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(x + r, t ) - f(x, t')](2) proportional to r(xi)delta(t - t') is considered on t he interval 0 < x < L. The properties of the probability density funct ion of velocity differences P(Delta u, r) are investigated for the thr ee cases xi = {0; 1/2; 2}. It is shown that the tail of the probabilit y density function in the interval Delta u/r(z) much less than -1; \De lta u\ much less than u(rms) and r much less than L is accurately desc ribed by the asymptotic algebraic relation P(Delta u, r) proportional to r/(Delta u)(gamma) with gamma = 1 + 1/z, where z = (xi + 1)/3. A de tailed numerical investigation, performed in this work, supports this result.