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

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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.
Plain TeX, 7 pages, 2 postscript figures, uses epsf.tex

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