On vortex intensification due to stretching out of weak satellites

Abstract

The interaction of two essentially unequal vortices is studied for the two-dimensional inviscid model. The curved stretching out of a weak satellite, localized at the periphery of the main vortex, is described analytically in the passive scalar approximation. The rate of energy transfer from the satellite to the main vortex is shown to increase with the curvature of the satellite orbit characterized by the ratio of the satellite size to its distance from the main vortex center. Such a mechanism of the energy cascade is distinct from previously considered symmetric deformations by external flows with a uniform strain rate when the energy is preserved for localized vortices with zero circulation in an unbounded domain. Therefore, asymmetric stretching out of satellites along curved orbits with the finite circumference is crucial for the vortex intensification and can serve as an important ingredient of inverse energy cascade in the two-dimensional turbulence.