Thermalization and free decay in surface quasigeostrophic flows

Teitelbaum, Tomas; Mininni, Pablo D.

doi:10.1103/physreve.86.016323

Cited by 4 publications

(2 citation statements)

References 53 publications

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“…The evolution to statistical equilibria can also be examined in terms of spectral properties. In this context, Teitelbaum and Mininni [57] showed that generalized enstrophy thermalizes (the spectra of buoyancy variance behaving as k for large k), while generalized energy condenses (piling up at the largest scale).…”

Section: Physical Properties Of the Cascadementioning

confidence: 99%

Surface Quasi-Geostrophy

Lapeyre

2017

Fluids

106

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International audienceOceanic and atmospheric dynamics are often interpreted through potential vorticity, as this quantity is conserved along the geostrophic flow. However, in addition to potential vorticity, surface buoyancy is a conserved quantity, and this also affects the dynamics. Buoyancy at the ocean surface or at the atmospheric tropopause plays the same role of an active tracer as potential vorticity does since the velocity field can be deduced from these quantities. The surface quasi-geostrophic model has been proposed to explain the dynamics associated with surface buoyancy conservation and seems appealing for both the ocean and the atmosphere. In this review, we present its main characteristics in terms of coherent structures, instabilities and turbulent cascades. Furthermore, this model is mathematically studied for the possible formation of singularities, as it presents some analogies with three-dimensional Euler equations. Finally, we discuss its relevance for the ocean and the atmosphere

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Section: Physical Properties Of the Cascadementioning

confidence: 99%

Surface Quasi-Geostrophy

Lapeyre

2017

Fluids

106

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“…In the simulations, energy was initially concentrated at low wave numbers and was let to cascade to larger ones, and a long transient following the previous description was observed before the system reached full thermalization. The results were extended to helical hydrodynamic flows [6], magnetohydrodynamics [7], compressible flows [8], quantum turbulence [9,10], gyrokinetic plasma systems [11], the dyamo problem [12,13], and also to study the decay of quasigeostrophic turbulence [14].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of partially thermalized solutions of the Burgers equation

2018

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The spectrally truncated, or finite dimensional, versions of several equations of inviscid flows display transient solutions which match their viscous counterparts, but which eventually lead to thermalized states in which energy is in equipartition between all modes. Recent advances in the study of the Burgers equation show that the thermalization process is triggered after the formation of sharp localized structures within the flow called "tygers". We show that the process of thermalization first takes place in well defined subdomains, before engulfing the whole space. Using spatio-temporal analysis on data from numerical simulations, we study propagation of tygers and find that they move at a well defined mean speed that can be obtained from energy conservation arguments.

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Large-scale anisotropy in stably stratified rotating flows

et al. 2014

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We present results from direct numerical simulations of the Boussinesq equations in the presence of rotation and/or stratification, both in the vertical direction. The runs are forced isotropically and randomly at small scales and have spatial resolutions of up to 1024 3 grid points and Reynolds numbers of ≈ 1000. We first show that solutions with negative energy flux and inverse cascades develop in rotating turbulence, whether or not stratification is present. However, the purely stratified case is characterized instead by an early-time, highly anisotropic transfer to large scales with almost zero net isotropic energy flux. This is consistent with previous studies that observed the development of vertically sheared horizontal winds, although only at substantially later times. However, and unlike previous works, when sufficient scale separation is allowed between the forcing scale and the domain size, the total energy displays a perpendicular (horizontal) spectrum with power law behavior compatible with ∼ k −5/3 ⊥ , including in the absence of rotation. In this latter purely stratified case, such a spectrum is the result of a direct cascade of the energy contained in the large-scale horizontal wind, as is evidenced by a strong positive flux of energy in the parallel direction at all scales including the largest resolved scales.

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Thermalization and free decay in surface quasigeostrophic flows

Cited by 4 publications

References 53 publications

Surface Quasi-Geostrophy

Surface Quasi-Geostrophy

Dynamics of partially thermalized solutions of the Burgers equation

Large-scale anisotropy in stably stratified rotating flows

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