Two-Dimensional Point Vortex

Consider a point vortex with the strength Г located at (x0, z0). Again using the definitions of the points, as in Fig. 10.2, and the results of Section 3-Я the increment to the velocity potential at a point P is

(10.8)

and the increments in the velocity components are

__T_____ Z ~Zq

u 2л(х – x0)2 + (z – 2o)2 – Г X – x0

Ш —- .1. —P —и

2я (x – x0)2 + (z – Zo)2

Note that all these point elements fulfill the requirements presented in Fig. 10.1. That is, the increments of the velocity components and potential at P depend on the geometry (x, z, x0, Zq) and the strength of the element.