The critical condition for the maintenance of turbulence in stratified flows

Theoretical models for predicting the critical Richardson number for the maintenance of turbulence in a stratified atmosphere are re-examined in the light of recent observations. It is proposed that the critical condition may first arise from the failure of the maintenance of steady shear in the presence of buoyancy forces. An expression for the critical flux Richardson number is derived from the consideration of the equations of Reynolds stress and turbulent energy. This gives a range of 0.15 – 0.25 for Rfer, in agreement with the results of direct observations.