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

Andrea Armaroli*, Debbie Eeltink, Maura Brunetti, and Jérôme Kasparian

  • GAP Nonlinearity and Climate, Institute for Environmental Sciences, Université de Genève, Boulevard Carl-Vogt 66, 1211 Genève 4, Switzerland

  • *andrea.armaroli@unige.ch
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Phys. Rev. Fluids 3, 124803 – Published 17 December, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.124803

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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Phys. Rev. Fluids 3, 124803– Published 17 December, 2018
  • Received 17 May 2018
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