A note on similarity theory for atmospheric boundary layers in the presence of background stable stratification

Simple but rather general arguments permit the construction of a new version of similarity theory for turbulent boundary layers in stratified rotating fluid. The failure of the Ekman boundary layer model in the presence of imposed background stable stratification is explained by introducing the scaling length L_N = u_*/N, where u_* is the friction velocity and N the buoyancy frequency, which is chosen to characterize the background stratification (can also be considered as initial stratification). The expressions for the maximum height of turbulent boundary layer under different external conditions are derived and compared with observations. Also some remarks are made on resistance laws for stratified boundary layers.