On Asymmetric Vortex Pair Interactions in Shear

This study examines the two-dimensional interaction of two unequal co-rotating viscous vortices in uniform background shear. Numerical simulations are performed for vortex pairs having various circulation ratios ?(0) = G(1,0)/G(2,0) = (?(1,0)/?(2,0))(a(1,0)(2)/a(2,0)(2)) = 1, corresponding to different initial characteristic radii ai,0 and peak vorticities ?i,0 of each vortex i = 1, 2, in shears of various strengths ?(0) = ?(S)/?(2,0), where ?(S) is the constant vorticity of the shear. Two primary flow regimes are observed: separations (?(0) < ?(sep) < 0), in which the vortices move apart continuously, and henditions (?(0) > ?(sep)), in which the interaction results in a single vortex (where ?(sep) is the adverse shear strength beyond which separation occurs). Vortex motion and values of ?(sep)(?(0)) are well-predicted by a point-vortex model for unequal vortices. In vortex-dominated henditions, shear varies the peak-peak distance b, and vortex deformation. The main convective interaction begins when core detrainment of one vortex is established, and proceeds similarly to the no-shear (?(0) = 0) case: merger occurs if the second vortex also detrains, engendering mutual entrainment; otherwise straining out occurs. Detrainment requires persistence of straining of both sufficient magnitude, as indicated by relative straining above a consistent critical value, (S/?)(i) > (S/?)(cr), where S is the strain rate magnitude at the vorticity peak, and conducive direction. Hendition outcomes are assessed in terms of an enhancement factor e = G(end)/G(2,start). Although e generally varies with ?(0), (a(1,0)(2)/a(2,0)(2)) and (?(1,0)/?(2,0)) in a complicated manner, this variation is well-characterized by the pair's starting enstrophy ratio, Z(2)/Z(1). Within a transition region between merger and straining out (approximately 1.65 < Z(2)/Z(1) < 1.9), shear of either sense may increase e.