Inverse cascade regime in shell models of two-dimensional turbulence.

  title={Inverse cascade regime in shell models of two-dimensional turbulence.},
  author={Thomas Gilbert and Victor S. L’vov and Anna Pomyalov and Itamar Procaccia},
  journal={Physical review letters},
  volume={89 7},
We consider shell models that display an inverse energy cascade similar to two-dimensional turbulence (together with a direct cascade of an enstrophylike invariant). Previous attempts to construct such models ended negatively, stating that shell models give rise to a "quasiequilibrium" situation with equipartition of the energy among the shells. We show analytically that the quasiequilibrium state predicts its own disappearance upon changing the model parameters in favor of the establishment of… 

Figures from this paper

Inverse energy cascade in nonlocal helical shell models of turbulence.
A modified version of helical shell models for turbulence with nonlocal triadic interactions is introduced, showing that there exists a class of models that exhibits a statistically stable inverse energy cascade, in close analogy with that predicted for the Navier-Stokes equations restricted to the same helical interactions.
Shell model of two-dimensional turbulence in polymer solutions
We address the effect of polymer additives on two-dimensional turbulence, an issue that was studied recently in experiments and direct numerical simulations. We show that the same simple shell model
Bridging inertial and dissipation range statistics in rotating turbulence
We perform a multifractal analysis of rotating turbulence to obtain an estimate of the (anomalous) scaling exponents in the inertial range in terms of the generalised dimensions associated with the
Chaotic and regular instantons in helical shell models of turbulence
Shell models of turbulence have a finite-time blowup in the inviscid limit, i.e., the enstrophy diverges while the single-shell velocities stay finite. The signature of this blowup is represented by
Analytical and Numerical Study of Certain Models of Turbulence May
  • Physics
  • 2009
In my thesis I study two different models of turbulence. The first part of my research concerns the, so-called, shell models of turbulence. Shell models had attracted a lot of interest as useful
How close are shell models to the 3D Navier–Stokes equations?
Shell models have found wide application in the study of hydrodynamic turbulence because they are easily solved numerically even at very large Reynolds numbers. Although bereft of spatial variation,
Emerging scale invariance in a model of turbulence of vortices and waves
It is put forward the hypothesis that the invariance of multipliers is due to an extreme non-locality of their interactions (similar to the appearance of mean-field properties in the thermodynamic limit for systems with long-range interaction) and provides a unique opportunity for an analytic study of emerging scale invariance in a system with strong interactions.
Regularity of inviscid shell models of turbulence.
This paper proves the global existence of weak solutions of the inviscid sabra shell model, and shows that these solutions are unique for some short interval of time, and proves that the solutions conserve energy.


Dynamical Systems Approach to Turbulence
Introduction 1. Turbulence and dynamical systems 2. Phenomenology of turbulence 3. Reduced models for hydrodynamic turbulence 4. Turbulence and coupled map lattices 5. Turbulence in the complex
  • Rev. E 53, 4785–4793
  • 1996
  • Fluids 10, 1417
  • 1967
  • Rev. E 61, R29
  • 2000
and A
  • Vulpiani, Dynamical Systems Approach to Turbulence
  • 1998
  • Rep. 362, 1
  • 2002
  • Rev. Lett. 60, 983
  • 1988
  • Rev. Lett. 71, 352
  • 1993
  • Rev. E 50, 4705
  • 1994
  • Akad. Nauk SSSR 209, 1046 (1973) [Sov. Phys. Dokl. 18, 216
  • 1973