$\Delta \zeta \equiv \zeta_{max}-\zeta_{min}$ obtained via numerical simulations with a resolution of $256^3$ of capillary waves with the fluid parameters of section \[sec:phys\_par\] initialized with axisymmetric perturbations $Y_5^0$ for two different viscosities, along with curves obtained from the low-viscosity theory of -. Table \[tab:Lamb\] gives the values of the decay rates and nonlinear frequencies from figure \[fig:decL5a3\], along with additional cases in which the spherical mode and the spatial resolution have been varied. As could be expected, the deviation is lowest when the resolution is higher ($256^3$) so that the simulation is more accurate, and when the viscosity is lower ($\nu_d=10^{-5}ms^{-2}$) so that the low-viscosity theory is more applicable. This best-case deviation is about 7% for $\lambda$ and 2% for $\omega^\prime$ for $\ell=5$ and only about 3% for $\lambda$ and 1% for $\omega^\prime$ for $\ell=4$.

Survey of cases studied {#sec:cases}
-----------------------

Table \[tab:forcing\_response\] lists the simulations which we will describe in this paper. As an initial condition, we perturb the spherical interface by one of the following combinations of spherical harmonics:

$$\begin{aligned}
&      \mbox{Axisymmetric} && \mbox{all } \ell && \zeta - {R}\propto Y_\ell^0 \label{eq:axisym}\\
&\mbox{Tetrahedral}  && \ell=3&& \zeta-{R}\propto Y_3^2 + {\rm c.c.}
  \label{eq:tetra}\\
&\mbox{Cubic} && \ell=4&& \zeta - {R}\propto \sqrt{7}\: 