We present a linear stability analysis of parametrically excited surface waves for the case of viscous fluids. We show that the inclusion of viscosity leads to an extension of Mathieu’s differential equation, which is valid for the case of inviscid fluids, in the form of an integrodifferential equation. We numerically solve this equation for the case of a single as well as a double frequency excitation.

• Received 16 May 1994

DOI:https://doi.org/10.1103/PhysRevE.51.1162