Universality of velocity gradients in forced burgers turbulence

Abstract

We demonstrate that Burgers turbulence subject to large-scale white-noise-in-time random forcing has a universal power-law tail with exponent -7/2 in the probability density function of negative velocity gradients, as predicted by E, Khanin, Mazel, and Sinai [Phys. Rev. Lett. 78, 1904 (1997)]. A particle and shock tracking numerical method gives about five decades of scaling. Using a Lagrangian approach, the -7/2 law is related to the shape of the unstable manifold associated to the global minimizer. © 2001 The American Physical Society.