A two-dimensional vortex merger in an external strain field

In a two-dimensional incompressible fluid, the merger of two Rankine vortices in an external strain field is studied analytically and numerically. In the absence of merger, the trajectory of the vortex centres is elliptical near the centre of the plane and hyperbolic at larger distances. When merger occurs, it can be accelerated or decelerated by the external strain field depending on the orientation of the strain axes, but in all the cases studied here, external strain decreases merger efficiency.