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A heurisitic model for evolution of the probability distribution (PDF) of transverse velocity gradient s in incompressible Navier-Stokes turbulence is distilled from an analytical closure for Burgers turbulence. At all Reynolds number scrR, the evolved PDF is ^-1/2 exp (-const/〈s^2〉^1/2) for large. The model suggests that skewness and flatnesses are asymptotically independent of scrR, and that cascade to smaller scales is not a fractal process. For Burgers dynamics, both simulations and the analytical closure give a PDF ^-1 exp (-const/〈^2〉^1/2) for large negative velocity gradient.
Robert H. Kraichnan (Mon,) studied this question.