On the Hamiltonian dynamics of vortex lattices

Abstract

The equations of motion for infinite doubly periodic configurations of point vortices are derived. A Hamiltonian for the motion, generalizing that of Kirchhoff for finite configurations, is found and used to deduce an expression for the energy of an arbitrary vortex lattice. The energy of a lattice with periodic defects is computed. Some special stationary lattice configurations are shown to exist and integral curves for some two- and three-vortex lattice motions are exhibited. © 1989 American Institute of Physics.