Improved shell model of turbulence

L’vov, Victor S.; Podivilov, E. V.; Pomyalov, Anna; Procaccia, Itamar; Vandembroucq, Damien

doi:10.1103/physreve.58.1811

Cited by 245 publications

(322 citation statements)

References 10 publications

Supporting

Mentioning

307

Contrasting

Order By: Relevance

“…The scale is fixed in the middle of the inertial range, n = 12, and the eddy-turnover time of the reference scale was τ 12 0.29. The average has been performed over approximately 500τ 12 , about 10 large eddy-turnover times. The presence of subleading terms in the first case (continuous line) is apparent.…”

Section: Single-scale Time Correlationsmentioning

confidence: 99%

Multi-time, multi-scale correlation functions in turbulence and in turbulent models

Biferale

Boffetta

Celani

et al. 1999

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

A multifractal-like representation for multi-time, multi-scale velocity correlation in turbulence and dynamical turbulent models is proposed. The importance of subleading contributions to time correlations is highlighted. The fulfillment of the dynamical constraints due to the equations of motion is thoroughly discussed. The predictions stemming from this representation are tested within the framework of shell models for turbulence.

show abstract

Section: Single-scale Time Correlationsmentioning

confidence: 99%

Multi-time, multi-scale correlation functions in turbulence and in turbulent models

Biferale

Boffetta

Celani

et al. 1999

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

“…Among these are shell models of turbulence, which have been investigated for many years (see [2,11,12,16,18]). Recently, some of these models, as well as some new ones, were extensively studied analytically.…”

Section: Introductionmentioning

confidence: 99%

Blow-up in finite time for the dyadic model of the Navier-Stokes equations

Cheskidov

2008

Trans. Amer. Math. Soc.

108

View full text Add to dashboard Cite

ABSTRACT. We study the dyadic model of the Navier-Stokes equations introduced by Katz and Pavlović. They showed a finite time blow-up in the case where the dissipation degree α is less than 1/4. In this paper we prove the existence of weak solutions for all α, energy inequality for every weak solution with nonnegative initial data starting from any time, local regularity for α > 1/3, and global regularity for α ≥ 1/2. In addition, we prove a finite time blow-up in the case where α < 1/3. It is remarkable that the model with α = 1/3 enjoys the same estimates on the nonlinear term as the 4D Navier-Stokes equations. Finally, we discuss a weak global attractor, which coincides with a maximal bounded invariant set for all α and becomes a strong global attractor for α ≥ 1/2.

show abstract

“…Here, we present the details for the SABRA shell model (see [24]), but the same results hold for the GOY shell model (see [21,25]). In recent years, there has been an increasing interest in these fluid dynamical models, both for the deterministic and the stochastic case (see also [3,5,9,10]).…”

Section: An Example: Shell Models Of Turbulencementioning

confidence: 99%

Invariant Measures of Gaussian Type for 2D Turbulence

Bessaih

Ferrario

2012

J Stat Phys

View full text Add to dashboard Cite

Gaussian measures μ β,ν are associated to some stochastic 2D models of turbulence. They are Gibbs measures constructed by means of an invariant quantity of the system depending on some parameter β (related to the 2D nature of the fluid) and the viscosity ν. We prove the existence and the uniqueness of the global flow for the stochastic viscous system; moreover the measure μ β,ν is invariant for this flow and is the unique invariant measure. Finally, we prove that the deterministic inviscid equation has a μ β,ν -stationary solution (for any ν > 0).

show abstract

Improved shell model of turbulence

Cited by 245 publications

References 10 publications

Multi-time, multi-scale correlation functions in turbulence and in turbulent models

Multi-time, multi-scale correlation functions in turbulence and in turbulent models

Blow-up in finite time for the dyadic model of the Navier-Stokes equations

Invariant Measures of Gaussian Type for 2D Turbulence

Contact Info

Product

Resources

About