EDDY VISCOSITY MODELS FOR WAVE BOUNDARY LAYERS

Ole Secher Madsen, Paulo Salles

Abstract


Motivated by recent experimental results on wave, current and combined wave-current flows over an artificially rippled bed, the boundary resistance experienced by waves over two-dimensional bottom roughness elements is formulated in terms of a drag law. The resulting empirical relationship for the drag coefficient suggests a flow resistance that is similar in nature to one obtained from a constant, pseudo-laminar eddy viscosity model for the wave boundary layer flow. Analysis of available experimental data on energy dissipation for oscillatory flow over movable rippled beds leads to a constant eddy viscosity model for wave boundary layers above naturally rippled beds. The constant eddy viscosity model is modified to include a near-bottom linear transition to make it zero at the bed. This hybrid eddy viscosity model is shown to capture the essential features of wave boundary layer flows for the full range of bottom roughnesses encountered, i.e. from sand grains to ripples. Application of the hybrid model requires knowledge of the equivalent bottom roughness for which empirical expressions are derived. The implication of the results, obtained here for waves, for combined wavecurrent boundary layer flows suggests modifications of the Grant-Madsen model that greatly improve this model's ability to predict observed current velocity profiles over rippled bottoms in the presence of waves.

Keywords


boundary layer; eddy; eddy viscosity; viscosity model

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