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February  2005, 5(1): 79-102. doi: 10.3934/dcdsb.2005.5.79

On the double cascades of energy and enstrophy in two dimensional turbulence. Part 1. Theoretical formulation

1. 

Department of Applied Mathematics, Box 352420, University of Washington, Seattle, WA, 98195-2420, United States

2. 

University of Washington, Department of Applied Mathematics, Box 352420, Seattle, WA 98195-2420

Received  October 2003 Revised  January 2004 Published  November 2004

The Kraichnan-Leith-Batchelor scenario of a dual cascade, consisting of an upscale pure energy cascade and a downscale pure enstrophy cascade, is an idealization valid only in an infi nite domain in the limit of in finite Reynolds number. In realistic situations there are double cascades of energy and enstrophy located both upscale and downscale of injection, as long as there are cascades. We outline the statistical theory governing the double cascades and predict the form of the energy spectrum. We show that in general the twin conservation of energy and enstrophy imply the presence of two constant fluxes in each inertial range. This gives rise to a more complicated energy spectrum, which cannot be predicted using dimensional arguments as in the classical theory.
Citation: Eleftherios Gkioulekas, Ka Kit Tung. On the double cascades of energy and enstrophy in two dimensional turbulence. Part 1. Theoretical formulation. Discrete & Continuous Dynamical Systems - B, 2005, 5 (1) : 79-102. doi: 10.3934/dcdsb.2005.5.79
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