|
This article is cited in 2 scientific papers (total in 2 papers)
Special Issue: 200th birthday of Hermann von Helmholtz
Something Old, Something New:
Three Point Vortices on the Plane
M. A. Stremler Department of Biomedical Engineering & Mechanics, Virginia Tech,
VA 24061 Blacksburg, USA
Abstract:
The classic problem of three point vortex motion on the plane is revisited by using the interior angles of the vortex triangle, $\theta_{j}$, $j=1,2,3$, as the key system variables instead of the lengths of the triangle sides, $s_j$, as has been used classically.
Similar to the classic approach, the relative vortex motion can be represented in a phase space, with the topology of the level curves characterizing the motion. In contrast to the classic approach, the alternate formulation gives a compact, consistent phase space representation and facilitates comparisons of vortex motion in a co-moving frame.
This alternate formulation is used to explore the vortex behavior in the two canonical cases of equal vortex strength magnitudes, $\Gamma_{1} = \Gamma_{2} = \Gamma_{3}$ and $\Gamma_{1} = \Gamma_{2} = -\Gamma_{3}$.
Keywords:
vortex dynamics, point vortices, three-vortex problem, potential flow.
Received: 21.06.2021 Accepted: 18.08.2021
Citation:
M. A. Stremler
Linking options:
https://www.mathnet.ru/eng/rcd1128
|
|