On the criterion for stability of a layer of viscous fluid heated from below

Abstract

1. An analogy has been drawn by the present writer between Bénard's problem of the modes of instability of a layer of viscous fluid initially at rest under gravity between horizontal plane boundaries heated below and cooled above, and Prof. G. I. Taylor's problem of the modes of instability of a viscous fluid initially in steady cyclic motion under inertia forces between concentric circular cylinders rotating with constant unequal angular velocities. Rayleigh obtained a solution of Bénard's problem for two boundaries with no tangential forces between boundary and fluid, while in Taylor's problem there are two boundaries with no slip.