Abstract
The stability of the free surface of a viscous liquid layer with a horizontally infinite extent under a vertical oscillation is investigated theoretically using linear perturbation theory. In this paper, the vertical oscillation is assumed to be sinusoidal. In the case that the liquid layer consists of a perfect fluid, this problem is reduced to Mathieu's equation. In regard to a viscous fluid, the approximate solutions of the given wave numbers are found analytically in the case of 1/2 subharmonic and harmonic resonance, and the stability boundaries for various wave numbers, i.e. the neutral stability curves, are obtained in the frequency-amplitude plane. It is found from these neutral stability curves that 1/2 subharmonic resonance arises within most of the parameter ranges, but harmonic resonance does so only in the case of a thin liquid layer.
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