Universal Statistics of Inviscid Burgers Turbulence in Arbitrary Dimensions

Abstract

We investigate the non-perturbative results of multi-dimensional forced Burgers equation coupled to the continuity equation. In the inviscid limit, we derive the exact exponents of two-point density correlation functions in the universal region in arbitrary dimensions. We then find the universal generating function and the tails of the probability density function (PDF) for the longitudinal velocity difference. Our results exhibit that in the inviscid limit, density fluctuations affect the master equation of the generating function in such a way that we can get a positive PDF with the well-known exponential tail. The exponent of the algebraic tail is derived to be -5/2 in any dimension. Finally we observe that various forcing spectrums do not alter the power law behaviour of the algebraic tail in these dimensions, due to a relation between forcing correlator exponent and the exponent of the two-point density correlation function.