Large-eddy simulations of stratified plane Couette flow using the anisotropic minimum-dissipation model

Abstract

The anisotropic minimum-dissipation (AMD) model for large-eddy simulation (LES) has been recently developed, and here the model performance is examined in strat- ified plane Couette flow. To our knowledge this is the first use of the AMD model for resolved LES of stratified wall-bounded flow. A comparison with previously pub- lished direct numerical simulations (DNS) provides insight into model and grid re- quirements. Prandtl numbers of P r = 0.7 − 70 and a range of Richardson numbers show that the AMD LES performs well even with a strong stabilising buoyancy flux. We identify three new requirements for accurate LES of stratified wall-bounded flow. First, the LES must resolve the turbulent structures at the edge of the viscous sublayer in order to satisfy the Obukov length scale condition, L+s > 200. Other- wise the LES solution may laminarise where the DNS solution remains turbulent. Second, the LES must have enough vertical grid resolution within the viscous and diffusive sublayers to resolve the wall fluxes. Third, the grid must be reasonably isotropic (vertical-to-horizontal grid aspect ratio > 0.25) at the edge of the sublayer and through the turbulent interior for the AMD LES to correctly simulate the scalar flux. When these model requirements are fulfilled the AMD LES performs very well, producing vertical mean profiles, friction Reynolds number and Nusselt number con- sistent with DNS solutions at significantly higher grid resolution.