On the Hydromagnetic Stability Analysis of Inviscid Compressible Annular Flows

The hydromagnetic stability of inviscid compressible flows with axial and azimuthal velocity components in an annular channel has been studied to axisymmetric disturbances. An estimate for the growth rate of arbitrary unstable disturbances is obtained. It is shown that the complex phase-velocity of any unstable magneto-subsonic axisymmetric mode must lie in a semiellipse-type region, which depends on the parameters of compressibility, stratification and the magnetic field. For a monotonic axial velocity profile, this semiellipse-type instability region reduces to the line \(c_{i}=0\) as the minimum Richardson number \({\widetilde{J}}_{m}\rightarrow \frac{1}{4}-\) in accord with the Richardson number criterion. Further, an semi-elliptical instability region depending on the minimum local Richardson number is also obtained for a class of magneto-supersonic axisymmetric disturbances.