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

  • Author(s): Braun, L
  • Younis, BA
  • Weigand, B
  • et al.
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.

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