KOLMOGOROV TURBULENCE IN A RANDOM-FORCE-DRIVEN BURGERS-EQUATION - ANOMALOUS SCALING AND PROBABILITY DENSITY-FUNCTIONS

High-resolution numerical experiments, described in this work, show that velocity fluctuations governed by the one-dimensional Burgers equation driven by a white-in-time random noise with the spectrum \f(k)\(2) proportional to k(-1) exhibit a biscaling behavior: All moments of velocity differences S-n less than or equal to 3(r)=\u(x+r)-u(x)\(n)=\Delta u\(n) proportional to r(n/3), while S-n>3(r)proportional to r(xi n) with xi(n) approximate to 1 for real n>0 [Chekhlov and Yakhot, Phys. Rev. E 51, R2739 (1995)]. The probability density function, which is dominated by coherent shocks in the interval Delta u<0, is P(Delta u,r)proportional to(Delta u,r)(-q) with q approximate to 4. A phenomenological theory describing the experimental findings is presented.