We exploit Monin–Obukhov similarity theory and Townsend’s attached-eddy hypothesis and arrive at a logarithmic-linear law for the streamwise velocity variance in the surface layer of stably stratified boundary layers. To test the logarithmic-linear law, we conduct large-eddy simulations (LES) of stably stratified turbulent boundary layers at various stratification conditions. The LES results give strong support to the scaling, and the logarithmic-linear law is found to be valid in the wake layer (i.e., outside the surface layer) of strongly stratified boundary layers. A detailed analysis shows that this is because stable thermal stratification suppresses the large-scale detached eddies in the wake layer.
