Simulation of Ekman Boundary Layers by Large Eddy Model with Dynamic Mixed Subfilter Closure

Abstract

Theoretical analysis of boundary layer turbulence has suggested a feasibility of sufficiently accurate turbulence resolving simulations at relatively coarse meshes. However, large eddy simulation (LES) codes, which employ traditional eddy-viscosity turbulence closures, fail to provide adequate turbulence statistics at coarse meshes especially within a surface layer. Manual tuning of parameters in these turbulence closures may correct low order turbulence statistics but severely harms spectra of turbulence kinetic energy (TKE). For more than decade, engineering LES codes successfully employ dynamic turbulence closures. A dynamic Smagorinsky turbulence closure (DSM) has been already tried in environmental LES. The DSM is able to provide adequate turbulence statistics at coarse meshes but it is not completely consistent with the LES equations. This paper investigates applicability of an advanced dynamic mixed turbulence closure (DMM) to simulations of Ekman boundary layers of high Reynolds number flows. The DMM differs from the DSM by explicit calculation of the Leonard term in the turbulence stress tensor. The Horizontal Array Turbulence Study (HATS) field program has revealed that the Leonard term is indeed an important component of the real turbulence stress tensor. This paper presents validation of a new LES code LESNIC. The study shows that the LES code with the DMM provides rather accurate low order turbulence statistics and the TKE spectra at very coarse meshes. These coarse LES maintain more energetic small scale fluctuations of velocity especially within the surface layer. This is critically important for success of simulations. Accurate representation of higher order turbulence statistics, however, requires essentially better LES resolution. The study also shows that LES of the Ekman boundary layer cannot be directly compared with conventionally neutral atmospheric boundary layers. The depth of the boundary layer is an important scaling parameter for turbulence statistics.