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Spiral structures and spectra in two-dimensional turbulence

Published online by Cambridge University Press:  21 April 2006

Andrew D. Gilbert
Andrew D. Gilbert
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge. Silver Street, Cambridge CB3 9EW, UK
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Abstract

Saffman argues that in decaying two-dimensional turbulence approximate dis-continuities of vorticity will form, and the energy spectrum will fall off as k−4 Saffman assumes that these discontinuities are well separated; in this paper, we examine how accumulation points of such discontinuities may give an energy spectrum of between k−4 and k−3. In particular we examine the energy spectra of spiral structures which form round the coherent vortices that are observed in numerical simulations of decaying two-dimensional turbulence. If the filaments of the spiral are assumed to be passively advected, the instantaneous energy spectrum has a $k^{-11/3}$ range. Thus we come some way to reconciling the argument of Saffman and the k−3 energy spectrum predicted by models of quasi-equilibrium two-dimensional turbulence based on a cascade of enstrophy in Fourier space.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 193 , August 1988 , pp. 475 - 497
Copyright
© 1988 Cambridge University Press

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