Motion of a vortex pair between parallel walls

• Published in: Journal of applied mechanics and technical physics Vol. 24; no. 5; pp. 663 - 667
• Main Authors: Geshev, P. I., Ezdin, B. S.
• Format: Journal Article
• Language: English
• Published: 01.01.1984
• Subjects: boundary layers; dynamics; turbulent flow; vortices
• ISSN: 0021-8944; 1573-8620
• DOI: 10.1007/BF00905879

In addition to ideal fluid hydrodynamics, the concept of point vortices is used in the theory of superfluid helium, as well as in the model of a strongly magnetized plasm where the behavior of the electrons and ions is mathematically equivalent to vortex motion. Although energy dissipation effects are always present in real phenomena occurring in a continuous medium, a large class of problems exists where these effects can be neglected. This is valid for any vortex system being examined in short time intervals. In liquid helium at temperatures close to absolute zero, the energy dissipation can generally be neglected, and the system of quantum vortices considered as ideal. The question of integrability of the vortex equations of motion is interesting. If the domain of vortex motion is bounded by impermeable walls, then the stochasticity already appears in a system of two vortices. It is shown in this paper that the motion of two vortices between parallel walls is still another exactly integrable case.