DYNAMICS AND STABILITY OF A VORTEX RING IMPACTING A SOLID BOUNDARY

Direct numerical simulations were used to study the dynamics of a vort ex ring impacting a wail at normal incidence. The boundary layer forme d as the ring approaches the wall undergoes separation and roll-up to form a secondary vortex ring. The secondary ring can develop azimuthal instabilities which grow rapidly owing to vortex stretching and tilti ng in the presence of the mean strain field generated by the primary V ortex ring. The stability of the secondary ring was investigated throu gh complementary numerical experiments and stability analysis. Both pe rturbed and unperturbed evolutions of the secondary ring were simulate d at a Reynolds number of about 645, based on the initial primary-ring propagation velocity and ring diameter. The linear evolution of the s econdary vortex-ring instability was modelled analytically by making u se of a quasi-steady approximation. This allowed a localized stability analysis following Widnall and Sullivan's (1973) earlier treatment of an isolated vortex ring. Amplitude evolution and growth-rate predicti ons from this analysis are in good agreement with the simulation resul ts. The analysis shows that the secondary vortex ring is unstable to l ong-wavelength perturbations, even though an isolated ring having simi lar characteristics would be stable.