Modulation-self-focusing instability of gravity-capillary waves in a wide range of angles and frequencies
https://doi.org/10.59887/2073-6673.2025.18(1)-4
Abstract
The theory of instability of gravity-capillary waves on the surface of a liquid taking into account linear and nonlinear dispersions is presented. Theoretical research is carried out on the basis of the use of an integrodiffrence operator to describe the linear dispersion of waves. Increments of instability are found. It is shown that the use of an integrodiffrence operator to describe the gravity wave linear dispersion without taking into account their nonlinear dispersion leads to the instability region limitation compared to the case of using the nonlinear Schrödinger equation, but does not change the increment value. The dispersion of the nonlinearity of gravity surface waves reduces increments, especially at large detunes. The structure of instability changes for gravity-capillary waves propagating with minimal phase and group velocities: as the wavelength decreases, the instability region narrows and then disappears. The boundaries of the disappearance of instability area are determined. With a further wavelength decrease, instability occurs again. It acquires the features of “collapse”, when the instability region becomes elliptical. The instability of waves with large wave numbers has a “self-focusing” character, in contrast to the modulation nature of the instability of waves with small wave numbers. Nonlinear dispersion in gravity-capillary waves, as well as in gravity waves, leads to the suppression of instability under large detunes.
Keywords
Supporting agencies: The study was funded by a grant from the Russian Science Foundation No 24-27-00363, https//rscf.ru/project/24-27-00363/.
About the Authors
V. V. Bakhanov
A. V. Gaponov-Grekhov Institute of Applied Physics RAS
Russian Federation
Russian Federation
WoS ResearcherID: ISV-2716-2023, Scopus AuthorID: 6603623205
46 Ulyanova Str., Nizhny Novgorod 603950
S. N. Vlasov
A. V. Gaponov-Grekhov Institute of Applied Physics RAS
Russian Federation
Russian Federation
Scopus AuthorID: 9635365600, AuthorID: 18637
46 Ulyanova Str., Nizhny Novgorod 603950
E. V. Koposova
A. V. Gaponov-Grekhov Institute of Applied Physics RAS
Russian Federation
Russian Federation
WoS ResearcherID: ABA-2386-2021, Scopus AuthorID: 6603370107
46 Ulyanova Str., Nizhny Novgorod 603950
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Review
For citations:
Bakhanov V.V., Vlasov S.N., Koposova E.V. Modulation-self-focusing instability of gravity-capillary waves in a wide range of angles and frequencies. Fundamental and Applied Hydrophysics. 2025;18(1):41-52. (In Russ.) https://doi.org/10.59887/2073-6673.2025.18(1)-4
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