Vortex pair (opposite circulation)

Figure 6.8: A pair of PVs with equal but opposite circulation.

Each PV in Figure (6.8) moves with the flow induced by the other - see $D\omega/Dt = 0$ (6.12). In terms of $(v_{x},v_{y})$

$${\bf v}(PV1) = (0,\Gamma_{0}/2\pi \ell),~~~~{\bf v}(PV2) = (0,\Gamma_{0}/2 \pi \ell)$$

Both PVs move in the $\hat{\bf y}$ direction with speed $v_{y} = \Gamma_{0}/2 \pi \ell$.
If we increase $\Gamma$ or decrease $\ell$ then $v_{y}$ increases.