The dynamical stability of differentially rotating discs - II

We extend our investigation of the dynamical stability of differentially rotating fluid tori of uniform entropy to the case in which there is a gradient of specific angular momentum. This case is much more complicated and in this paper we limit ourselves to an analytic approach. Our overall conclusions are that (i) the dynamical instabilities found to exist in constant specific angular momentum tori persist in this case; (ii) additional unrelated Kelvin–Helmholtz-like instabilities are introduced by allowing a gradient in specific angular momentum and (iii) the general unstable mode is a mixture of these two.