Effect of Detuning on the Development of Marginally Unstable Baroclinic Vortices

Gauthier, Pierre (1990). « Effect of Detuning on the Development of Marginally Unstable Baroclinic Vortices ». Journal of the Atmospheric Sciences, 47(8), pp. 999-1011.

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This paper is concerned with the weakly nonlinear inviscid dynamics of a marginally unstable baroclinic wave near the point of minimum critical shear of a two-layer quasi-geostrophic model on the β-plane. In previous studies by Pedlosky and by Warn and Gauthier (WG), the parameters of the model were chosen in a specific way in order to be exactly at the minimum. They showed that at this particular point, a complete inviscid coarse-grain homogenization of the potential vorticity occurs in the bottom layer causing the amplitude of the unstable wave to equilibrate. It is the purpose of the present paper to investigate the behavior of the dynamics when the problem is not exactly at the minimum and more specifically, to establish how one goes from the analytical solution of WG to the single wave theory that one expects to be valid away from minimum critical shear. The nonlinear evolution equations of WG are extended in order to include a “detuning parameter” σ associated with a perturbation of the aspect ratio of the periodic channel. An analytical solution not being available when σ ≠ 0, a spectral form of these equations similar to those found in Pedlosky is integrated numerically at high resolution. The results show that for a fixed supercritical shear and arbitrary but sufficiently small initial conditions, the size of the vortices is decreasing with σ causing the potential vorticity to mix only in part of the domain and the amplitude of the unstable wave to oscillate around a nonzero mean. When σ is sufficiently large, closed streamlines are no longer possible and no vortices are developing. At that point, the single wave theory is becoming a better approximation to the dynamics.

Type: Article de revue scientifique
Informations complémentaires: © Copyright [1990] AMS (https://www.ametsoc.org/ams/index.cfm/publications/authors/journal-and-bams-authors/author-resources/copyright-information/copyright-policy/)
Mots-clés ou Sujets: Baroclinic vortice, detuning, periodic channel, potential vorticity, super critical shear, unstable baroclinic wave
Unité d'appartenance: Faculté des sciences > Département des sciences de la Terre et de l'atmosphère
Déposé par: Pierre Gauthier
Date de dépôt: 26 avr. 2016 18:00
Dernière modification: 26 mai 2016 14:20
Adresse URL : http://archipel.uqam.ca/id/eprint/8304


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