A Numerical Algorithm for Optimal Control Problems with a Viscous Point Vortex

The dynamics of passive tracers in flows dominated by perfect or viscous point vortices is a broad area of research that continues to attract the attention of numerous studies. Recently, there has been a particular interest in the application of control theory to these issues. Viscous point vortices are singular solutions of the two-dimensional incompressible Navier-Stokes equations in which the vorticity is concentrated at a finite number of points in the flow domain, each of which carries a certain amount of time-invariant circulation. By definition, a passive tracer is a point vortex with zero circulation. This paper describes some numerical investigations of passive tracers performed by viscous point vortices to find the energy-optimal displacement of a passive particle. The numerical results show the existence of near/quasi-optimal controls.