Abstract
An analytical expression for the profile of a periodic wave of finite amplitude on the surface of a deep viscous conducting liquid is obtained for the first time. The formula admits the transition to a limiting case of the ideal liquid. It is shown that the position of an internal nonlinear resonance of these capillary-gravitational waves depends neither on the medium viscosity nor on the surface charging. It is established that, during the resonance interaction, the energy is pumped from longwave capillary-gravitational oscillations with the wavenumber \(k_* \equiv \sqrt {\rho g/2\gamma } \) to shortwave oscillations with \(k_0 \equiv \sqrt {\rho g/2\gamma } \).
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Translated from Pis’ma v Zhurnal Tekhnichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 29, No. 8, 2003, pp. 1–7.
Original Russian Text Copyright © 2003 by Belonozhko, Grigor’ev.
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Belonozhko, D.F., Grigor’ev, A.I. On the internal nonlinear resonance of capillary-gravitational waves on the charged surface of a deep viscous liquid. Tech. Phys. Lett. 29, 309–311 (2003). https://doi.org/10.1134/1.1573300
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DOI: https://doi.org/10.1134/1.1573300