Some specific mathematical constraints on 2D turbulence

Dascaliuc, Radu; Foiaş, Ciprian; Jolly, Michael S.

doi:10.1016/j.physd.2008.07.004

Cited by 14 publications

(11 citation statements)

References 24 publications

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“…The estimates from Section 6, (see Proposition 6.1 and Corollary 6.2) show that, as was the case in the 2-D flows [22], the 3-D turbulent flows are characterized by highly restrictive scaling. Our results confirm classical ''dimensional'' estimates from Kolmogorov theory of turbulence, but we obtain them through the Grashof number, i.e.…”

Section: Discussionmentioning

confidence: 73%

On the asymptotic behavior of average energy and enstrophy in 3D turbulent flows

Dascaliuc

Foiaş

Jolly

2009

Physica D: Nonlinear Phenomena

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Section: Discussionmentioning

confidence: 73%

On the asymptotic behavior of average energy and enstrophy in 3D turbulent flows

Dascaliuc

Foiaş

Jolly

2009

Physica D: Nonlinear Phenomena

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“…If one assumes the power spectrum (which a priori says nothing about energy transfer rates), however, one does obtain lower bounds on κ σ and κ η , or equivalently by (4.4) and (4.7), sufficient conditions for the enstrophy and energy cascades. In 2D we have the following estimate from [5].…”

Section: Indicators For Cascadesmentioning

confidence: 99%

Energy spectra and passive tracer cascades in turbulent flows

Jolly

Wirosoetisno

2018

Journal of Mathematical Physics

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We study the influence of the energy spectrum on the extent of the cascade range of a passive tracer in turbulent flows. The interesting cases are when there are two different spectra over the potential range of the tracer cascade (in 2D when the tracer forcing is in the inverse energy cascade range, and in 3D when the Schmidt number Sc is large). The extent of the tracer cascade range is then limited by the width of the range for the shallower of the two energy spectra. Nevertheless, we show that in dimension d = 2, 3 the tracer cascade range extends (up to a logarithm) to κ p dD , where κ dD is the wavenumber beyond which diffusion should dominate and p is arbitrarily close to 1, provided Sc is larger than a certain power (depending on p) of the Grashof number. We also derive estimates which suggest that in 2D, for Sc ∼ 1 a wide tracer cascade can coexist with a significant inverse energy cascade at Grashof numbers large enough to produce a turbulent flow.

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“…Here, we follow many of the ideas of [10,11,12,13] which investigated the relationship between energy, enstrophy, and palenstrophy in the attractor of the 2D Navier-Stokes equations.…”

Section: The Energy-enstrophy Planementioning

confidence: 99%

On the attractor for the semi-dissipative Boussinesq equations

Biswas

Foiaş

Larios

2017

Ann. Inst. H. Poincaré Anal. Non Linéaire

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In this article, we study the long time behavior of solutions of a variant of the Boussinesq system in which the equation for the velocity is parabolic while the equation for the temperature is hyperbolic. We prove that the system has a global attractor which retains some of the properties of the global attractors for the 2D and 3D Navier-Stokes equations. Moreover, this attractor contains infinitely many invariant manifolds in which several universal properties of the Batchelor, Kraichnan, Leith theory of turbulence are potentially present. Résumé. Dans cet article nousétudions le comportment au temps infini des solutions d'une partiellement dissipative system du Boussinesq, dont une est parabolique et l'autre est hyperbolique. Dans ce but nous introduire un attracteur universel qui retient plusieurs proprietés des attracteurs universels deséquations de Navier-Stokes en dimension deux ou trois, qui, in particulier, contient une infinité de varietés invariantes dans lesquelles plusieurs proprietés universelles de la théorie de la turbulence bidimensionnelle de Batchelor, Kraichnan et Leith, sont potentiellement présentes.

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Some specific mathematical constraints on 2D turbulence

Cited by 14 publications

References 24 publications

On the asymptotic behavior of average energy and enstrophy in 3D turbulent flows

On the asymptotic behavior of average energy and enstrophy in 3D turbulent flows

Energy spectra and passive tracer cascades in turbulent flows

On the attractor for the semi-dissipative Boussinesq equations

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