We consider the linear stability of a thin differentially rotating gaseous disc with reflecting boundaries against non-axisymmetric perturbations. We assume the unperturbed disc to be in centrifugal equilibrium with the gravitational attraction of a central mass M, and consider discs whose mass can be neglected relative to M. We discuss the relevant conservation laws for the energy and angular momentum of linear non-axisymmetric modes in a thin rotating disc without self-gravity and illustrate the basic mode amplification mechanisms with help of some of our numerical solutions [1].
