On the equilibrium of circular flows under gravity

This paper investigates the stability of an incompressible inviscid rotatory couette flow confined between two corotating and coaxial vertical cylinders under the force field of gravity. The stationary distributions of density and pressure are functions of the radial and axial coordinates with the azimuthal component of velocity being an arbitrary function of radial coordinate. The perturbations concerned are axisymmetric and infinitesimaly small in nature. Sufficient criteria of instability are derived for both vertically stable and unstable density stratifications¹ and this clearly shows that the necessary and sufficient character of Rayleigh's criterion does not hold good in the present circumstances.