Dispersion and viscous attenuation of capillary waves with finite amplitude
1 Department of Mechanical Engineering, Imperial College London, Exhibiton Road, London, SW7 2AZ, UK
2 Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, 75005 Paris, France
a e-mail: email@example.com
Received: 29 June 2016
Revised: 23 August 2016
Published online: 2 May 2017
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.
© The Author(s) 2017
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