anticyclonic background rotation, there exist eigenmodes which decay as r ?? Ro < ?1), there is a centrifugal instability as shown in Sec. V. Figure 19 shows the frequency and the growth rate for f/ =? 0.4 (centrifugally unstable) and f/ =?2 (centrifugally stable) We see that there are two frequency branches: one starts from ? = f at non-zerõ k and increases with?kwith? with?k, while the other starts at ? =? f and decreases with?kwith? with?k (Figure 19(a)) For f/ =? 0, these frequency branches meet at a finite?kfinite? finite?k and become unstable for larger?klarger? larger?k when they meet while for f/ =?2, they do not meet and remains neutral whatever?kwhatever? whatever?k, p.86601, 2013. ,
Vibrations of a columnar vortex, Philos. Mag. Ser, vol.10, issue.61, pp.155-168, 1880. ,
Vortex Dynamics, 1992. ,
Kelvin waves and the singular modes of the Lamb???Oseen vortex, Journal of Fluid Mechanics, vol.551, issue.-1, pp.235-274, 2006. ,
DOI : 10.1017/S0022112005008463
Instability of a vertical columnar vortex in a stratified fluid, Experiments in Fluids, vol.448, issue.5, pp.673-681, 2010. ,
DOI : 10.1007/s00348-010-0833-0
URL : https://hal.archives-ouvertes.fr/hal-00431323
Radiative instability of the flow around a rotating cylinder in a stratified fluid, Journal of Fluid Mechanics, vol.228, pp.130-146, 2011. ,
DOI : 10.1017/S0022112075000742
URL : https://hal.archives-ouvertes.fr/hal-01349128
Waves on a columnar vortex in a strongly stratified fluid, Physics of Fluids, vol.21, issue.10, p.106602, 2009. ,
DOI : 10.1063/1.3248366
URL : https://hal.archives-ouvertes.fr/hal-00421934
Radiative instability in stratified vortices, Physics of Fluids, vol.21, issue.9, p.96602, 2009. ,
DOI : 10.1063/1.3241995
Damping and pumping of a vortex Rossby wave in a monotonic cyclone: Critical layer stirring versus inertia???buoyancy wave emission, Physics of Fluids, vol.16, issue.5, p.1334, 2004. ,
DOI : 10.1063/1.1651485
Conditions That Inhibit the Spontaneous Radiation of Spiral Inertia???Gravity Waves from an Intense Mesoscale Cyclone, Journal of the Atmospheric Sciences, vol.63, issue.2, p.435, 2006. ,
DOI : 10.1175/JAS3641.1
The Spontaneous Imbalance of an Atmospheric Vortex at High Rossby Number, Journal of the Atmospheric Sciences, vol.65, issue.8, p.2498, 2008. ,
DOI : 10.1175/2007JAS2490.1
The instability of an axisymmetric vortex with monotonic potential vorticity in rotating shallow water, Journal of Fluid Mechanics, vol.183, issue.-1, pp.303-334, 1994. ,
DOI : 10.1175/1520-0469(1985)042 2.0.CO;2
Acoustic Destabilization of Vortices, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.290, issue.1372, p.353, 1979. ,
DOI : 10.1098/rsta.1979.0003
Radiative instability of an anticyclonic vortex in a stratified rotating fluid, Journal of Fluid Mechanics, vol.707, pp.381-392, 2012. ,
DOI : 10.1063/1.1369125
URL : https://hal.archives-ouvertes.fr/hal-01025047
Instability of an Axisymmetric Vortex in a Stably Stratified, Rotating Environment, Theoretical and Computational Fluid Dynamics, vol.11, issue.3-4, pp.305-322, 1998. ,
DOI : 10.1007/s001620050095
Baroclinic instability of Kirchhoff's elliptic vortex, Journal of Fluid Mechanics, vol.35, issue.-1, pp.253-271, 1994. ,
DOI : 10.1017/S0022112076001584
The strato-rotational instability of Taylor???Couette and Keplerian flows, Journal of Fluid Mechanics, vol.130, pp.147-161, 2010. ,
DOI : 10.1103/RevModPhys.70.1
An asymptotic description of vortex Kelvin modes, Journal of Fluid Mechanics, vol.542, issue.-1, pp.69-96, 2005. ,
DOI : 10.1017/S0022112005005185
Advanced Mathematical Methods for Scientists and Engineers, 1978. ,
DOI : 10.1007/978-1-4757-3069-2
Temporal instability modes of supersonic round jets, Journal of Fluid Mechanics, vol.597, pp.173-196, 2010. ,
DOI : 10.1063/1.869196
URL : https://hal.archives-ouvertes.fr/hal-00457627
On the dynamics of revolving fluids, Proc. R. Soc. London 93, pp.148-154, 1917. ,
An experimental study of unstable barotropic vortices in a rotating fluid, Journal of Fluid Mechanics, vol.35, issue.-1, pp.1-24, 1991. ,
DOI : 10.1063/1.864781
Asymptotics and Special Functions, 1974. ,
Generalized Rayleigh criterion for non-axisymmetric centrifugal instabilities, Journal of Fluid Mechanics, vol.542, issue.-1, pp.365-379, 2005. ,
DOI : 10.1017/S0022112005006464
URL : https://hal.archives-ouvertes.fr/hal-00015707
Inertial instability of intense stratified anticyclones. Part 1. Generalized stability criterion, Journal of Fluid Mechanics, vol.605 ,
DOI : 10.1063/1.869273
URL : https://hal.archives-ouvertes.fr/hal-01098636