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 ${\mathrm{l}}_{\mathrm{D}}$∼${\mathrm{t}}^{1\mathrm{/}2}$ for very large r and a superdiffusive scale L(t)∼${\mathrm{t}}^{\mathrm{\alpha }}$ for r≪${\mathrm{l}}_{\mathrm{D}}$, where α=(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.