Turbulence without pressure in d dimensions

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Abstract
The randomly driven Navier-Stokes equation without pressure in d-dimensional space is considered as a model of strong turbulence in a compressible fluid. We derive a closed equation for the velocity-gradient probability density function. We find the asymptotics of this function for the case of the gradient velocity field (Burgers turbulence), and provide a numerical solution for the two-dimensional case. Application of these results to the velocity-difference probability density function is discussed.

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