The Mixing Efficiency of Stratified Turbulent Boundary Layers

The mixing efficiency observed in stratified turbulent boundary layers is considered within the framework of the Monin-Obukhov similarity theory. It is shown that the efficiency within the layer increases with distance from the boundary. Near the boundary, the efficiency is proportional to the distance from the boundary scaled with the Monin-Obukhov length. Far from the boundary, the efficiency relaxes to a value that depends on the overall thickness of the layer relative to the Monin-Obukhov layer. This value approaches 1/6 when the thickness is larger than 1/2 of the Monin-Obukhov length. The same analysis shows that the buoyancy Reynolds number cannot be used to unequivocally predict the efficiency. The 21/2 scaling between the efficiency and buoyancy Reynolds number that has been observed in field measurements and experiments is shown to depend on an extra dimensional scale and thus is not universal.