Two-dimensional turbulence in three-dimensional flows

Xia, Hua; Nicolas, François

doi:10.1063/1.5000863

Cited by 38 publications

(33 citation statements)

References 71 publications

(130 reference statements)

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“…We also remark that rapidly rotating turbulence, and magnetohydrodynamic and quasi-static magnetohydrodynamic turbulence with strong external magnetic field exhibits quasi 2D behaviour [12][13][14][15][16][17][18]. Sharma et al [14] employed the enstrophy flux derived in Sec.…”

Section: Discussionmentioning

confidence: 99%

Energy and enstrophy spectra and fluxes for the inertial-dissipation range of two-dimensional turbulence

et al. 2019

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In this paper, using Pao's conjecture [Y.-H. Pao, Phys. Fluids 8, 1063(1965], we derive expressions for the spectra and fluxes of kinetic energy and enstrophy for two-dimensional (2D) forced turbulence that extend beyond the inertial range. In these expressions, the fluxes and the spectra contain additional factors of the exponential form. To validate these model predictions, we perform numerical simulations of 2D turbulence with external force applied at k = k f in the intermediate range. The numerical results match with the model predictions, except for the energy and enstrophy fluxes for k < k f , where the fluxes exhibit significant fluctuations. We show that these fluctuations arise due to the unsteady nature of the flow at small wavenumbers. For the k < k f , the shellto-shell energy transfers computed using numerical data show forward energy transfers among the neighbouring shells, but backward energy transfers for other shells.

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Section: Discussionmentioning

confidence: 99%

Energy and enstrophy spectra and fluxes for the inertial-dissipation range of two-dimensional turbulence

et al. 2019

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“…Bursts are more frequent than transitions in the bistable regime and their statistics therefore are more easily accessible. Furthermore, given the large experimental literature (see Xia et al 2011;Xia & Francois 2017) on the transition between 3-D turbulence and condensation in thin layers, it would be exciting and very important to study the observed bistability experimentally. The biggest advantage of an experiment compared to DNS would be that much longer observation times are possible as well as higher Re.…”

Section: Discussionmentioning

confidence: 99%

Rare transitions to thin-layer turbulent condensates

2019

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Turbulent flows in a thin layer can develop an inverse energy cascade leading to spectral condensation of energy when the layer height is smaller than a certain threshold. These spectral condensates take the form of large-scale vortices in physical space. Recently, evidence for bistability was found in this system close to the critical height: depending on the initial conditions, the flow is either in a condensate state with most of the energy in the two-dimensional (2-D) large-scale modes, or in a three-dimensional (3-D) flow state with most of the energy in the small-scale modes. This bistable regime is characterised by the statistical properties of random and rare transitions between these two locally stable states. Here, we examine these statistical properties in thin-layer turbulent flows, where the energy is injected by either stochastic or deterministic forcing. To this end, by using a large number of direct numerical simulations (DNS), we measure the decay time τ d of the 2-D condensate to 3-D flow state and the build-up time τ b of the 2-D condensate. We show that both of these times τ d , τ b follow an exponential distribution with mean values increasing faster than exponentially as the layer height approaches the threshold. We further show that the dynamics of large-scale kinetic energy may be modeled by a stochastic Langevin equation. From time-series analysis of DNS data, we determine the effective potential that shows two minima corresponding to the 2-D and 3-D states when the layer height is close to the threshold.

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“…Condensates in thin layers have been observed experimentally: the first study by (Sommeria 1986) was followed by the important contributions of (Paret & Tabeling 1997, 1998 and more recently by (Shats et al 2005(Shats et al , 2007Xia et al 2008Xia et al , 2009Xia et al , 2011Byrne et al 2011). An up-to-date review of relevant experiments is presented in (Xia & Francois 2017). These experiments operate primarily in the long-time limit in which the condensate is fully developed.…”

Section: Introductionmentioning

confidence: 99%

Condensates in thin-layer turbulence

Kan

Alexakis

2019

J. Fluid Mech.

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We examine the steady state of turbulent flows in thin layers using direct numerical simulations. It is shown that when the layer thickness is smaller than a critical height, an inverse cascade arises which leads to the formation of a steady state condensate where most of the energy is concentrated in the largest scale of the system. For layers of thickness smaller than a second critical height, the flow at steady state becomes exactly twodimensional. The amplitude of the condensate is studied as a function of layer thickness and Reynolds number. Bi-stability and intermittent bursts are found close to the two critical points. The results are interpreted based on a mean-field three-scale model that reproduces some of the basic features of the numerical results.

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Two-dimensional turbulence in three-dimensional flows

Cited by 38 publications

References 71 publications

Energy and enstrophy spectra and fluxes for the inertial-dissipation range of two-dimensional turbulence

Energy and enstrophy spectra and fluxes for the inertial-dissipation range of two-dimensional turbulence

Rare transitions to thin-layer turbulent condensates

Condensates in thin-layer turbulence

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