Townsend's hypothesis, coherent structures and Monin-Obukhov similarity

Abstract

Townsend's hypothesis states that turbulence near a wall can be divided into an active part that transports momentum, and an inactive part that does not, and that these two kinds of turbulence do not interact. Active turbulence is generated by wind shear and has properties that scale on local parameters of the flow, while inactive turbulence is the product of energetic processes remote from the surface and scales on outer-layer parameters. Both kinds of motion can be observed in the atmospheric surface layer, so Monin-Obukhov similarity theory, which is framed in terms of local parameters only, can apply only to active motions. If Townsend's hypothesis were wrong, so that active and inactive motions do interact in some significant way, then transport processes near the ground would be sensitive to outer-layer parameters such as boundary-layer depth, and Monin-Obukhov theory would fail. Experimental results have shown that heat transport near the ground does depend on processes in the outer layer. We propose a mechanism for this whereby inactive motions initiate active, coherent ejection/sweep structures that carry much of the momentum and heat. We give the evidence that the inactive motions take the form of streak patterns of faster and slower air, and argue that these are induced by the pressure effects of large eddies passing overhead. The streak pattern includes regions where faster streams of air overtake and engulf slower-moving streaks. Transverse vortices form across the spines of the streaks at these places and some of them develop into horseshoe vortices. These horseshoe vortices grow rapidly and are rotated forward in the sheared flow so they soon contact the ground, squirting the air confined between the legs of the horseshoe vortex outwards as a forceful ejection. This model is consistent with a wide range of results from the field and laboratory experiments. Heat transport is significantly affected, so undermining the dimensional assumptions of Monin-Obukhov similarity theory.