A NOTE ON THE STABILITY OF SWIRLING FLOWS WITH RADIUS-DEPENDENT DENSITY WITH RESPECT TO INFINITESIMAL AZIMUTHAL DISTURBANCES

Abstract

We study the stability of inviscid, incompressible swirling flows of variable density with respect to azimuthal, normal mode disturbances. We prove that the wave velocity of neutral modes is bounded. A further refinement of Fung’s semi-elliptical instability region is given. This new instability region depends not only on the minimum Richardson number, and the lower and upper bounds for the angular velocity like Fung’s semi-ellipse, but also on the azimuthal wave number and the radii of the inner and outer cylinders. An estimation for the growth rate of unstable disturbances is obtained and it is compared to some of the recent asymptotic results.