Universality of Velocity Gradients in Forced Burgers Turbulence

Abstract

It is demonstrated 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 (1997, Phys. Rev. Lett. 78, 1904). 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.