Dynamical Scaling in Dissipative Burgers Turbulence

Details Dynamical Scaling in Dissipative Burgers Turbulence Dynamical Scaling in Dissipative Burgers Turbulence

1997-04-14

arxiv.org/abs/cond-mat/9704119v1

Physics

Condensed Matter

Statistical Mechanics

30 pages, Revtex, no figures

Scientific paper

10.1103/PhysRevE.55.6989

An exact analysis is performed for the two-point correlation function C(r,t) in dissipative Burgers turbulence with bounded initial data, in arbitrary spatial dimension d. Contrary to the usual scaling hypothesis of a single dynamic length scale, it is found that C contains two dynamic scales: a diffusive scale l_{D} \sim t^{1/2} for very large r, and a super-diffusive scale L(t) \sim t^{a} for r \ll l_{D}, where a = (d+1)/(d+2). The consequences for conventional scaling theory are discussed. Finally, some simple scaling arguments are presented within the `toy model' of disordered systems theory, which may be exactly mapped onto the current problem.

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