A new family of exact solutions to the two-dimensional steady incompressible Euler
equation is presented. The solutions provide a class of hybrid equilibria comprising
two point vortices of unit circulation – a point vortex pair – embedded in a smooth sea
of non-zero vorticity of ‘Stuart-type’ so that the vorticity ω and the stream function
ψ are related by ω = ae
bψ − δ(x − x0) − δ(x + x0), where a and b are constants. We
also examine limits of these new Stuart-embedded point vortex equilibria where the
Stuart-type vorticity becomes localized into additional point vortices. One such limit
results in a two-real-parameter family of smoothly deformable point vortex equilibria
in an otherwise irrotational flow. The new class of hybrid equilibria can be viewed
as continuously interpolating between the limiting pure point vortex equilibria. At
the same time the new solutions continuously extrapolate a similar class of hybrid
equilibria identified by Crowdy (Phys. Fluids, vol. 15, 2003, pp. 3710–3717).