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-intime random noise with the spectrum |f(k)| ∝ k exhibit a biscaling behavior: All moments of velocity differences Sn≤3(r) = |u(x+ r)− u(x)| n ≡ |∆u| ∝ rn/3, while Sn>3(r) ∝ r ξn with ξn ≈ 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 ∆u < 0, is P(∆u, r) ∝ (∆u)−q with q ≈ 4. A phenomenological theory describing the experimental findings is presented.