7.2 Counter-rotating vortex pair

In this section we study the flow due to two counter-rotating vortices in free space. For this flow, convection is nontrivial even for the exact solution. We will first present the governing equations of the flow in subsection 7.2.1. The numerical results to validate the performance of the redistribution method are presented in subsection 7.2.2; we will compare the computed vorticity at small times with analytical solutions Van Dommelen & Shankar [230]. We compare the long time numerical results with analytical predictions in subsection 7.2.3.