A family of steady, translating vortex pairs with distributed vorticity

An efficient relaxation method is developed for computing the properties of a family of vortex pairs with distributed vorticity, propagating without change of shape through a homogeneous, inviscid fluid. The numerical results indicate that a steady state exists even when the gap between vortices is arbitrarily small, and that as the gap closes the steady state approaches a limiting vortex pair with a cusp on the axis of symmetry. Comparison is made with an approximate theory due to Saffman, and agreement is found to be good until the vortices are almost touching. The energy of members of the family is computed, and possible means of experimental production are discussed.