Abstract

If the matter rotates around a point-mass gravitating body it can form an axisymmetric torus that has a rotational profile determined by its pressure gradient distribution. Although a thick torus with a non-keplerian rotation bounded by the free surface has a set of global exponentially growing modes when it approaches a thin disc with an almost keplerian rotation this global acoustic instability ceases promptly and we get a nearly stable shearing flow. However, a substantial transient growth of linear perturbations measured by the evolution of their acoustic energy is possible even in this case. This fact is demonstrated for a simple model of a non-viscous polytropic thin disc of a finite radial size where small global adiabatic perturbations are considered as linear combinations of neutral modes with a corotational radius located beyond the outer boundary of the flow.