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

I. A. Pastukhov ; A. I. Rudenko

Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 47 (2024) no. 2, pp. 117-128

Résumé

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

Détail

Keywords: capillary-gravity waves, current function trace, velocity potential, wave profile
Mots-clés : vortex dipole.