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 equat ion in the vorticity streamfunction formulation. The interaction with a cylinder with a diameter equal to the diameter of the dipole has bee n simulated in the inviscid case with free-slip boundaries. This case has been considered as a way to perturb the initial dipole, which spli ts into two vortices that rejoin at a different location on the cylind er depending on the initial displacement of the cylinder from the cent erline of the primary vortex pair. By the scatter plots it was shown t hat the Lamb dipole after the perturbation relaxes to its initial k2ps i functional relationship. The case of no-slip interaction has been co nsidered 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 simulati ons, that is a thin vorticity layer is generated at the cylinder, it r olls up and forms dipolar and tripolar structures, depending on the in itial displacement of the cylinder from the centerline of the incoming dipole. Scatter plots of the vortex pair formed by the primary and se condary vorticity show a linear distribution similar to that of the La mb dipole. The dependence on the Reynolds number has been investigated .