Wave runup and overwash on a prototype-scale sand barrier
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Swash
Overwash
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The nonlinear shallow water equations can be used to model broken waves within the surf and swash zone. Here we detail the development of several numerical schemes that have been taken from gas dynamics and adapted for use in the surf zone. The numerical schemes can be applied in one or two horizontal dimensions, they have the advantage over shallow water models used at present that they are faster and more accurate.
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A numerical model based on a high order non-oscillatory MacCormack TVD scheme is presented for the solution of the non-linear Saint Venant equations in surf and swash zones. A comparison with measurements of surface elevations on a beach (True Vert Beach, France), shows that the model is capable of predicting accurately the transformation of irregular waves in the surf zone.
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New field observations of sediment overwash on a natural beach are presented and compared to predictions from a process based hydrodynamic and swash sediment transport model. The observations were made at an intermittently closed and open lake or lagoon (ICOLL) and show rapid vertical growth of an initially low beach berm as a result of swash overtopping and sediment overwash. Total sediment overwash volumes passing the crest of the beach for a series of high tide overtopping events were obtained from survey data over a period of 12 days either side of spring tides. A process based model for monochromatic swash is extended to random wave conditions through robust parameterisations of wave runup, wave runup distributions and sediment transport and is applied to predict the total overwash transport. This approach avoids the requirement for a surf zone transformation model to obtain nearshore bore heights. The sediment transport calculations use independently determined friction factors from both field and laboratory studies. Predicted sediment transport overwash rates are well correlated with the measurements (r2=0.93), and agree with observed tidal and cumulative overwash rates to within about 20%. The model has applications over a wide range of beach and wave conditions and represents a first step in modelling the growth and recovery of natural beach berms.
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Coastal engineering
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The hydrodynamics of surf and swash on natural beaches are presented. Wave height evolution in the surf zone is investigated with data from ten predominantly swell dominated, micro-tidal, sandy beaches. Wave height evolution is presented in terms of wave height-to-water depth ratios (γ=H/h), and both a conventional time-averaged analysis (γrms) and a new wave-by-wave analysis (γw) are performed. Data clearly show unsaturated surf conditions are typical for these beaches, with γ values increasing with increasing offshore wave height (Ho). Values of γ increased slowly in the deeper water depths of the surf zone and increased rapidly in the shallower water depths, with the change in the rate of increase of γ occurring at h/Ho=0.5. No dependence of γ on either absolute or relative beach slope was observed. The skewness of the distributions of γw is consistent with waves that are not depth limited. For the observed unsaturated surf, the terminal bore height at the shoreline is shown to be approximated by Hb≅0.12Ho. Two wave height transformation models are investigated: a monochromatic model and a random wave model. Two different wave transformation regimes are observed in the monochromatic wave model results: a regime termed over-dissipative with concave up wave height transformation curves following breaking and a regime termed under-dissipative with concave down wave height transformation curves following breaking. The boundary between these two regimes has constant γ values immediately following breaking, which is characteristic of saturated and depth limited surf. A relative beach slope parameter, βγ, is derived to distinguish between these regimes. This can also be regarded as a new surf similarity parameter that has a different power relationship for wave steepness when compared to the conventional parameter. In all monochromatic model results, however, values of γ are shown to increase rapidly in the shallow water depths of the surf zone, and in no cases is a constant value of γ observed close to the shoreline. In comparison, the random wave model predicts only under-dissipative conditions, with γ values always increasing shoreward. For all model-data comparisons, the value of the model fitting parameter, B, needs to be increased to obtain more accurate model predictions, indicating that the basic model assumptions do not generate sufficient dissipation to accurately model surf in the laboratory or on natural beaches. The distributions of observed wave heights are compared to theoretical Rayleigh and normal distributions and found to be more normally distributed. The observed wave height distribution is also found to become narrower as depth decreases. The kinematics of the swash zone are investigated using optical remote sensing techniques to examine the flow asymmetry at the surf-swash boundary. This is examined in relation to new solutions to the non-linear shallow water equations where the flow asymmetry is parameterised using a variable, k, that represents the relative duration of inflow into the swash zone. For natural swash it is shown that there is significant variability in k, with a range of -1
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The wave characteristics affecting coastal sediment transport include wave height, wave period and breaking wave direction. Wave height is a critical factor in determining the amount of sediment transport in the coastal area. The force of sediment transport is much more intense under breaking waves than under non-breaking waves. Breaking waves exhibit various patterns, principally depending on the incident wave steepness and the beach slope. Based on the equations of conservation of mass, momentum and energy, a theoretical model for wave deformation in and outside the surf zone was obtained, which is used to calculate the wave shoaling, wave set-up and setdown and wave height distributions in and outside the surf zone. The analysis and comparison were made about the breaking point location and the wave height decay caused by the wave breaking and the bottom friction. Flume experiments relating to the spilling wave height distribution across the surf zone were conducted to verify the theoretical model. Advanced wave maker, data sampling devices and data processing system were utilized in the flume experiments with a slope covered by sands of different diameters to facilitate the observation and research on the wave transformation and breaking. The agreement between the theoretical and experimental results is good.
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A detailed understanding of the behaviour of waves in the nearshore is essential for coastal engineers as these waves cause beach erosion, coastal flooding and damage to coastal structures. Significantly, the influence of reflected waves is often neglected in surf zone studies, although they are known to influence wave properties and circulation in the nearshore. In this paper, a phase-resolving model is rigorously applied to model conditions from the prototype-scale BARDEXII experiment in order to examine and assess the influence of swash-based reflection on surf zone hydrodynamics at both the individual wave and time-averaged timescales. Surface elevation is separated into incoming and outgoing signals using the Radon Transform and a crest tracking algorithm is used to extract incident and reflected wave properties. It is found that on steep beaches (tanβ>1:9) the swash-based reflection - the reflection generated in the swash during the backwash - contributes significantly to the intrawave variability of individual wave properties such as the wave height to water depth ratio γ, through the generation of quasi-nodes/antinodes system. For γ expressed with individual wave heights, variations up to 25% and 40% are obtained for the modelled regular and irregular wave tests, whereas it reaches 15% when it is based on the significant wave height. The outgoing wave field-induced hydrodynamics is also found to affect time-averaged parameters: undertow and horizontal velocity skewness. The undertow is mainly strengthened, particularly in the shoaling region where the outgoing component dominates over the contribution from the incoming wave field. Offshore of the bar, an onshore-directed flow streaming close to the bed is also generated under the outgoing wave field, and is suspected to help in stabilising the bar position. This, along with the influence of the outgoing wave field on the horizontal velocity skewness and the presence of quasi-standing waves, suggests a complex contribution of the hydrodynamics induced by swash-based reflection into sediment transport rates and nearshore bar generation/migration.
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