Three-dimensional modelling of coastal circulations with different k– ε closures

Abstract

The actual tendency in 3D turbulent closure models for stratified shallow water flows is to come back to closure models with two transport equations for turbulent variables or to algebraic flux models. We retain the simpler k– ε closure model. For a simplified coastal upwelling circulation, we studied the relevance of the isotropic eddy viscosity assumption of the standard k–ε model for stratified and shallow-water flows submitted to the Coriolis force with two corrected k–ε models: STRAT–COR and ASPECT. We considered two mean sources of coastal turbulence production: the surface current shear generated by wind and the bottom shear. In order to understand the processes involved, we have modelled academic configurations such as constant depth ones or one-dimensional vertical problems. For a simplified coastal upwelling circulation, we have studied the pertinence of the isotropic eddy viscosity assumption of the standard k–ε model for stratified and shallow-water flows submitted to the Coriolis force. In order to take into account those non-isotropic behaviour of turbulence, we have used two corrected k–ε models: STRAT–COR and ASPECT. But, the mean deficiency of this model is the isotropic eddy viscosity assumption. In order to take into account the non-isotropic behaviour of turbulence due to buoyancy and Coriolis forces, a hybrid turbulence model (STRAT–COR) combining the standard k– ε and algebraic Reynolds stress models, is used. For shallow-water flows ( δ=( L)/( H)≫1) two eddies length scales can be pointed out: L for the large horizontal structures and H for the smaller but 3D ones. These effects are represented by a correction to the standard k– ε model, based on the separation of two turbulence scales, respectively associated to L and H. We focus our study onto two main sources of turbulent oceanic energy: the surface current shear induced by wind and the bottom stress due to tidal circulation. The k– ε closure model corrected to account for non-isotropic effects is used to model idealised wind-driven stratified coastal flows such as coastal upwelling. Parameterization of such a model is discussed for basic barotropic and baroclinic coastal flows as induced by tides, wind, stratification or a combination of them. Numerical experiments show that for upwelling and tidal coastal flows, the aspect effect is dramatically dominant when stratification and Coriolis non-isotropic corrections, weakly affect the solution.