the next flow characteristics of the swash and regions of incident bore arrives at that location. These results different flow acceleration in the x–t plane and these have significant implications for sediment transport are consistent with the present observations. Final- modelling in the inner surf and swash, since new ly, the observations show that the total fluid models now incorporate pressure gradient or accel- acceleration is predominantly negative or offshore eration terms directly (e.g. Teakle and Nielsen, throughout the swash. The swash boundary layer is 2003; Hsu and Hanes, 2004). The pressure gradients therefore subject to a weak adverse pressure are also relevant for calculating forces on immersed gradient during uprush and a stronger favourable bodies during long wave runup, where the inertia pressure gradient during the backwash. These force is again proportional to the pressure gradient, gradients may counter any influence from infiltra- not necessarily the local acceleration. Finally, the tion and exfiltration on the swash boundary layer. influence of the adverse and favourable pressure The observations have significant implications for gradients on the boundary layer during uprush and sediment transport modelling. backwash, respectively, may counter any effects of infiltration or exfiltration on the boundary layer, Acknowledgements although it must be noted that near the swash front the boundary layer is highly non-uniform. The authors gratefully acknowledge funding from 5. Conclusions the CRC for Sustainable Tourism, the Australian Research Council (Grant numbers: LX0454743 and A10009206) and University of Queensland staff Field observations of instantaneous water surface grants. We would like to thank all those who slopes in the swash zone have been presented, and participated during the field trips, particularly Felicia these are likely a very close approximation to the Weir and Dave Mitchell (University of Sydney). The horizontal pressure gradient. Observations were comments of the referees are appreciated for improv- made using a simple but novel technique, from ing the manuscript. Thanks to Matt Barnes for which the water surface slope can be determined exactly to be either seaward or shoreward dipping at extracting some of the digital data from the images. We are grateful to the EPA, QLD, and MHL, NSW certain locations. The method also provides data on for providing the offshore wave data. the instantaneous mean surface slope over distances from 1 to 10 m. Further, it may also be used to determine the water surface slopes either side of inner surf zone bores, together with the shape of the References bore roller and the instantaneous depth profile of Alsina, J.M., Baldock, T.E., Hughes, M.G., Weir, F., Sierra, J.P., the swash lens. Large-scale studies of dam break 2005. Sediment transport numerical modelling in the swash free-surface profiles is another potential use of the zone. To appear in Proceedings of Coastal Dynamics ‘05, technique. Barcelona, ASCE. ARTICLE IN PRESS T.E. Baldock, M.G. Hughes / Continental Shelf Research 26 (2006) 574–588 587
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