  We present a comprehensive study of the dispersion of capillary waves with
finite amplitude, based on direct numerical simulations. The presented results
show an increase of viscous attenuation and, consequently, a smaller frequency
of capillary waves with increasing initial wave amplitude. Interestingly,
however, the critical wavenumber as well as the wavenumber at which the maximum
frequency is observed remain the same for a given two-phase system,
irrespective of the wave amplitude. By devising an empirical correlation that
describes the effect of the wave amplitude on the viscous attenuation, the
dispersion of capillary waves with finite initial amplitude is shown to be, in
very good approximation, self-similar throughout the entire underdamped regime
and independent of the fluid properties. The results also shown that analytical
solutions for capillary waves with infinitesimal amplitude are applicable with
reasonable accuracy for capillary waves with moderate amplitude.
