Geodesic
Formation of capillary-gravity waves in the flow under the influence of a system consisting of two vortices
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 47 (2024) no. 2, pp. 117-128 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Keywords: capillary-gravity waves, current function trace, velocity potential, wave profile
Mots-clés : vortex dipole. 
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I. A. Pastukhov; A. I. Rudenko. Formation of capillary-gravity waves in the flow under the influence of a system consisting of two vortices. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 47 (2024) no. 2, pp. 117-128. http://geodesic.mathdoc.fr/item/VKAM_2024_47_2_a7/

[1] Sretenskii L. N., Teoriya volnovykh dvizhenii zhidkosti, Nauka, M., 1977, 816 pp.

[2] Gill A., Dinamika atmosfery i okeana, V 2-kh tomakh, v. 1, Mir, M., 1986, 399 pp.

[3] Uizem Dzh., Lineinye i nelineinye volny, Mir, M., 1977, 638 pp.

[4] Landau L. D., Lifshits E. M., Gidrodinamika, Nauka, M., 1986, 736 pp. | MR

[5] Ovsyannikov L. V., Zadacha o nestatsionarnom dvizhenii zhidkosti so svobodnoi granitsei, Nauka, Novosibirsk, 1967, 108 pp.

[6] Kamenkovich V. M., Koshlyakov M. N., Monin A. S., Sinopticheskie vikhri v okeane, 2-e izdanie, Gidrometeoizdat, L., 1987, 510 pp.

[7] Lamb G., Gidrodinamika, Gostekhizdat, M., 1947, 928 pp.

[8] Gabov S. L., Vvedenie v teoriyu nelineinykh voln, Izd-vo MGU, M., 1988, 287 pp. | MR

[9] Keldysh M. V., Izbrannye trudy. Mekhanika, Nauka, M., 1985, 568 pp. | MR

[10] Vladimirov V. S., Zharinov V. V., Uravnenie matematicheskoi fiziki, Fiziko-matematicheskaya literatura, M., 2000, 400 pp.

[11] Lavrentev M. A., Shabat B. V., Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1965, 716 pp. | MR

[12] Monin A. S., Krasitskii V. P., Yavleniya na poverkhnosti okeana, Gidrometeoizdat, L., 1985, 375 pp.