Analytic study of shell models of turbulence

Peter Constantin, Boris Levant, Edriss S. Titi

Research output: Contribution to journalArticle

33 Scopus citations

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 languageEnglish (US)
Pages (from-to)120-141
Number of pages22
JournalPhysica D: Nonlinear Phenomena
Volume219
Issue number2
DOIs
StatePublished - 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

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