  Standing waves appear at the surface of a spherical viscous liquid drop
subjected to radial parametric oscillation. This is the spherical analogue of
the Faraday instability. Modifying the Kumar & Tuckerman (1994) planar solution
to a spherical interface, we linearize the governing equations about the state
of rest and solve the resulting equations by using a spherical harmonic
decomposition for the angular dependence, spherical Bessel functions for the
radial dependence, and a Floquet form for the temporal dependence. Although the
inviscid problem can, like the planar case, be mapped exactly onto the Mathieu
equation, the spherical geometry introduces additional terms into the analysis.
The dependence of the threshold on viscosity is studied and scaling laws are
found. It is shown that the spherical thresholds are similar to the planar
infinite-depth thresholds, even for small wavenumbers for which the curvature
is high. A representative time-dependent Floquet mode is displayed.

Fluid Dynamics