Wave height variation across beaches of arbitrary profile

An intuitive expression for the spatial change in energy flux associated with waves breaking in the surf zone is developed. Using shallow water linear wave theory, analytical solutions for wave height transformation due to shoaling and breaking on a flat shelf, a plane slope, and an “equilibrium” beach profile are derived and then compared to laboratory data with favorable results. The effect of beach slope on wave decay is included explicitly, while wave steepness effects are included implicitly by specification of the incipient conditions. Set-down/set-up in the mean water level, bottom friction losses, and bottom profiles of arbitrary shape are introduced, and solutions are obtained numerically. The model is calibrated and verified using laboratory data with very good results for the wave decay but not so favorable results for set-up. A test run on a prototype scale profile containing two bar and trough systems demonstrates the model's ability to describe the shoaling, breaking, and wave re-forming process commonly observed in nature. Bottom friction is found to play a negligible role in wave decay in the surf zone when compared to shoaling and breaking.

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