Inviscid limits for a stochastically forced shell model of turbulent flow

Susan Friedlander, Nathan Glatt-Holtz, Vlad Vicol

Research output: Contribution to journalArticle

Abstract

We establish the anomalous mean dissipation rate of energy in the inviscid limit for a stochastic shell model of turbulent fluid flow. The proof relies on viscosity independent bounds for stationary solutions and on establishing ergodic and mixing properties for the viscous model. The shell model is subject to a degenerate stochastic forcing in the sense that noise acts directly only through one wavenumber.We show that it is hypo-elliptic (in the sense of Hörmander) and use this property to prove a gradient bound on the Markov semigroup.

Original languageEnglish (US)
Pages (from-to)1217-1247
Number of pages31
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume52
Issue number3
DOIs
StatePublished - Aug 1 2016

Fingerprint

Inviscid Limit
Shell Model
Turbulent Flow
Markov Semigroups
Stationary Solutions
Forcing
Anomalous
Fluid Flow
Stochastic Model
Dissipation
Viscosity
Gradient
Energy
Shell
Model

Keywords

  • Dissipation anomaly
  • Ergodicity
  • Invariant measures
  • Inviscid limits
  • Shell models

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Inviscid limits for a stochastically forced shell model of turbulent flow. / Friedlander, Susan; Glatt-Holtz, Nathan; Vicol, Vlad.

In: Annales de l'institut Henri Poincare (B) Probability and Statistics, Vol. 52, No. 3, 01.08.2016, p. 1217-1247.

Research output: Contribution to journalArticle

Friedlander, Susan ; Glatt-Holtz, Nathan ; Vicol, Vlad. / Inviscid limits for a stochastically forced shell model of turbulent flow. In: Annales de l'institut Henri Poincare (B) Probability and Statistics. 2016 ; Vol. 52, No. 3. pp. 1217-1247.
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