Buoyancy-surface tension instability by the method of energy

The energy theory, giving a sufficient condition for stability, is developed for the motions in a horizontal, heated layer subject to buoyancy and surface tension effects. The free surface is assumed to be non-deformable (Pearson's 1958 model). It is shown that the equations governing the energy theory are the symmetric part of the time-independent linear theory problem, and that the surface tension terms behave like a bounded perturbation to the Bénard problem. The qualitative behaviour of the optimal stability boundary as a function of its parameters is given. The optimal stability boundary is computed, and compared with previous linear and non-linear stability theories in terms of allowable subcritical instabilities.