Thin shear layers – The key to turbulence structure?

Sharply sheared interfaces determine the structure of turbulent motions both on large and small scales, as recent experiments and simulations have demonstrated. Shear layers form along contours defined by very large gradients in turbulence intensity and/or large gradients in the large scale velocity field. Inhomogeneous eddy motions adjacent to these layers stretch and distort the larger scale vorticity so as to counter the tendency of the interface to thicken by small scale eddy diffusion.These concepts are applied to the structure of high Reynolds number turbulence by focusing on the dynamics of the flow within and near the shear layers that are observed to exist between large eddies. The numerical simulations of Ishihara et al. (2009) show that on the edges of the layers and in their interiors thin viscous layers form, with thickness approximately equal to the Taylor microscale. Intermittent small-scale vortices within these viscous layers are stretched and amplified, as their thickness reduces to a limiting value determined by viscous diffusion, which is equal to the Kolmogorov micro length scale. But the root-mean -square values of vorticity and velocity, and also their flatness factors, are given by statistical averaging across these layers, taking into account the degree to which the thin layers are sufficiently convoluted to be ‘space-filling’. Through the blocking of the external scale eddies outside the layers as they impinge onto the interfaces, upscale and downscale energy transfer processes which are of comparable magnitude lead to distorted inertial-range motions with a wide range of length scales and characteristic self-similar power-law spectra. Here the skewness of the velocity derivatives becomes negative. The upscale motions are essential for maintaining the large structures and the thin shear layers between them, as two-dimensional experiments demonstrate. A significant implication of this ‘interface dynamics’ mechanism is that small scale turbulence is produced as much by larger eddy structures, as by interactions between progressively smaller, and more numerous, self-similar eddies – the ‘cascade’ mechanism proposed by L.F. Richardson. The latter mechanism, which is dynamically equivalent to the Kolmogorov–Obukhov statistical-physics models for homogeneously distributed fluctuations, implies that turbulence structure evolves more slowly than is observed. By contrast the model presented here for the statistics and dynamics of high Reynolds number turbulence is based on a quasi-deterministic zonal analysis within and adjacent to intermittently distributed thin shear layers, which occupy a finite fraction of the flow and cause the eddy motions to have different ranges of length scales in separate parts of the local flow fields. The structure does not change qualitatively as the Reynolds number varies, but is significantly changed if the turbulence is forced at small as well as large scales.