Stochastic dynamics of relativistic turbulence

Abstract

We apply generalized Kolmogorov scaling to continuous time random walks, coupled in space and time, to obtain anomalous diffusion laws for relativistic turbulent media. Richardson's law for the mean square separation of two particles that are initially close together 〈${\mathit{R}}^{2}$〉\ensuremath{\sim}${\mathit{t}}^{3}$ is recovered in the nonrelativistic limit, while the ultrarelativistic limit is characterized by a different power law 〈${\mathit{R}}^{2}$〉\ensuremath{\sim}${\mathit{t}}^{2}$. Intermediate velocities are treated numerically, showing a smooth transition from one regime to the other. \textcopyright{} 1996 The American Physical Society.