A Turbulence Closure Study of the Flow and Thermal Fields in the Ekman Layer

Abstract

We assess the performance of turbulence closures of varying degrees of sophistication in the prediction of the mean flow and the thermal fields in a neutrally-stratified Ekman layer. The Reynolds stresses that appear in the Reynolds-averaged momentum equations are determined using both eddy-viscosity and complete differential Reynolds-stress-transport closures. The results unexpectedly show that the assumption of an isotropic eddy viscosity inherent in eddy-viscosity closures does not preclude the attainment of accurate predictions in this flow. Regarding the Reynolds-stress transport closure, two alternative strategies are examined: one in which a high turbulence-Reynolds-number model is used in conjunction with a wall function to bridge over the viscous sublayer and the other in which a low turbulence-Reynolds-number model is used to carry out the computations through this layer directly to the surface. It is found that the wall-function approach, based on the assumption of the applicability of the universal logarithmic law-of-the-wall, yields predictions that are on par with the computationally more demanding alternative. Regarding the thermal field, the unknown turbulent heat fluxes are modelled (i) using the conventional Fourier's law with a constant turbulent Prandtl number of 0.85, (ii) by using an alternative algebraic closure that includes dependence on the gradients of mean velocities and on rotation, and (iii) by using a differential scalar-flux transport model. The outcome of these computations does not support the use of Fourier's law in this flow.