Analytic study of shell models of turbulence

Peter Constantin, Boris Levant, Edriss S. Titi

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


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
Issue number2
StatePublished - Jul 15 2006

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


  • Dynamic models
  • Navier-Stokes equations
  • Shell models
  • Turbulence


Dive into the research topics of 'Analytic study of shell models of turbulence'. Together they form a unique fingerprint.

Cite this