Abstract
The motion of three interacting point vortices in the plane can be thought of as the motion of three geometrical points endowed with a dynamics. This motion can therefore be reformulated in terms of dynamically evolving geometric quantities, viz., the circle that circumscribes the vortex triangle and the angles of the vortex triangle. In this study, we develop the equations of motion for the center, , and radius, , of this circumcircle; and for the angles of the vortex triangle, , and ; and for the triangle orientation given by . The equations of motion for , and form an autonomous dynamical system. A number of known results in the three-vortex problem follow readily from the equations, giving an alternate geometrical perspective on the problem.
- Received 25 May 2017
DOI:https://doi.org/10.1103/PhysRevFluids.3.024702
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