Surface tension driven oscillatory instability in a rotating fluid layer

Abstract

Oscillatory convective instability is shown to occur in a rotating fluid layer when convection is caused by surface-tension gradients at a free surface. The asymptotic equations, valid when the Taylor number approaches infinity, are solved analytically, and the critical Marangoni number is evaluated numerically. Fluids with Prandtl numbers above 0·201 will exhibit only stationary instability. Fluids with smaller Prandtl numbers will exhibit oscillatory instability with the critical Marangoni number varying as M0T½ where M0 depends on the Prandtl number and T is the Taylor number.