# Dispersion and viscous attenuation of capillary waves with finite amplitude

## TL;DR

This study uses numerical simulations to analyze how finite amplitude affects the dispersion and viscous attenuation of capillary waves, revealing amplitude-dependent attenuation but amplitude-independent critical wavenumber.

## Contribution

It provides an empirical correlation for amplitude effects and demonstrates the self-similarity of wave dispersion across regimes, extending analytical solutions to moderate amplitudes.

## Key findings

- Viscous attenuation increases with wave amplitude.
- Critical wavenumber remains unchanged regardless of amplitude.
- Analytical solutions are applicable to moderate amplitudes.

## Abstract

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.