Turbulence and Multiscaling in the Randomly Forced Navier Stokes Equation

Abstract

We present an extensive pseudospectral study of the randomly forced Navier-Stokes equation (RFNSE) stirred by a stochastic force with zero mean and a variance $\sim k^{4-d-y}$, where $k$ is the wavevector and the dimension $d=3$. We present the first evidence for multiscaling of velocity structure functions in this model for $y\ge 4$. We extract the multiscaling exponent ratios ${\zeta }_p/{\zeta }_2$ by using extended self similarity (ESS), examine their dependence on $y$, and show that, if $y=4$, they are in agreement with those obtained for the deterministically forced Navier-Stokes equation ($3d$NSE). We also show that well-defined vortex filaments, which appear clearly in studies of the $3d$NSE, are absent in the RFNSE.

4 pages (revtex), 6 figures (postscript)

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• Kolmogorov turbulence in a random-force-driven Burgers equation
• Inertial- and Dissipation-Range Asymptotics in Fluid Turbulence
• Scaling of Low-Order Structure Functions in Homogeneous Turbulence

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