Dynamical scaling in dissipative Burgers turbulence
T. J. Newman
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
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∼ t^1/2 for very large r, and a super-diffusive scale L(t) ∼ t^a for r ≪ l_D, where a = (d+1)/(d+2). The consequences for conventional scaling theory are discussed. Finally, some
... e scaling arguments are presented within the 'toy model' of disordered systems theory, which may be exactly mapped onto the current problem.