Kolmogorov turbulence in a random-force-driven Burgers equation

Abstract

The dynamics of velocity fluctuations, governed by the one-dimensional Burgers equation, driven by a white-in-time random force f with the spatial spectrum ‖f(k)${\mathrm{\Vert }}^2$∝${\mathit{k}}^{\mathrm{-}1}$, is considered. High-resolution numerical experiments conducted in this work give the energy spectrum E(k)∝${\mathit{k}}^{\mathrm{-}\mathrm{\beta }}$ with β=5/3±0.02. The observed two-point correlation function C(k,ω) reveals ω∝${\mathit{k}}^{\mathit{z}}$ with the ‘‘dynamic exponent’’ z≊2/3. High-order moments of velocity differences show strong intermittency and are dominated by powerful large-scale shocks. The results are compared with predictions of the one-loop renormalized perturbation expansion.