Analytic Study of Shell Models of Turbulence

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.

References in corpus (3)

• An optimal shell model of turbulence
• Sharp estimates for the number of degrees of freedom for the damped-driven 2D Navier--Stokes equations
• How the viscous subrange determines inertial range properties in turbulence shell models

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