Vortex collapse from the viewpoint of complex-time singularity

Abstract

Under certain initial and parametric conditions, point vortices will collide, and we can locate a singularity on the real time axis. If some of the conditions deviate from the collapse conditions, the singularity splits into one or more complex-conjugate pairs. Recently, we proposed a scaling law between the deviation of an initial condition from the collapse condition and the resulting shift in the position of the singularity away from the real axis for a system of point vortices. We verify this scaling law for collisions of three and four point vortices.