A Zermelo navigation problem with a vortex singularity

Helhmoltz–Kirchhoff equations of motions vortices an incompressible fluid in the plane define a dynamics with singularities and this leads to Zermelo navigation problem describing ship travel such field where control is heading angle. Considering one vortex, we time minimization which can be analyzed technics geometric optimal combined numerical simulations, frame being extension Randers metrics punctured plane, rotational symmetry. Candidates as minimizers are parameterized thanks Pontryagin Maximum Principle extremal solutions Hamiltonian vector field. We analyze minimal solution transfer between two points during either strong current region vicinity vortex or weak region. The analysis based on micro-local classification extremals using mainly integrability properties due discussion complex related existence isolated (Reeb) circle singularity. explicit computation cut curves cease given spheres described case at initial point weak.