Dynamical Scaling in Dissipative Burgers Turbulence

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.