Turbulence and Multiscaling in the Randomly Forced Navier Stokes Equation

Details Turbulence and Multiscaling in the Randomly Forced Navier Stokes Equation Turbulence and Multiscaling in the Randomly Forced Navier Stokes Equation

1997-12-29

arxiv.org/abs/chao-dyn/9801002v1

Nonlinear Sciences

Chaotic Dynamics

4 pages (revtex), 6 figures (postscript)

Scientific paper

10.1103/PhysRevLett.81.4377

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 $y \geq 4$. 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.

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