On extension of Malkus' theory of turbulence to stably stratified shear flow

Malkus' theory of turbulent shear flow and turbulent convection is extended to stably stratified shear flow. The local Richardson number is found to be close to its critical value throughout the turbulent flow. Assuming a strong interaction between velocity and density fields requires that their profiles depend linearly on height. From this, for stratified shear flow at sufficiently high Reynolds numbers, a combination of logarithmic and linear profiles is expected. The purely linear and the log-linear profile are both observed in laboratory channel flow and in atmospheric boundary layer flow.