, Volume 97, Issue 6, pp 1186-1200

Generation of large-scale coherent structures in the KPZ equation and multidimensional Burgers turbulence

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Abstract

The development of multiple-scale random fluctuations in the problem of interface growth is analyzed. The evolution of the interface is described by the Kardar-Parisi-Zhang (KPZ) equation, and the gradient vector field satisfies the multidimensional Burgers equation. It is shown that the nonlinear effects in the evolution of statistically inhomogeneous multiple-scale fluctuations lead to the generation of large-scale coherent structures. Due to combined effects of nonlinearity and dissipation, localized disturbances tend to exhibit universal long-time behavior.

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Translated from Zhurnal Éksperimental’no \(\overset{\lower0.5em\hbox{\(\smash{\scriptscriptstyle\smile}\)}}{l} \) i Teoretichesko \(\overset{\lower0.5em\hbox{\(\smash{\scriptscriptstyle\smile}\)}}{l} \) Fiziki, Vol. 124, No. 6, 2003, pp. 1329–1344.
Original Russian Text Copyright © 2003 by Gurbatov, Moshkov.