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arXiv · 1805.06777

Viscous damping of gravity-capillary waves: Dispersion relations and nonlinear corrections

Andrea Armaroli·Debbie Eeltink·Maura Brunetti·Jérôme Kasparian
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Abstract

We discuss the impact of viscosity on nonlinear propagation of surface waves at the interface of air and a fluid of large depth. After a survey of the available approximations of the dispersion relation, we propose to modify the hydrodynamic boundary conditions to model both short and long waves. From them, we derive a nonlinear Schrödinger equation where both linear and nonlinear parts are modified by dissipation and show that the former plays the main role in both gravity and capillary-gravity waves while, in most situations, the latter represents only small corrections. This provides a justification of the conventional approaches to damped propagation found in the literature.

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Andrea Armaroli, Debbie Eeltink, Maura Brunetti, Jérôme Kasparian. 2018-12-17. Viscous damping of gravity-capillary waves: Dispersion relations and nonlinear corrections. https://doi.org/10.1103/physrevfluids.3.124803

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