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

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.