Abstract
In this paper we study analytically the viscous "sabra" shell model of the 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 an exponentially decaying energy dissipation range for sufficiently smooth forcing.
Original language | English (US) |
---|---|
Pages (from-to) | 120-141 |
Number of pages | 22 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 219 |
Issue number | 2 |
DOIs | |
State | Published - Jul 15 2006 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics
Keywords
- Dynamic models
- Navier-Stokes equations
- Shell models
- Turbulence