Non-Gaussianity and coherent vortex simulation for two-dimensional turbulence using an adaptive orthogonal wavelet basis

Farge, Marie; Schneider, Kai; Kevlahan, Nicholas

doi:10.1063/1.870080

Cited by 308 publications

(301 citation statements)

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“…The coherent vorticity field is obtained by filtering the wavelet coefficients, which thus exploits the intermittency of turbulence and yields a sparse representation. Examples of CVS can be found in [17][18][19][20] for two-dimensional turbulent flows and in [21] for three-dimensional turbulent mixing layers. For highly anisotropic turbulence, the wavelet-based simulation method is expected to become more efficient, if one takes into account the anisotropy and intermittency of the turbulence.…”

Section: Resultsmentioning

confidence: 99%

“…A wavelet-based turbulence model, the Coherent Vorticity Simulation (CVS), which is based on the deterministic computation of the coherent vorticity field using an adaptive wavelet basis, was proposed in [17,18], for a review we refer to [15]. The coherent vorticity field is obtained by filtering the wavelet coefficients, which thus exploits the intermittency of turbulence and yields a sparse representation.…”

Section: Resultsmentioning

confidence: 99%

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Directional and scale-dependent statistics of quasi-static magnetohydrodynamic turbulence

et al. 2011

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Abstract. Anisotropy and intermittency of quasi-static magnetohydrodynamic (MHD) turbulence in an imposed magnetic field are examined, using three-dimensional orthonormal wavelet analysis. Wavelets are an efficient tool to examine directional scale-dependent statistics, since they are based on well-localized functions in space, scale and direction. The analysis is applied to two turbulent MHD flows computed by direct numerical simulation with 512 3 grid points and with different intensities of the imposed magnetic field. It is found that the imposed magnetic field plays an important role on the amplification of anisotropy and intermittency of the flow.Résumé. L'anisotropie et l'intermittence de la turbulence magnétohydrodynamique (MHD) dans l'approximation quasi-statiqueavec un champ magnétique imposé sont examinés en utilisant l'analyse par ondelettes orthogonales. Les ondelettes sont un outil efficace pour examiner les statistiques directionnelles en fonction de l'échelle, car elles sont basées sur des fonctions bien localisées dans l'espace, l'échelle et l'orientation. L'analyse est appliquéeà deuxécoulements MHD turbulents calculés par simulation numérique directe avec 512 3 points de la grilleà différentes intensités du champ magnétique imposé. Il se trouve que le champ magnétique imposé joue un rôle important sur l'amplification de l'anisotropie et de l'intermittence de l'écoulement.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Directional and scale-dependent statistics of quasi-static magnetohydrodynamic turbulence

et al. 2011

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“…Evolution of the vortices is slow relative to the background fluctuations which permits a separation of the flow into coherent and fluctuating components in the spirit of [20,21]. The highest amplitude coefficients of the wavelet transformed vorticity are assigned to the coherent component and the remainder to the incoherent component.…”

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Dynamics of Energy Condensation in Two-Dimensional Turbulence

et al. 2007

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We report a numerical study, supplemented by phenomenological explanations, of "energy condensation" in forced 2D turbulence in a biperiodic box. Condensation is a finite size effect which occurs after the standard inverse cascade reaches the size of the system. It leads to emergence of a coherent vortex dipole. We show that the time growth of the dipole is self-similar, and it contains most of the injected energy, thus resulting in an energy spectrum which is markedly steeper than the standard k −5/3 one. Once the coherent component is subtracted, however, the remaining fluctuations have a spectrum close to k −1 . The fluctuations decay slowly as the coherent part grows.PACS numbers: 47.27.E-,92.60.hk A big difference between 2D and 3D turbulence is the generation of large scale structures from small scale motions [1,2]. This occurs because, if pumped at intermediate scales, the 2D Navier-Stokes equations favor energy transfer to larger scales [3,4,5,6], a phenomenon known as an inverse cascade. Simulations [7,8] and experiments [9,10,11] show that large scale accumulation of energy is observed if conditions permit the energy to reach the system size. In this letter, we study the "condensate" emerging in the form of two coherent vortices in a biperiodic box in 2D. Let us begin by briefly reviewing the classical 2D turbulence theory of Kraichnan, Leith and Batchelor (KLB) [3,4,5]. The essential difference with 3D turbulence is the presence of a second inviscid invariant, in addition to energy, the enstrophy. Stirring the 2D flow leads to emergence of two cascades. Enstrophy cascades from the forcing scale, l, to smaller scales (direct cascade) while energy cascades from the forcing scale to larger scales (inverse cascade). Viscosity dissipates enstrophy at the Kolmogorov scale, η, which is much smaller than l when the Reynolds number is large. The energy cascade is blocked at a scale ζ, ζ ≫ l, by a frictional dissipation (usually due to friction between the fluid and substrate although other mechanisms can be imagined) after a transient in time quasi-stationary regime. Then a stationary KLB turbulence is established [3,4,5]. Applying Kolmogorov phenomenology (see e.g.[1]) KLB predicts an energy spectrum scaling as k −3 in the direct cascade, and as k −5/3 in the inverse cascade. Here k is the modulus of the wave-vector. The KLB spectra imply that velocity fluctuations at a scale r, δv r scale as ǫ 1/3 l −2/3 r and (ǫr) 1/3 in the direct and inverse cascade ranges respectively. KLB theory is confirmed by simulations [12,13] and experiments [2,14], where a sufficient range of scales was available to form the cascades. If the frictional dissipation is weak so that ζ exceeds the system size L then ultimately the "condensate" regime emerges [3,7] where the standard KLB does not apply.One of the primary motivations for studying 2D turbulence is that it is structurally and phenomenologically similar to quasi-geostrophic turbulence [15,16] which describes planetary atmospheres [17]. In addition, a recent resurgence i...

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“…Analysis of incompressible, e.g. [13][14][15], and compressible flow [11] show that coherent structures can be efficiently extracted and the statistics of the original fields is well preserved with a reduced set of degrees of freedom.…”

Section: Wavelet Filtered Equationsmentioning

confidence: 99%

Adaptive wavelet simulation of weakly compressible flow in a channel with a suddenly expanded section

Okamoto¹,

Domingues²,

Yoshimatsu³

et al. 2016

ESAIM: Proc.

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Abstract. We present an adaptive multiresolution simulation method for computing weakly compressible flow bounded by solid walls of arbitrary shape, using a finite volume (FV) approach coupled with wavelets for grid adaptation. A volume penalization method is employed to compute the flow in the Cartesian geometry and to impose the boundary conditions. A dynamical adaption strategy to advance both the locally refined grid and the flow in time uses biorthogonal wavelet transforms at each time step. We assess the quality and efficiency of the method for a two-dimensional flow in a periodic channel with a suddenly expanded section. The results are compared with a reference flow obtained by a non-adaptive FV simulation on a uniform grid. It is shown that the adaptive method allows for substantial reduction of CPU time and memory, while preserving the time evolution of the velocity field obtained with the non-adaptive simulation.Résumé. Nous développons une méthode de simulation multi-résolution adaptative pour calculer leś ecoulements faiblement compressibles délimités par des parois solides de forme arbitraire, en utilisant des ondelettes et une approcheen volume fini (FV). La pénalisation en volume est employée pour calculer l'écoulement dans une géométrie cartésienne. Une stratégie d'adaptation dynamique pour avancerà la fois la grille raffinée localement et le flux en temps utilise les ondelettes biorthogonalesà chaque pas de temps. Onévalue la qualité et l'efficacité de la méthode pour unécoulementà deux dimensions dans un canal avec une section soudainementélargie, en comparant avec un calcul de référence obtenu par une méthode en FV non adaptatif. Il est montré que la méthode adaptative permet une réduction substantielle du temps de calcul, tout en préservant l'évolution temporelle du champ de vitesse obtenu avec la simulation non adaptatif.

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Non-Gaussianity and coherent vortex simulation for two-dimensional turbulence using an adaptive orthogonal wavelet basis

Cited by 308 publications

References 14 publications

Directional and scale-dependent statistics of quasi-static magnetohydrodynamic turbulence

Directional and scale-dependent statistics of quasi-static magnetohydrodynamic turbulence

Dynamics of Energy Condensation in Two-Dimensional Turbulence

Adaptive wavelet simulation of weakly compressible flow in a channel with a suddenly expanded section

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