Application of roughness-dependent boundary conditions to turbulent oscillatory flows

Abstract

Abstract The purpose of this paper is to model wave-induced oscillatory flows traversing rough beds using high-Reynolds number turbulence models based on boundary conditions that are sensitized to the local state of bed roughness (be it hydraulically smooth, transitional, or fully rough). Such boundary conditions replace more traditional approaches (based on a no-slip velocity condition), which are, hitherto, most commonly applied to the majority of oceanographic and estuarine calculations. Both eddy-viscosity and differential second-moment (DSM) closures are implemented and compared with experimental data. It is shown that the linear length scale used in the eddy-viscosity k- l model will lead to serious errors. This paper should, therefore, convey the message to coastal and marine engineers that, eddy-viscosity models, such as the k- l model, that are still employed in the vast majority of coastal engineering simulations and are used to calculate parameterized flow coefficients used in large-scale three-dimensional hydrodynamic codes, such as those for predicting internal tides and sediment transport, should be replaced by advanced turbulence transport models. The other aim of this paper is to show how near-bed predictions of turbulent kinetic energy profiles on rough boundary layers, whose roughness is related to Nikuradse sand grains, can be improved. It is demonstrated that when wall-function boundary conditions (sensitized to the bed roughness) are used, in favour of a more traditional non-slip velocity strategy, a better agreement with experimental data is achieved.