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

Figure 10

Functions 𝑦=±𝑠√𝑡²+1 (red lines), their asymptotes (yellow), and the straight line 𝑦=𝑝−𝑞𝑡 (red) versus 𝑡, for (a) 𝑝=1.5, 𝑞=0.5<𝑠=1 and (b) 𝑞=1>𝑠=0.5. In (a) also the tangent lines at 𝑝=±𝑠²−𝑞² are drawn with green lines. Intersection points are marked with blue symbols.

(a)

(b)