Analytic Study of Shell Models of Turbulence
Fluid Dynamics
2009-11-11 v2
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.
Cite
@article{arxiv.physics/0511075,
title = {Analytic Study of Shell Models of Turbulence},
author = {Peter Constantin and Boris Levant and Edriss S. Titi},
journal= {arXiv preprint arXiv:physics/0511075},
year = {2009}
}