Vestnik КRAUNC. Fiz.-Mat. nauki. 2024. vol. 47. no. 2. P. 117 – 128. ISSN 2079-6641

PHYSICS
https://doi.org/10.26117/2079-6641-2024-47-2-117-128
Research Article
Full text in Russian
MSC 76B15

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Formation of capillary-gravity waves in the flow under the influence of a system consisting of two vortices

I. A. Pastukhov^\ast¹, A. I. Rudenko²

¹Immanuel Kant Baltic Federal University, 236041, Kaliningrad, st. A. Nevsky, 14, Russia
²Kaliningrad State Technical University, 236022, Kaliningrad, Sovetsky Ave., 1, Russia

Abstract. Capillary-gravity waves significantly change the general circulation of the water surface of the World Ocean: attenuation and collapse of longer waves, gas exchange and mixing in the upper layer, kinematics of surface suspensions, and, therefore, require additional study. In the framework of a twodimensional problem, the paper considers surface capillary-gravity waves without taking into account wind effects, but taking into account the isobaric approximation. The approach proposed by Keldysh is chosen as a quantitative basis. The object of perturbation located at a finite depth is a vortex dipole with constant curl. Two asymptotic solutions were obtained on the basis of analytical calculations: the first solution describes the profile of capillary-gravity waves located behind the vortex dipole; the second solution is the profile of capillary-gravity waves in front of the perturbation source. It is shown that the capillary component of the wave dominates in the formation of waves in front of the perturbation source, and the gravitational component dominates behind the obstacle. The relations between isobaric and barotropic effects on the free surface are qualitatively analyzed. The case for the gravitational component is considered; for this purpose, the technique of representing the wave profile using a Taylor polynomial was used.

Key words: capillary-gravity waves, current function trace, velocity potential, wave profile, vortex dipole.

Received: 29.06.2024; Revised: 16.08.2024; Accepted: 18.08.2024; First online: 26.08.2024

For citation. Pastukhov I. A., Rudenko A. I. Formation of capillary-gravity waves in the flow under the influence of a system consisting of two vortices. Vestnik KRAUNC. Fiz.-mat. nauki. 2024, 47: 2, 117-128. EDN: IMNHVJ. https://doi.org/10.26117/2079-6641-2024-47-2-117-128.

Funding. The grant of the Russian Science Foundation No. 22-19-20157 (https://rscf.ru/project/22-19-20157) and the grant in the form of a subsidy from the budget of the Kaliningrad region No. 14-C/2023.

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

^\astCorrespondence: E-mail: paigor@stud.kantiana.ru

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Pastukhov I. A., Rudenko A. I., 2024

© Institute of Cosmophysical Research and Radio Wave Propagation, 2024 (original layout, design, compilation)

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Information about the authors

Pastukhov Igor Andreevich – Postgraduate student in the field of ”Physics of Condensed Matter”, research assistant, Immanuel Kant Baltic Federal University, Kaliningrad, Russia, ORCID 0009-0006-0925-9686.

Rudenko Aleksey Ivanovich – Ph.D.(Phys. and Math.), Associate Professor, Dep. of Applied Mathematics and Information Technology, Kaliningrad State Technical University, Kaliningrad, Russia, ORCID 0000-0002-5666-9841.

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