Abstract
The dynamics of point vortices is generalized in two ways: first by making the strengths complex, which allows for sources and sinks in superposition with the usual vortices, second by making them functions of position. These generalizations lead to a rich dynamical system, which is nonlinear and yet has conservation laws coming from a Hamiltonian-like formalism. We then discover that in this system the motion of a pair mimics the behavior of rays in geometric optics. We describe several exact solutions with optical analogues, notably Snell's law and the law of reflection off a mirror, and perform numerical experiments illustrating some striking behavior. © 2011 Elsevier B.V. All rights reserved.
Original language | English |
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Pages (from-to) | 1636-1643 |
Number of pages | 7 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 240 |
Issue number | 20 |
DOIs | |
Publication status | Published - 1 Oct 2011 |
Keywords
- Complex variable strengths
- Geometric optics
- Hybrid systems
- Snell's law
- Vortex dynamics