Two-dimensional asymmetric vortex merger: Contour dynamics experiment

Abstract

The two-dimensional asymmetric merger of two like-signed uniform vorticity patches with different sizes (r i ) and vorticities (q i ) was examined with contour dynamics experiments. We determined the critical centroid distances for merger (d merger), which vortex survived the interaction and the processes involved in the merger. An explicit empirical critical merger distance was established asd merger/r 1 =a·(q 2/q 1)1/2·(r 2/r 1)+b (subscript 1 denotes the properties of the losing [destroyed] vortex and 2 the winning [not destroyed] vortex). The relationship seems applicable for wide range of parameters. The winning vortex was found to be determined primarily by vorticity rather than size. A small but strong enough vortex is absorbed into a larger and weaker vortex and becomes the high vorticity core of the merged vortex. A small and weak vortex is strained out to a thin filament. The vorticity ratio which determined when the first vortex was destroyed while the second survived, (q 2/q 1)win, was established empirically as a function of radius ratio,r 1/r 2. Forr 1/r 2∼1, (q 2/q 1)win is almost identical with the vorticity ratio (q 2/q 1)dmin which gives the minimum critical merger distance for the particular size ratior 1/r 2. For extremely large size ratio, (q 2/q 1)win>(q 2/q 1)dmin Partial mergers were seen for a centroid distance which is close to and less than the critical merger distance.