Collapse and backward motion of axisymmetric toroidal vortices in an accretion flow

The problem of the interaction of two coaxial, counter-rotating ring vortices in the presence of a convergent (accretion) flow with a sink at the center of symmetry has been solved. The vortices that would recede from each other in the absence of a flow (the problem inverse to the Helmholtz problem) are shown to be brought closer together by the flow and then ejected with acceleration along the axis of symmetry. The ejection velocity increases with sink strength. However, if the sink strength exceeds some critical value that depends on the initial conditions, then no ejection occurs and the vortices are captured by the flow and collapse. A similar capture and collapse are also possible during the motion of a single vortex in a flow. The difference from the planar case, where no collapse occurs, is significant. The detected phenomenon can be applied when studying nonlinear processes in atmospheric vortices as well as in active galactic nuclei and planetary atmospheres.