Kolmogorov turbulence in a random-force-driven Burgers equation: anomalous scaling and probability density functions

Abstract

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 $\overline{|f(k){|}^2}\propto k^{-1}$ exhibit a biscaling behavior: All moments of velocity differences $S_{n\le 3}(r)=\overline{|u(x+r)-u(x){|}^n}\equiv \overline{|\Delta u{|}^n}\propto r^{n/3}$, while $S_{n>3}\propto r^{{\zeta }_n}$ with ${\zeta }_n\approx 1$ for real $n>0$ (Chekhlov and Yakhot, Phys. Rev. E {\bf 51}, R2739, 1995). The probability density function, which is dominated by coherent shocks in the interval $\Delta u<0$, is $\mathcal{P}(\Delta u,r)\propto (\Delta u{)}^{-q}$ with $q\approx 4$.

12 pages, psfig macro, 4 figs in Postscript, accepted to Phys. Rev. E as a Brief Communication

References in corpus (2)

• SCALING AND INTERMITTENCY IN BURGERS' TURBULENCE
• Kolmogorov turbulence in a random-force-driven Burgers equation

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