Forced Burgers Turbulence in 3-Dimensions

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We investigate non-perturbative results of inviscid forced Burgers equation supplemented to continuity equation in three-dimensions. The exact two-point correlation function of density is calculated in three-dimensions. The two-point correlator <ρ(x₁) ρ(x₂)> behaves as | x₁ - x₂|⁻α³ and in the universal region α₃ = 7/2 while in the non-universal region α₃ = 3. In the non-universal region we drive a Kramers-Moyal 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 Urms enters in the PDF of velocity difference.