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

Figure 6

Qualitative behaviour of the phase difference Δ𝜔. Notice that if the point 𝐱⁺_𝑖𝑜 moves counterclockwise on 𝐶_𝑖(𝑡) to reach 𝐱⁻_𝑖𝑜, then Δ𝜔^⋆>0. The angle Δ𝜔^⋆ holds identically +𝜑 (a) or −𝜑 (b) on 𝐶_𝑖(𝑡) (bold line).

(a)

(b)