A vortex pair in a weak external flow: a singular control approach

Dmitri Vainchteine and Igor Mezic

DEAS, Harvard University, Cambridge, 02138, USA

Abstract: The problem of controlling the position of a pair of point vortices using a strain field or a field of a single souce/sink is considered using the methods of singular control and the theory of perturbations of dynamical systems. We show that the averaging over the fast rotation of vortices around the center of vorticity reduces the order of system of evolution equations and allows us to achieve desired control using a single control field. We use the Pontrygin maximum principle to construct an optimal control. We discuss how these results can be applied to a more complicated structures in fluids.