Length scales, subgrid TKE models, and the representation of the stable boundary layer

Large-eddy simulations of the stable boundary layer quickly suffer from a lack of resolved motions, even for a relatively fine grid resolution. In this case the results become almost fully determined by the subfilter-scale (SFS) turbulent kinetic energy (TKE) model, with the shear, buoyancy and viscous dissipation dominating the SFS-TKE budget. This implies that a prognostic SFS-TKE equation behaves approximately as a classical Smagorinsky model including a buoyancy flux. The SFS-TKE dominated simulations show a strong sensitivity of the turbulent mixing to the grid resolution. The analytical solutions for the turbulent mixing functions derived from the Smagorinsky model are compared with observed Monin-Obukhov (MO) similarity theory relations. This allows to derive the critical conditions for which the SFS-TKE scheme will produce spurious mixing. A constant and a stability dependent length scale are considered, with LD = (DxDyDz)^1/3 related to the grid sizes in the three directions, and L_dd depending on the Brunt-Vaisaila frequency and the TKE. Because for both length scales the eddy viscosity is proportional to LD^2 , the intensity of subfilter mixing will increase for increasing grid resolution. The findings are also relevant for high-resolution numerical weather prediction models that use a Smagorinsky type of TKE closure.