Europhys. Lett.
Volume 48, Number 1, October 1999
Page(s) 49 - 52
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 01 September 2002
DOI: 10.1209/epl/i1999-00112-5

Europhys. Lett, 48 (1), pp. 49-52 (1999)

Capillary-gravity waves: The effect of viscosity on the wave resistance

D. Richard and E. Raphaël

Collège de France, Physique de la Matière Condensée, URA 792 du CNRS
11 place Marcelin Berthelot, 75231 Paris cedex 05, France

(received 12 March 1999; accepted in final form 8 August 1999)

PACS. 47.35+i - Hydrodynamic waves.
PACS. 68.10-m - Fluid surfaces and fluid-fluid interfaces.


The effect of viscosity on the wave resistance experienced by a two-dimensional perturbation moving at uniform velocity over the free surface of a fluid is investigated. The analysis is based on Rayleigh's linearized theory of capillary-gravity waves. It is shown in particular that the wave resistance remains bounded as the velocity of the perturbation approaches the minimum phase speed $c^{\rm min} = (4 g
\gamma /\rho)^{1/4}$ ($\rho$ is the liquid density, $\gamma$ is the liquid-air surface tension, and g the acceleration due to gravity), unlike what is predicted by the inviscid theory.


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