Models of intermittency in hydrodynamic turbulence

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 ∝‖s${\mathrm{\Vert }}^{\mathrm{-}1/2}$ exp(-const×‖s‖/〈${\mathit{s}}^2$ ${\mathrm{〉}}^{1/2}$) for large ‖s‖. 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 ∝‖ξ${\mathrm{\Vert }}^{\mathrm{-}1}$ exp(-const×‖ξ‖/〈${\xi }^2$ ${\mathrm{〉}}^{1/2}$) for large negative velocity gradient ξ.