VORTEX DIPOLES IMPINGING ON CIRCULAR-CYLINDERS

Vortex pairs interacting with a circular cylinder have been simulated by the numerical simulation of the two-dimensional Navier-Stokes equation in the vorticity streamfunction formulation. The interaction with a cylinder with a diameter equal to the diameter of the dipole has been simulated in the inviscid case with free-slip boundaries. This case has been considered as a way to perturb the initial dipole, which splits into two vortices that rejoin at a different location on the cylinder depending on the initial displacement of the cylinder from the centerline of the primary vortex pair. By the scatter plots it was shown that the Lamb dipole after the perturbation relaxes to its initial k2psi functional relationship. The case of no-slip interaction has been considered when the cylinder is two orders of magnitude smaller than the dipole. The same features observed in the experiment of Homa et al. [J. Fluid Mech. 197, 571 (1988)] are obtained by the numerical simulations, that is a thin vorticity layer is generated at the cylinder, it rolls up and forms dipolar and tripolar structures, depending on the initial displacement of the cylinder from the centerline of the incoming dipole. Scatter plots of the vortex pair formed by the primary and secondary vorticity show a linear distribution similar to that of the Lamb dipole. The dependence on the Reynolds number has been investigated.