On the principle of exchange of stabilities for the viscous flow between two co-axial rotating cylinders

Abstract

In the first part of this paper we have derived an adjoint system of equations for the set of equations characterising the solution of the stability of viscous flow between two rotating cylinders, when the marginal stability is assumed not to be stationary. Then the adjoint system of differential equations has been solved to arrive at a simpler secular equation than the one obtained by Chandrasekhar. By a different approach than that of Chandrasekhar's, an attempt is made to show that for μ, which is defined as the ratio of the velocities Ω1 and Ω2 with which the inner and outer cylinders are rotated, greater than zero, there is no possibility of the instability setting in as overstability.