Interaction of two equal co-rotating viscous vortices in the presence of background shear

The interactions of two equal co-rotating vortices under the influence of both viscosity and uniform background shear are investigated using two-dimensional numerical simulations. A range of values of the shear strength parameter, zeta(0) = -S/omega(0,) and initial aspect ratio, a(0)/b(0), are considered for two values of circulation Reynolds number Re-Gamma = vertical bar Gamma(0)vertical bar/nu. The primary effect of viscosity is to increase the core size a(t) in time while the primary effect of shear is to vary the separation distance b(t) in time. For sufficiently separated vortices, the motion of the vortices is well-described by a point vortex model with linear shear. The present simulations show that for a viscous symmetric vortex pair there are two distinct flow regimes, merger and separation, with the boundaries separating these regimes well-predicted by the point vortex model and largely independent of Re-Gamma over the range tested. Results also indicate that the onset of merging occurs when a(t)/b(t) attains the critical value (a/b)(cr) found for vortex pairs without shear.