Vortex Merger in Shallow Water Model

An inviscid, nonlinear shallow water model is applied to study the formation of filaments and merging of potential vorticity (PV, pi). We confirm that misalignment of vorticity with the streamlines is crucial to merger. Flow creates positive PV tendency (pi(t)) on the lee side of pi ridge, which increases the angle between streamlines and PV contours and the efficiency of vorticity transport along the parallel but oppositive direction in the positive quadrants of pi(t). So, the vortices move closer while rotating around each other. Filamentation starts as weak vorticity shatters from the outer edge of vortex core. The filament grows and rotates around the cores, but shows little effects to positive PV advection or vortex merging in the inner core, evidenced by the steady core area integrated PV trends. Consecutive PV transfer from lower to higher interval levels are observed during merger process while elongated filamentation is dissolving into the lower level PV regime. The vortices never merge when negative pi(t) prevails between two vortices. Distance between the vortex cores show direct correspondence to positive pi(t) between them. Hence, the advance of positive pi(t) provides a simple mechanism of merging. The Rossby radius of deformation (L-D) is confirmed to be another strong indicator for vortex pair merger where L-D comparable or smaller than the initial vortex core separation length scale makes merger more likely due to geostrophic adjustment. The Rossby number (Ro) affected the overall flow interaction speed speed when L-D is fixed.