Algebraic Tails of Probability Density Functions in the Random-Force-Driven Burgers Turbulence.

The dynamics of velocity fluctuations governed by the Burgers equation, driven by the white-in-time random forcing function with f fsx 1 r , td 2 fsx, t0dg2 ~ rdst 2 t0d is considered on the interval 0 , x , L. The properties of the probability density function of velocity differences PsDu, rd are investigated for the three cases j ­ h0; 1y2; 2j. It is shown that the tail of the probability density function in the interval Duyrz ø 21; jDuj ø urms and r ø L is accurately described by the asymptotic algebraic relation P sDu, rd ~ rysDud with g ­ 1 1 1yz, where z ­ sj 1 1dy3. A detailed numerical investigation, performed in this work, supports this result. [S0031-9007(96)01384-1]