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 with the spatial spectrum $\overline{|f(k)|^2}\proptok^{-1}$, is considered. High-resolution numerical experiments conducted in this work give the energy spectrum $E(k)\propto k^{-\beta }$ with $\beta =5/3\pm 0.02$. The observed two-point correlation function $C(k,\omega )$ reveals $\omega \propto k^z$ with the "dynamical exponent" $z\approx 2/3$. 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.

13 LaTeX pages, psfig.sty macros, Phys. Rev. E 51, R2739 (1995).

References in corpus (1)

• Two-Loop Renormalization Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation

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