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Paper   IPM / Physic / 7163
School of Physics
  Title:   Universal and Non-Universal PDF's of the Forced Burgers Turbulence in 3-Dimensions
1.  J. Davoudi
2.  A.R. Rastegar
3.  M.R. Rahimi Tabar
  Status:   Preprint
  No.:  0
  Year:  1999
  Supported by:  IPM
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 |x1x2|−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.

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