Analytic Study of Shell Models of Turbulence

Details Analytic Study of Shell Models of Turbulence Analytic Study of Shell Models of Turbulence

2005-11-09

arxiv.org/abs/physics/0511075v2

Physics

Fluid Dynamics

Scientific paper

10.1016/j.physd.2006.05.015

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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