Analytic study of shell models of turbulence Academic Article uri icon


  • 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. © 2006 Elsevier Ltd. All rights reserved.

author list (cited authors)

  • Constantin, P., Levant, B., & Titi, E. S.

citation count

  • 32

publication date

  • July 2006