Interaction of two vortices in a flued with lower stagnation pressure

The flow field induced by two point vortices of strength $\Gamma$ at a distance $2h$ apart in a quiescent field with lower stagnation pressure is investigated. The flow field around the vortices is bounded by a free streamline with constant velocity $U$ determined by the difference in the stagnation pressures. For the parameter $\Lambda = 2\pi hU/\Gamma > 1$, the flow field around each vortex is isolated from the other and is bounded by a circular free streamline of radius $\Gamma /\left ( {2\pi U} \right )$. When $\Lambda = 1$, the two circular free streamlines just touch each other. When $\Lambda < 1$ the two flows merge and they are enclosed inside a single convex free streamline. Analytical solutions are presented for the merged flow field and the free streamline for the entire range of the parameter $\Lambda$.