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The enstrophy cascade in forced two-dimensional turbulence

Published online by Cambridge University Press:  31 January 2011

ANDREAS VALLGREN  and
ERIK LINDBORG
ANDREAS VALLGREN*
Affiliation:
Linné FLOW Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
ERIK LINDBORG
Affiliation:
Linné FLOW Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
*
†Email address for correspondence: vallgren@mech.kth.se
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Abstract

We carry out direct numerical simulations of two-dimensional turbulence with forcing at different wavenumbers and resolutions up to 327682 grid points. In the absence of large-scale drag, a state is reached where enstrophy is quasi-stationary while energy is growing. In the enstrophy cascade range the energy spectrum has the form E(k) = εω2/3k−3, without any logarithmic correction, where εω is the enstrophy dissipation and is of the order of unity. However, is varying between different simulations and is thus not a perfect constant. This variation can be understood as a consequence of large-scale dissipation intermittency, following the argument by Landau (Landau & Lifshitz, Fluid Mechanics, 1959, Pergamon). In the presence of a large-scale drag, we obtain a slightly steeper spectrum. When forcing is applied at a scale which is somewhat smaller than the computational domain, no vortices are formed, and the statistics remain close to Gaussian in the enstrophy cascade range. When forcing is applied at a smaller scale, long-lived coherent vortices form at larger scales than the forcing scale, and intermittency measures become very large at all scales, including the scales of the enstrophy cascade. We conclude that the enstrophy cascade with a k−3-spectrum is a robust feature of the two-dimensional Navier–Stokes equations. However, there is a complete lack of universality of higher-order statistics of vorticity increments in the enstrophy cascade range.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulence theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 671 , 25 March 2011 , pp. 168 - 183
Copyright
Copyright © Cambridge University Press 2011

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