Inviscid limits for a stochastically forced shell model of turbulent flow

Susan Friedlander; Nathan Glatt-Holtz; Vlad Vicol

doi:10.1214/14-AIHP663

Inviscid limits for a stochastically forced shell model of turbulent flow

Susan Friedlander, Nathan Glatt-Holtz, Vlad Vicol

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	1217-1247
Number of pages	31
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	52
Issue number	3
DOIs	https://doi.org/10.1214/14-AIHP663
State	Published - Aug 2016

Keywords

Dissipation anomaly
Ergodicity
Invariant measures
Inviscid limits
Shell models

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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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 H{\"o}rmander) and use this property to prove a gradient bound on the Markov semigroup.",

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AU - Friedlander, Susan

AU - Glatt-Holtz, Nathan

AU - Vicol, Vlad

N1 - Publisher Copyright: © Association des Publications de l'Institut Henri Poincaré, 2016.

PY - 2016/8

Y1 - 2016/8

N2 - 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.

AB - 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.

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KW - Ergodicity

KW - Invariant measures

KW - Inviscid limits

KW - Shell models

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Inviscid limits for a stochastically forced shell model of turbulent flow

Abstract

Keywords

ASJC Scopus subject areas

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