Note on Forced Burgers Turbulence

Details Note on Forced Burgers Turbulence Note on Forced Burgers Turbulence

1999-01-21

arxiv.org/abs/chao-dyn/9901023v2

Nonlinear Sciences

Chaotic Dynamics

Expanded and updated to conform with version to appear in Phys. Fluids. Six pages revtex, no figures

Scientific paper

10.1063/1.870235

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 $\alpha\ge3$, if dissipation within the powerlaw 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 $\alpha\ge3$ can be realized by suitably constructed homogeneous, non-Gaussian initial data and forcing.

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