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

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  • 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.
    Mathematics Subject Classification: 76FXX, 60G60.

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