A. Chekhlov et V. Yakhot, KOLMOGOROV TURBULENCE IN A RANDOM-FORCE-DRIVEN BURGERS-EQUATION - ANOMALOUS SCALING AND PROBABILITY DENSITY-FUNCTIONS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 52(5), 1995, pp. 5681-5684
High-resolution numerical experiments, described in this work, show th
at velocity fluctuations governed by the one-dimensional Burgers equat
ion 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 ve
locity differences S-n less than or equal to 3(r)=\u(x+r)-u(x)\(n)=\De
lta 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 phenomenolo
gical theory describing the experimental findings is presented.