On the decay of Burgers turbulence

Abstract

This work is devoted to the decay ofrandom solutions of the unforced Burgers equation in one dimension in the limit of vanishing viscosity. The initial velocity is homogeneous and Gaussian with a spectrum proportional to $k^n$ at small wavenumbers $k$ and falling off quickly at large wavenumbers. In physical space, at sufficiently large distances, there is an ``outer region'', where the velocity correlation function preserves exactly its initial form (a power law) when $n$ is not an even integer. When $1 1$. A systematic derivation is given in which both the leading term and estimates of higher order corrections can be obtained. High-resolution numerical simulations are presented which support our findings.