Kolmogorov turbulence in a random-force-driven Burgers equation.

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 \ensuremath{\Vert}f(k)${\mathrm{\ensuremath{\Vert}}}^{2}$\ensuremath{\propto}${\mathit{k}}^{\mathrm{\ensuremath{-}}1}$, is considered. High-resolution numerical experiments conducted in this work give the energy spectrum E(k)\ensuremath{\propto}${\mathit{k}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\beta}}}$ with \ensuremath{\beta}=5/3\ifmmode\pm\else\textpm\fi{}0.02. The observed two-point correlation function C(k,\ensuremath{\omega}) reveals \ensuremath{\omega}\ensuremath{\propto}${\mathit{k}}^{\mathit{z}}$ with the ``dynamic exponent'' z\ensuremath{\approxeq}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.