Forced Burgers Turbulence in 3-Dimensions
Abstract
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(
x
1
)ρ(
x
2
)>
behaves as
|
x
1
−
x
2
|
−
α
3
and in the universal region
α
3
=7/2
while in the non-universal region
α
3
=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 {\bf 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.