Universality of Velocity Gradients in Forced Burgers Turbulence

Details Universality of Velocity Gradients in Forced Burgers Turbulence Universality of Velocity Gradients in Forced Burgers Turbulence

2001-03-20

arxiv.org/abs/nlin/0103029v2

Phys. Rev. Lett. 87, 104501, 2001

Nonlinear Sciences

Chaotic Dynamics

4 pages, 2 figures, RevTex4, published version

Scientific paper

10.1103/PhysRevLett.87.104501

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.

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