Uniqueness for the Circular Vortex-Pair in a Uniform Flow
In the x-y-plane, there is a well-known example of an exact formula for a steady ideal fluid flow, that is symmetric in the x-axis, that contains a pair of vortices bounded by a single circle, and whose far-field approaches a uniform flow in the x-direction. 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 x-axis. The present work proves a uniqueness theorem for this boundary-value 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.
Proceedings of the Royal Society of London Series A
- Pub Date:
- October 1996