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A universal law for tails of density pdf's in multi-dimensional Burgers turbulence

J. Bec·U. Frisch·K. Khanin·B. Villone
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Abstract

Extending work of E, Khanin, Mazel and Sinai (1997 PRL 78:1904-1907) on the one-dimensional Burgers equation, we show that density pdf's have universal power-law tails with exponent -7/2. This behavior stems from singularities, other than shocks, whose nature is quite different in one and several dimensions. We briefly discuss the possibility of detecting singularities of Navier-Stokes turbulence using pdf tails.

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J. Bec, U. Frisch, K. Khanin, B. Villone. 2001-01-17. A universal law for tails of density pdf's in multi-dimensional Burgers turbulence. https://arxiv.org/abs/astro-ph/0101298

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