Turbulence and Multiscaling in the Randomly Forced Navier-Stokes Equation

We present a pseudospectral study of the randomly forced Navier-Stokes equation (RFNSE) stirred by a stochastic force with zero mean and a variance ~k4-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 zeta p/ zeta 2 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