Parametric instability in a fluid with temperature-dependent surface tension

Stability of the free surface of a viscous fluid with temperature-dependent surface tension, vibrated sinusoidally in the vertical direction, is presented. The onset of surface waves in a thick layer of fluid is delayed by the inhomogeneity in the surface tension. The latter pushes the marginal stability curves corresponding to harmonic waves upward in the forcing amplitude–wave-number plane more than those corresponding to subharmonic waves in thin layers of low Prandtl number fluids. This leads to an interesting possibility of a multicritical point at the instability onset that may involve only subharmonic waves of different wave numbers