Dynamical scaling in dissipative Burgers turbulence

An exact asymptotic 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) similar to t(1/2) for very large r and a superdiffusive scale L(t)similar to t(alpha) for r much less than l(D), where alpha=(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.