Turbulence and multiscaling in the randomly forced Navier-Stokes equation

Abstract

We present a pseudospectral study of the randomly forced Navier-Stokes equation (RFNSE) stirred by a stochastic force with zero mean and a variance ~k^4-d-y, with k the wave vector and the dimension d=3. We provide the first evidence for multiscaling of velocity structure functions for y≥4. We extract the multiscaling exponent ratios ζ_p/ζ₂ by using extended self-similarity, examine their dependence on y, and show that, if y=4, they are in agreement with those obtained for the Navier-Stokes equation forced at large spatial scales (3DNSE). Also well-defined vortex filaments, which appear clearly in studies of the 3DNSE, are absent in the RFNSE.