Oscillatory instabilities in the Rayleigh–Bénard problem with a free surface

Abstract
The linear stability theory of the Rayleigh–Bénard problem when the fluid is bounded above by a free deformable surface is studied numerically. When the free surface is thermally insulated and the lower surface is isothermic the marginal curve for the onset of oscillatory convection lies below the marginal curve for the exchange of stabilities.