Parametric resonance with a point-vortex pair in a nonstationary deformation flow

The movement of a pair of point vortices with arbitrary intensities, embedded in a nonstationary shear and rotational flow, is studied. The expression for the vorticity center is shown to be reduced to a Riccati equation. In the particular case of harmonic oscillations, parametric resonance, which results in unbounded motion of the vortex pair, is found and analyzed. Using the fast oscillation averaging, an analytical estimate for the main zone in the parametric space is obtained. With the help of numerical calculations, the reliability of the estimate is asserted and a family of the minor zones is obtained. -- Highlights: ► Motion of an arbitrary intensity point-vortex pair in a shear flow is studied. ► Expression for the vorticity center of the pair is reduced to a Riccati equation. ► A parametric resonance leading to unbounded motion of the pair is analyzed. ► An analytical estimate for the main zone in the parametric space is obtained. ► Using numerical calculation, a family of minor zones is obtained.