Viscous merging of three vortices

Abstract

Localizing critical points of the vorticity of saddle and center type along with vorticity contours through saddle points provide a way to systematically investigate vorticity dynamics in two-dimensional viscous flow. Following this approach we investigate vortex interaction and merging using extremal points of the vorticity as a vortex identifier. Three Gaussian vortices with same strength are initially placed equidistantly and the vorticity contours of the flow is assessed as time progresses. Two transitions in the flow are observed for Re≤400 - a triangle bifurcation and three simultaneous cusp bifurcations. The core-growth model is shown to approximate well the vorticity transport equation in this case, providing quantitative and qualitative insights in the merging process, allowing for an analytical expression of the position of critical points of vorticity and a simple analytical expression for the triangle bifurcation observed in the flow.