Two-dimensional shielded vortices in a shear current

Abstract

The interaction of shielded vortices, with a continuous vorticity distribution, and a shear current of weak vorticity amplitude but similar velocity compared to the vortex amplitude is numerically investigated in two-dimensional isochoric flows. Different types of axisymmetric shielded vortices, namely, a neutral unstable vortex, a neutral robust vortex, and a non-neutral vortex are considered. The vortices are linear combinations of vorticity layer-modes, which consist of conveniently normalized cylindrical Bessel functions of order 0, truncated by a zero of the Bessel function of order 1. The vortex–current interaction is investigated by superposing initially the vortices at different initial locations along the cross-flow axis in the shear current. The numerical results show that some shielded vortices, as well as the shear current, remain robust while the vortices cross the shear current and reach a stable equilibrium location, which is of the same sign vorticity as its amount of circulation. There exist two unstable equilibrium locations where most of the vortices persist during a relatively short time interval before heading to their stable equilibrium region in the shear current.