Instability Modes Acoustically Excited in Baroclinic Vortices

The normal mode linear analysis is applied to investigate stability of a circular compressible vortex with the emphasis of studying the barclinic effect, Le., the effect of entropy stratification of the basic flow on stability properties. The vortex to be studied has a 'Igylor-type velocity distribution. The stratillcation of entropy is modelled by a Gaussian twoparametric profile, whose parameters control the maximal deviation from the homentropic distribution and the extent of the entropic zone. The results presented concern the effect of these parameters and the vortex intensity as well on instability characteristics, as the growth rate and the azimuthal phase frequency. Particularly, the Taylor homentropic vortex is found to be stable for sufficiently high intensities only, and ceases to be stable as the vortex intencity weakens. It is also presented an example situation, where unstable normal modes are excited. This is the scattering of sound waves by the vortex. By simulating this process numerically, we show that the scattered field due to incident of sound waves on the vortex becomes unstable, and takes a typical angular regular structure. The characteristics of this instability, Le., the growth rate and the azimuthal phase frequency coincides with those of unstable normal modes very closely, which definitely indicates the excitation of these normal modes in the sound scattering process. Keyword: Compressible vortex, Linear-stability analysis, Sound scattering