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

Turbulence intensities in the outer part of the atmospheric boundary layer are typically much higher than in outer parts of laboratory flows. As a result, experiments in the atmospheric surface layer (ASL) can provide a strong test of the common assumption that ‘active’ (flux-carrying) turbulence processes in the inner part of turbulent boundary layers are independent of any larger-scale 'inactive' motions that derive from turbulence in the outer part of the boundary layer. This principle is known as Townsend’s hypothesis. It is implicit in the law of the wall in engineering, and Monin-Obukhov similarity theory in atmospheric modelling.

Scalar spectra and cospectra from the ASL show that large-scale motions that scale on outer-layer parameters do interact with ‘active’ motions that scale on inner-layer parameters. It is proposed that this is so because outer-layer motions control the areal pattern of surface wind velocities, and because coherent structures are triggered where strong local convergence of the surface wind intensifies local shear stress. The locations and sizes of coherent turbulent structures, which carry most of the flux, are thereby controlled by outer-layer motions. This case is supported by drawing on results from wall-bounded shear flows in both the ASL and the laboratory. Such flows have many similarities despite great differences in Reynolds numbers and roughness of the walls. We conclude that transport processes in the ASL depend on the outer-layer scales, that Townsend’s hypothesis fails and therefore that Monin-Obukhov similarity theory is flawed.