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

Published in Physical Review Fluids. 2018, vol. 3, no. 12, p. 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.
Keywords Fluid mechanicsSurface wavesNonlinear wavesViscosity
arXiv: 1805.06777
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Research groups Groupe Kasparian
ISE Climat
ISE Pôle Sciences
Projects FNS: 200020-175697
FNS: 200021-155970
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ARMAROLI, Andrea et al. Viscous damping of gravity-capillary waves: Dispersion relations and nonlinear corrections. In: Physical Review Fluids, 2018, vol. 3, n° 12, p. 124803. https://archive-ouverte.unige.ch/unige:112386

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Deposited on : 2018-12-18

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