Note on forced Burgers turbulence

A putative powerlaw range of the probability density of velocity gradient in high-Reynolds-number forced Burgers turbulence is studied. In the absence of information about shock locations, elementary conservation and stationarity relations imply that the exponent - alpha in this range satisfies alpha greater than or equal to 3, if dissipation within the power-law range is due to isolated shocks. A generalized model of shock birth and growth implies alpha = 7/2 if initial data and forcing are spatially homogeneous and obey Gaussian statistics. Arbitrary values alpha greater than or equal to 3 can be realized by suitably constructed homogeneous, non-Gaussian initial data and forcing. (C) 1999 American Institute of Physics. [S1070-6631(99)00112-9].