A UNIVERSAL LAW FOR TAILS OF DENSITY PDF'S IN MULTI-DIMENSIONAL BURGERS TURBULENCE

Extending work of E, Khanin, Mazel and Sinai [1] 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.