| Issue |
MATEC Web Conf.
Volume 211, 2018
The 14th International Conference on Vibration Engineering and Technology of Machinery (VETOMAC XIV)
|
|
|---|---|---|
| Article Number | 04008 | |
| Number of page(s) | 7 | |
| Section | DS: Dynamic Stability, Deterministic, Chaotic and Random Post-Critical States; TP10: Vibration and waves; TP13: Wave propagation | |
| DOI | https://doi.org/10.1051/matecconf/201821104008 | |
| Published online | 10 October 2018 | |
Study of finite amplitude capillary waves stability
1
Institute for Problems in Mechanics RAS,
Pr. Vernadskogo 101-1,
119526
Moscow,
Russia
2
Moscow Institute of Physics and Technology,
Institutskiy per. 9,
141700
Dolgoprudny,
Russia
* e-mail: petrovipmech@gmail.com
** e-mail: masha.alexandra@gmail.com
The direct Lyapunov method is used to study capillary waves. The dynamic equations of the capillary wave are presented in the form of an infinite Euler-Lagrange chain of equations for the Stokes coefficients. The stationary solution found for these equations is the Crapper solution for capillary waves. With the help of energy and momentum conservation laws the Lyapunov function is constructed. It is shown that the Lyapunov function is positive definite with respect to any perturbations of waves surfaces with the period that is a multiple of the wave period.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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