The governing equations of motion of two point vortices in an ideal fluid in the plane has a Hamiltonian formulation that is completely integrable, so the dynamics are regular in the sense that one has quasiperiodic solutions confined to invariant two-dimensional tori accompanied by periodic orbits. Moreover, it is well known that the same is true of the dynamics of two point vortices in an ideal fluid in a standard half-plane (with a straight line boundary). It is natural to ask if this is also the case for half-planes whose boundaries are perturbations of a straight line. We prove here that there are such Hamiltonian perturbations of two vortex dynamics in the half-plane that generate chaotic - and a fortiori nonintegrable - dynamics, thereby answering an open question of rather long standing. Our proof, like most demonstrations of this kind, is based on Melnikov's method. © 2008 Springer.
CITATION STYLE
Blackmore, D. (2008). Nonintegrable perturbations of two vortex dynamics. In Solid Mechanics and its Applications (Vol. 6, pp. 331–340). Springer Verlag. https://doi.org/10.1007/978-1-4020-6744-0_29
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