Instability of isolated compressible entropy-stratified vortices

Abstract

The normal mode linear analysis is applied to investigate the stability of a circular isolated compressible vortex with the emphasis on studying the effect of entropy stratification of the basic flow on stability properties. We study a family of vortices that have zero total circulation, with the swirl velocity being presented by a Taylor-type distribution in the radial direction. The stratification of entropy is modeled by a Gaussian two-parametric profile whose parameters control the maximal deviation from the homentropic distribution and the extent of the entropic zone. Results presented concern the effect of these parameters and the vortex intensity on instability characteristics. In particular, in the case of homentropic flow, vortices considered are found to be stable only for sufficiently high intensities and cease to be stable as the intensity weakens. As an example of the situation where unstable normal modes can be excited, the scattering of sound waves by the vortex flow is considered. By simulating this process numerically, we show that the scattered field becomes unstable in the course of time and acquires a typical periodical pattern in polar angle. The characteristics of this instability ͑viz., the growth rate and the azimuthal phase frequency͒ coincide with those of the linear analysis very closely. This fact shows conclusively that the instability is caused by the induction of unstable normal modes in the vortex by means of sound irradiation.

Gravitational instability and the formation of planetary systems of solar-type stars. Analytical review of relected rapers

“…-задачи Эмдена [63]; -задач Лидова [64]; -задачи о вихре газа [65]. Эти расчеты показали, что результаты, полученные с помощью разработанного численного метода, достаточно хорошо согласуются с решениями вышеуказанных задач.…”

Nonlinear stability of two-dimensional axisymmetric vortices in compressible inviscid medium in a rotating reference frame

“…In [38], [13], authors discuss different situation of instability in an inviscid compressible media. There exist works, where a linear analysis of stability of compressible vortex was performed in various setting, see [22], [30], [54], [12], [40], [27] and references therein. In [4], [14], [1] steady compressible vortices were constructed using hodograph plane transformations.…”