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Paper IPM / Physic / 7163  


Abstract:  
We investigate nonperturbative results of inviscid forced Burgers equation supplemented to continuity equation in threedimensions. The exact twopoint correlation function of density is calculated in threedimensions. The twopoint correlator < ρ(x_{1}) ρ(x_{2}) > behaves as x_{1} − x_{2}^{−α3} and in the universal region α_{3} = 7/2 while in the nonuniversal region α_{3} = 3. In the nonuniversal region we drive a KramersMoyal equation governing the evolution of the probability density function (PDF) of longitudinal velocity increments for three dimensional Burgers turbulence. In this region we prove Yakhot's conjecture [Phys. Rev. E 57, 1737 (1998)] for the equation of PDF for three dimensional Burgers turbulence. We also derive the intermittency exponents for the longitudinal structure functions and show that in the inertial regime one point U_{rms} enters in the PDF of velocity difference.
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