Diffusive instabilities of baroclinic lenticular vortices

Labarbe, Joris and Kirillov, Oleg N. (2021) Diffusive instabilities of baroclinic lenticular vortices. Physics of Fluids, 33 (10). p. 104108. ISSN 1070-6631

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Official URL: https://doi.org/10.1063/5.0068311

Abstract

We consider a model of a circular lenticular vortex immersed into a deep and vertically stratified viscous fluid in the presence of gravity and rotation. The vortex is assumed to be baroclinic with a Gaussian profile of angular velocity both in the radial and axial directions. Assuming the base state to be in a cyclogeostrophic balance, we derive linearized equations of motion and seek for their solution in a geometric optics approximation to find amplitude transport equations that yield a comprehensive dispersion relation. Applying algebraic Bilharz criterion to the latter, we establish that stability conditions are reduced to three inequalities that define stability domain in the space of parameters. The main destabilization mechanism is either monotonic or oscillatory axisymmetric instability depending on the Schmidt number (Sc), vortex Rossby number and the difference between the radial and axial density gradients as well as the difference between the epicyclic and vertical oscillation frequencies. We discover that the boundaries of the regions of monotonic and oscillatory axisymmetric instabilities meet at a codimension-2 point, forming a singularity of the neutral stability curve. We give an exhaustive classification of the geometry of the stability boundary, depending on the values of the Schmidt number. Although we demonstrate that the centrifugally stable (unstable) Gaussian lens can be destabilized (stabilized) by the differential diffusion of mass and momentum and that destabilization can happen even in the limit of vanishing diffusion, we also describe explicitly a set of parameters in which the Gaussian lens is stable for all Sc>0.

Item Type: Article
Additional Information: J.L. was supported by a Ph.D. Scholarship from Northumbria University and by a Postdoctoral Fellowship from the Institut de Mécanique et d’Ingénierie at Aix-Marseille Université. The research of O.N.K. was supported in part by the Royal Society grant IES\R1\211145.
Uncontrolled Keywords: vortex, Rotating shear flow, Stability analysis, Hydrodynamics, atmospheric turbulence, geophysics, mathematical modelling, asymptotic analysis
Subjects: F300 Physics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: John Coen
Date Deposited: 05 Oct 2021 08:17
Last Modified: 20 Oct 2021 13:30
URI: http://nrl.northumbria.ac.uk/id/eprint/47423

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