EULERIAN MEAN VELOCITIES UNDER NON-BREAKING WAVES ON HORIZONTAL BOTTOMS

Peter Nielsen, Zai-Jin You

Abstract


A model is presented for the Eulerian time-mean velocities in combined wave-current flows. The typical, measured profiles of weak currents are well modelled. This includes the "toe" of forward drift in the wave boundary layer and the very flat (as opposed to the parabolic shape of laminar models) current profile between the bottom boundary layer and the wave trough. The model relies on a local force balance like Longuet-Higgirts' (1953) diffusion solution rather than on advective influence from the end conditions. This seems justified by experiments, probably because a sufficient amount of turbulent diffusivity is present even for very weak currents. In its present form the model can only handle currents which are so weak that their influence on the wave motion is negligible. However, agreement with measurements of stronger currents can be obtained by modification of the wave Reynolds stress to account the influence of the current on the wave motion. Application to surf zone conditions also require modifications, but the essential structure of the model is globally applicable.

Keywords


mean velocity; Eulerian velocity; nonbreaking waves; horzontal bottom

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