Pdf's of Derivatives and Increments for Decaying Burgers Turbulence

A Lagrangian method is used to show that the power-law with a -7/2 exponent in the negative tail of the pdf of the velocity gradient and of velocity increments, predicted by E, Khanin, Mazel and Sinai (1997 Phys. Rev. Lett. 78, 1904) for forced Burgers turbulence, is also present in the unforced case. The theory is extended to the second-order space derivative whose pdf has power-law tails with exponent -2 at both large positive and negative values and to the time derivatives. Pdf's of space and time derivatives have the same (asymptotic) functional forms. This is interpreted in terms of a "random Taylor hypothesis".