Velocity Induced by a Plane Uniform Vortex Having the Schwarz Function of Its Boundary with Two Simple Poles

Table 2

Behaviour with respect to the second property, consequences on the map 𝐳↦𝐱 and corresponding constraints on the poles 𝐳₁, 𝐳₂.

Kind	𝐱(𝒜)	Position of 𝒞^⋆	Constraints on 𝐳1, 𝐳2
1	Inside 𝑃	Internal to 𝒞	One inside and one outside 𝒞
		External to 𝒞	Both inside 𝒞
2	Outside 𝑃	Internal to 𝒞	Both outside 𝒞
		External to 𝒞	One inside and one outside 𝒞