Resonance Type Instabilities in the Gaseous Disks of the Flat Galaxies I. The Acoustical Resonance Type Instability and the Absence of Vortex Sheet Stabilization on Shallow Water

Linear analysis of vortex sheet stability in the rotating gaseous disk or shallow water layer shows that presence of a central reflecting surface changes system stability significantly. An effect of absence of vortex sheet stabilization has been found as compressibility exceeds Landau criterion. The properties of multimode short-scale instability of acoustical resonance type are investigated and probability of its influence upon experiments on the rotating shallow water is discussed.