Kolmogorov turbulence in a random-force-driven Burgers equation

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

1995-06-23

arxiv.org/abs/adap-org/9506002v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

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

Scientific paper

10.1103/PhysRevE.51.R2739

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.

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