Dynamical scaling in dissipative Burgers turbulence

T. J. Newman
1997 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
more » ... e scaling arguments are presented within the 'toy model' of disordered systems theory, which may be exactly mapped onto the current problem.
doi:10.1103/physreve.55.6989 fatcat:g3lkqg2aqzhc5gn4o4n2yzxutm