Mechanism for the Faraday instability in viscous liquids

The wave number selection mechanism in the Faraday instability which occurs when standing waves form on the free surface of a liquid subjected to vertical sinusoidal oscillation, is discussed, focusing on the strong viscous effects. The relationship between Faraday instability and Rayleigh-Taylor instability is presented by performing linear stability calculations. In the case of deep water and strong viscous effects, the preferred wave number in the Faraday instability is primarily determined through a Rayleigh-Taylor instability. In shallow water, the difference between the Rayleigh-Taylor and Faraday wave numbers is evident due to the interaction between the oscillatory motion of the standing waves and the bottom boundary.