0.09424 & 0.10\

![Comparison of evolution of spherical harmonic spectra $Y_6^m$ for resolutions (a) $128^3$ and (b) $256^3$.[]{data-label="fig:valid_mspectra"}](fig4.eps){width="\textwidth"}

Figure \[fig:valid\_mspectra\] compares the time evolution of the envelope of the spherical harmonic coefficients $|\zeta_\ell^m|$ for capillary wave simulations using resolutions $128^3$ and $256^3$. The fluid parameters are again those of section \[sec:phys\_par\] and table \[tab:forcing\_response\] for the $\ell=6$ case. Starting from an icosahedral initial condition, the solution evolves similarly for the two spatial resolutions. The main difference is that near-zero modes grow more slowly for the higher resolution, which can be understood as a manifestation of the lower level of noise introduced in the simulation.

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   ![Free decay of a shape-deformed drop to the spherical shape. The evolution of $\Delta \zeta \equiv \zeta_{max}-\zeta_{min}$ with time is shown for $\ell=5$ for a resolution of $256^3$. The blue curve corresponds to the output from numerical simulations which is fitted by a nonlinear least-square method (dashed red). The green curve corresponds to the small-viscosity-limit prediction for viscosity (a) $\nu_d=10^{-5} m^2s^{-1}$ and (b) $\nu_d=10^{-4} m^2s^{-1}$.[]{data-label="fig:decL5a3"}](fig5.eps "fig:"){width="\textwidth"}
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  --------------------------------------------------- -------------------------------------- ------------ ------------------------------------------------ ------------------------------------------------------ ------------------------------------------------ ------------------------------------------------------ ------------------------------------ ------------------------------------------------ --
                       Viscosity                                  Spherical Mode              Numerical                                                                                                                                                                                                                                                                                                         
                                                                                              resolution                                                                                                                                                                                                                                                                                                        
   $\begin{array}{c}{\nu_d}\\(m^2s^{-1})\end{array}$   $\begin{array}{c}\ell\\~\end{array}$                $\begin{array}{c}\lambda\\(s^{-1})\end{array}$   $\begin{array}{c}\omega^\prime\\(s^{-1})\end{array}$   $\begin{array}{c}\lambda\\(s^{-1})\end{array}$   $\begin{array}{c}\omega^\prime\\(s^{-1})\end{array}$   $\dfrac{|\Delta\lambda|}{\lambda}$   $\dfrac{|\Delta\omega^\prime|}{\omega^\prime}$  
                       $10^{-5}$                                        5                      $128^3$                         0.122                                               3.711                                               