Motion of Two Identical Point Vortices in a Simple Shear Flow

Motion of two identical point vortices in a simple shear flow is studied. According to the competition between the strength of the shear flow and that of the vortices, two vortices either separate being carried by the flow or rotate on a periodic orbit. The critical ratio of these strength is found, and computer simulations are made for various situations according to this criterion. The integrability of this system is also considered as a Hamiltonian system. Though the Hamiltonian is less symmetric than that of the case without a boundary or an external flow, the system is integrable according to the Liouville theorem.