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Analytic Study of Shell Models of Turbulence

Peter Constantin·Boris Levant·Edriss S. Titi
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Abstract

In this paper we study analytically the viscous `sabra' shell model of energy turbulent cascade. We prove the global regularity of solutions and show that the shell model has finitely many asymptotic degrees of freedom, specifically: a finite dimensional global attractor and globally invariant inertial manifolds. Moreover, we establish the existence of exponentially decaying energy dissipation range for the sufficiently smooth forcing.

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Peter Constantin, Boris Levant, Edriss S. Titi. 2006-07-04. Analytic Study of Shell Models of Turbulence. https://doi.org/10.1016/j.physd.2006.05.015

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