Hydrodynamics of surf and swash on natural beaches

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<k<1.5 and a mean value of k≅0.7. This varies significantly from the classical Shen and Meyer solution of the non-linear shallow water equations, which has a single swash boundary condition corresponding to k=0, and which therefore suggests that all swash are hydrodynamically similar. Consistent with the theory, k is shown not to correlate with horizontal swash excursion or swash period. It is shown, however, that k is affected by swash-swash interaction. The variation in inflow is expected to affect swash velocities, and therefore sediment transport rates in the swash zone. Links between the surf and swash zones on natural beaches are also investigated. Surf zone hydrodynamics are compared to swash flow asymmetry (k) on both a time-averaged and wave-by-wave basis. No correlations are observed between the surf and swash for the parameters selected on either time-scale investigated. The value of k is shown to correlate with the tidal water level on a beach with a strongly concave up profile, but not on a beach with a profile that is approximately planar, suggesting that the wave history effect in the surf zone can influence conditions in the swash zone. It is shown qualitatively that in some cases, the value of k is controlled by the duration of the inflow in the surf zone, while in other cases, k is controlled by swash interactions. This variation indicates that it is necessary to investigate surf and swash conditions together to gain a thorough understanding of the processes that occur. Given the observed influence of swash-swash interaction on swash behaviour, it is clear that accurate modelling of the swash zone will require a more detailed understanding of swash-swash interaction. This is an area of study that needs further attention.