New stationary solutions to the problem of three vortices in a two-layer fluid

Mikhail Sokolovskiy , Jacques Verron (1)

1 LEGI - Laboratoire des Écoulements Géophysiques et Industriels [Grenoble]

The universally integrable problem of three vortices [1, 4–6] has attracted the interest of researchers for over one hundred years [6]. This is not associated only with the vortex problem in itself but also has numerous analogies in the mechanics of solids, astrophysics, the dynamics of superfluid helium, and mathematical biology [1, 5]. A new peak of interest in this problem was stimulated by the discovery of so-called three-polar structures [13], i.e., symmetric triples of vortices and by later observation of their spontaneous origin from chaos [12]. In most studies [1, 4–7, 10, 12–15], the dynamics of vortices was analyzed in the framework of the homogeneous-fluid model. At the same time, the geophysical problems (some of them were discussed in [2, 3, 8, 11]) are characterized by noticeable density stratification. In this paper, we analyze the problem of three vortices that exist in a twolayer fluid and have zero total intensity.

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Mikhail Sokolovskiy, Jacques Verron. New stationary solutions to the problem of three vortices in a two-layer fluid. Doklady Akademii Nauk, 2002, 47 (3), pp.233-237. ⟨10.1134/1.1467869⟩. ⟨hal-00230191⟩