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Scaling exponents in weakly anisotropic turbulence from the Navier–Stokes equation

  • SIEGFRIED GROSSMANN (a1), ANNA VON DER HEYDT (a1) (a2) and DETLEF LOHSE (a2)
Abstract

The second-order velocity structure tensor of weakly anisotropic strong turbulence is decomposed into its SO(3) invariant amplitudes dj(r). Their scaling is derived within a scaling approximation of a variable-scale mean-field theory of the Navier–Stokes equation. In the isotropic sector j = 0 Kolmogorov scaling d0(r) ∝ r2/3 is recovered. The scaling of the higher j amplitudes (j even) depends on the type of the external forcing that maintains the turbulent flow. We consider two options: (i) for an analytic forcing and for decreasing energy input into the sectors with increasing j, the scaling of the higher sectors j > 0 can become as steep as dj(r) ∝ rj+2/3; (ii) for a non-analytic forcing we obtain dj(r) ∝ r4/3 for all non-zero and even j.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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