SIMPLE MODELS FOR EQUILIBRIUM PROFILES UNDER BREAKING AND NON-BREAKING WAVES

Abstract

Simple theoretical models are presented to calculate the equilibrium profile shape under breaking and non-breaking waves. For the case of breaking waves the seaward transport in the undertow at equilibrium is locally balanced by a net vertical sedimentation so that no bottom changes occur. The parameterization of the water and sediment flux in the surfzone yields a power curve for the equilibrium profile with a power of 2/3. Three different models are developed to derive the profile shape under non-breaking waves, namely (]) a variational formulation where the wave energy dissipation in the bottom boundary layer is minimized over the part of the profile affected by non-breaking waves, (2) an integration of a small-scale sediment transport formula over a wave period where the slope conditions that yield zero net transport determine equilibrium, and (3) a conceptual formulation of mechanisms for onshore and offshore sediment transport where a balance between the mechanisms defines equilibrium conditions. All three models produce equilibrium profile shapes of power type with the power typically in the range 0.15-0.30. Comparisons with laboratory and field data support the results obtained indicating different powers for the equilibrium profile shape in the surfzone and offshore zone.