Journal of Fluid Mechanics

Table of Contents - Volume 699 - 2012  

Papers

Isotropization at small scales of rotating helically driven turbulence

P. D. Mininnia1‡, D. Rosenberga1 and A. Pouqueta1 c1

a1 National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307, USA

Abstract

We present numerical evidence of how three-dimensionalization occurs at small scale in rotating turbulence with Beltrami ($\mathit{ABC}$) forcing, creating helical flow. The Zeman scale ${\ell }_{\Omega } $ at which the inertial and eddy turn-over times are equal is more than one order of magnitude larger than the dissipation scale, with the relevant domains (large-scale inverse cascade of energy, dual regime in the direct cascade of energy $E$ and helicity $H$, and dissipation) each moderately resolved. These results stem from the analysis of a large direct numerical simulation on a grid of $307{2}^{3} $ points, with Rossby and Reynolds numbers, respectively, equal to $0. 07$ and $2. 7\ensuremath{\times} 1{0}^{4} $. At scales smaller than the forcing, a helical wave-modulated inertial law for the energy and helicity spectra is followed beyond ${\ell }_{\Omega } $ by Kolmogorov spectra for $E$ and $H$. Looking at the two-dimensional slow manifold, we also show that the helicity spectrum breaks down at ${\ell }_{\Omega } $, a clear sign of recovery of three-dimensionality in the small scales.

(Received September 20 2011)

(Reviewed January 26 2012)

(Accepted February 10 2012)

(Online publication April 13 2012)

Key Words:

  • isotropic turbulence;
  • rotating turbulence;
  • wave–turbulence interactions

Correspondence:

c1 Email address for correspondence: pouquet@ucar.edu

Footnotes

‡ Also at Departamento de Fí sica, Facultad de Ciencias Exactas y Naturales and IFIBA, CONICET, Ciudad Universitaria, 1428 Buenos Aires, Argentina.

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