Surface Quasi-Geostrophy

Lapeyre, Guillaume

doi:10.3390/fluids2010007

Cited by 106 publications

(88 citation statements)

References 154 publications

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“…The physical motivation for the inviscid SQG equation comes from the 3D quasi-geostrophic (QG) equation, which is an approximate description for the motion of a rotating stratified fluid with small Rosby number and small Froude number in which potential vorticity is conserved [41,27]. The SQG equation is obtained from the QG equation by assuming the potential vorticity is identically zero.…”

Section: Generalized Surface Quasi-geostrophic Equationmentioning

confidence: 99%

Justification of the Point Vortex Approximation for Modified Surface Quasi-Geostrophic Equations

Rosenzweig¹

2020

SIAM J. Math. Anal.

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Section: Generalized Surface Quasi-geostrophic Equationmentioning

confidence: 99%

Justification of the Point Vortex Approximation for Modified Surface Quasi-Geostrophic Equations

Rosenzweig¹

2020

SIAM J. Math. Anal.

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“…Noting the significance of surface buoyancy gradients (a fact missed in the aforementioned first baroclinic mode framework), it has been suggested that surface QG (SQG) dynamics (Blumen, ; Held et al, ; Lapeyre, ) is a more appropriate framework for the oceans' surface (Klein et al, ; Lapeyre & Klein, ; Sasaki & Klein, ), and is reflected in the altimeter measurements (Lapeyre, ). Though the variance of buoyancy is transferred downscale (Pierrehumbert et al, ; Sukhatme & Pierrehumbert, ), even in the presence of an ambient buoyancy gradient (Sukhatme & Smith, ), surface KE actually flows upscale in SQG dynamics (Capet et al, ; Smith et al, ), consistent with the flux calculations using altimetry data.…”

Section: Introductionmentioning

confidence: 99%

Surface Ocean Enstrophy, Kinetic Energy Fluxes, and Spectra From Satellite Altimetry

et al. 2018

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Spectra and fluxes of enstrophy and kinetic energy (KE) are estimated in different parts of the midlatitudinal oceans using geostrophic currents derived from altimetry data. The presence of a strong inverse flux of surface KE is confirmed at scales larger than approximately 200 km, whereas a robust enstrophy cascading regime, accompanied by an approximate k−3 KE spectrum, is observed from about 200 to 100 km. The character of fluxes and spectra is shown to compare favorably with those from a comprehensive Earth system model. In addition, as gridded altimeter data are affected by smoothening and interpolation, the qualitative robustness of the results is verified by sensitivity experiments using space and time‐filtered output from the Earth system model. Given the rotational character of the flow, this large‐scale inverse KE and smaller‐scale forward enstrophy transfer scenario is consistent with expectations from three‐dimensional rapidly rotating and strongly stratified turbulence studies as well as detailed analyses of spectra and fluxes in the upper‐level midlatitude troposphere. In further accord with results from the atmosphere, decomposing the currents into stationary and eddy components (demarcated here by variability greater and less than 100 days, respectively), it is seen that, in addition to the eddy‐eddy contribution, the stationary‐eddy and stationary‐stationary fluxes play a significant role in the inverse (forward) flux of KE (enstrophy). Thus, it is quite possible that, from about 200 to 100 km, the altimeter is capturing the rotationally dominated portion of a surface oceanic counterpart of the upper tropospheric Nastrom‐Gage spectrum.

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“…[3][4][5][6][7][8][9][10][11][12][13]). In the present article, we focus on the surface quasi-geostrophic (SQG) model [1,[14][15][16] obtained when α = 1. This model emerges in the study of atmospheric and oceanic dynamics when the active scalar is given by the temperature at one of the boundaries (e.g.…”

Section: Introductionmentioning

confidence: 99%

Collapse of generalized Euler and surface quasigeostrophic point vortices

Badin

Barry

2018

Phys. Rev. E

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Point-vortex models are presented for the generalized Euler equations, which are characterized by a fractional Laplacian relation between the active scalar and the stream function. Special focus is given to the case of the surface quasigeostrophic (SQG) equations, for which the existence of finite-time singularities is still a matter of debate. Point-vortex trajectories are expressed using Nambu dynamics. The formulation is based on a noncanonical bracket and allows for a geometrical interpretation of trajectories as intersections of level sets of the Hamiltonian and Casimir. Within this setting, we focus on the collapse of solutions for the three-point-vortex model. In particular, we show that for SQG the collapse can be either self-similar or non-self-similar. Self-similarity occurs only when the Hamiltonian is zero, while non-self-similarity appears for nonzero values of the same. For both cases, collapse is allowed for any choice of circulations within a permitted interval. These results differ strikingly from the classical point-vortex model, where collapse is self-similar for any value of the Hamiltonian, but the vortex circulations must satisfy a strict relationship. Results may also shed a light on the formation of singularities in the SQG partial differential equations, where the singularity is thought to be reached only in a self-similar way.

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Surface Quasi-Geostrophy

Cited by 106 publications

References 154 publications

Justification of the Point Vortex Approximation for Modified Surface Quasi-Geostrophic Equations

Justification of the Point Vortex Approximation for Modified Surface Quasi-Geostrophic Equations

Surface Ocean Enstrophy, Kinetic Energy Fluxes, and Spectra From Satellite Altimetry

Collapse of generalized Euler and surface quasigeostrophic point vortices

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