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Multiscaling in the randomly forced and conventional Navier–Stokes equations

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  • Sain, Anirban
  • Pandit, Rahul

Abstract

We present an overview of some results we have obtained recently (A. Sain, Manu and R. Pandit, Phys. Rev. Lett. 81 (1998) 4377) from 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 wavevector and the dimension d=3. These include the multiscaling of velocity structure functions for y⩾4 and a demonstration that the multiscaling exponent ratios ζp/ζ2 for y=4 are in agreement with those obtained for the Navier–Stokes equation forced at large spatial scales (3dNSE). We also study a coarse-graining procedure for the 3dNSE and examine why it does not lead to the RFNSE.

Suggested Citation

  • Sain, Anirban & Pandit, Rahul, 1999. "Multiscaling in the randomly forced and conventional Navier–Stokes equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(1), pages 190-203.
    • Handle: RePEc:eee:phsmap:v:270:y:1999:i:1:p:190-203
    DOI: 10.1016/S0378-4371(99)00119-3
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