Hollow vortex in a corner

Equilibrium solutions for hollow vortices in straining flow in a corner are obtained by solving a free-boundary problem. Conformal maps from a canonical doubly connected annular domain to the physical plane combining the Schottky-Klein prime function with an appropriate algebraic map lead to a problem similar to Pocklington's propagating hollow dipole. The result is a two-parameter family of solutions depending on the corner angle and on the non-dimensional ratio of strain to circulation.

Automated summary

Equilibrium solutions for hollow vortices in straining flow in a corner are obtained by solving a free-boundary problem. The solutions depend on the corner angle and on the non-dimensional ratio of strain to circulation, resulting in a two-parameter family of solutions.