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Field Observations of Instantaneous Water Slopes and Horizontal Pressure Gradients in the Swash-Zone

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Field Observations of Instantaneous Water Slopes and Horizontal Pressure Gradients in the Swash-Zone 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 À1/100th 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.
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