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{}{∝}k^-1 exhibit a biscaling behavior: All moments of velocity differences S_n≤3(r)={}u(x+r)-u(x)ⁿ{}{≡}{}{Δ}uⁿ{} {∝}rn/3, while Sn>3(r){∝}rₙ^ξ 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 {Δ}u0, is scrP({Δ}u,r){∝}({Δ}u)^-q with q{}4. A phenomenological theory describing the experimental findings is presented.