A Similarity Model of Subfilter-Scale Energy for Large-Eddy Simulations of the Atmospheric Boundary Layer

A scale-similarity model to estimate the subfilter-scale energy using the trace of the Leonard stress tensor is proposed and evaluated for large-eddy simulations of the atmospheric boundary layer (ABL). The model is derived from a stability-dependent model of the energy spectrum in the ABL, which accounts for the effects of buoyancy and mean shear as a function of z/L, the Monin–Obukhov stability variable. An a priori test using ABL turbulence data demonstrates that the model has accurate performance for dimensionless filter widths of Δ/z = 2, 1, and 0.5 for stabilities of −1 ≤ z/L ≤ 0.5, and improves considerably upon a similar model that is derived using an infinite κ −5/3 spectrum. This improvement is especially significant in the first several grid points near the surface in large-eddy simulations of the ABL, where Δ/z is necessarily large. The modelling procedure is then extended to develop a similarity model for the subfilter-scale scalar variance; it is shown to have robust performance for temperature.