Uniqueness for the Circular VortexPair in a Uniform Flow
Abstract
In the xyplane, there is a wellknown example of an exact formula for a steady ideal fluid flow, that is symmetric in the xaxis, that contains a pair of vortices bounded by a single circle, and whose farfield approaches a uniform flow in the xdirection. The stream function in this case has the form psi  y where psi obeys the partial differential equation Δ psi = (psi  y)_{+} for y > 0 while approaching 0 at infinity and vanishing on the xaxis. The present work proves a uniqueness theorem for this boundaryvalue problem, by using the consequences of the maximum principle to establish symmetry properties of its solutions. An isoperimetric property of the flow is also established.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 October 1996
 DOI:
 10.1098/rspa.1996.0125
 Bibcode:
 1996RSPSA.452.2343B