Abstract
The problem of locating stagnation points in the
flow produced by a system of N
interacting point vortices in two dimensions is considered. The general
solution follows
from an 1864 theorem by Siebeck, that the stagnation points are the foci
of a certain
plane curve of class N−1 that has all lines
connecting vortices pairwise as tangents. The
case N=3, for which Siebeck's curve is a conic,
is considered in some detail. It is
shown that the classification of the type of conic coincides with the known
classification
of regimes of motion for the three vortices. A similarity result for the
triangular
coordinates of the stagnation point in a flow produced by three vortices
with sum of
strengths zero is found. Using topological arguments the distinct streamline
patterns
for flow about three vortices are also determined. Partial results are
given for two
special sets of vortex strengths on the changes between these patterns
as the motion
evolves. The analysis requires a number of unfamiliar mathematical tools
which are
explained.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
30 articles.
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