2-DIMENSIONAL ASYMMETRIC VORTEX MERGER - MERGER DYNAMICS AND CRITICALMERGER DISTANCE

Two-dimensional asymmetric merger of two like-signed vorticity monopol es with different sizes and vorticities is examined by combining simpl ified analytical models and contour dynamics experiments. The model re sults can capture the key dynamics and hence allow the prediction of t he critical merger distance in a number of the situations. The models ignore deformation of one of the two vortices, replacing it with a poi nt vortex, and employ a corotating frame of reference with a rotation rate estimated by point vortices. Thus, the two vortex problem becomes two separate problems of a single vortex in a background shear flow. Vortex merger is found to happen when the vortex cannot resist the bac kground shear flow. Vortex merger and merging processes depend on the centroid distance d, the circulation ratio, alpha = Gamma(2)/Gamma(1) = q(2) r(2)(2)/q(1) r(1)(2) (q(i) and r(i) are the vorticity and radiu s, respectively) and initial conditions. In the lowest order, the back ground flow is approximated by a uniform shear field, and the behavior of an elliptical vortex can be described by the Kida (1981) equation supplemented with one describing the time evolution of the centroid di stance. This model reveals that merger takes place because the natural rotation of an elliptical vortex is overcome by the background unifor m shear flow; the ellipse inversely rotates and is drawn out by the ba ckground straining field. The vortex deformation in a background flow field induces an inward flow at the position of the other vortex; as a result, the centroid distance decreases and two vortices merge. The c ritical merger distance from this model agrees quite well with the res ults from contour dynamics experiments for two vortices. Inclusion of higher order non-uniform shear in the background flow extends the crit ical merger distance, which gives almost perfect estimates for the exp eriments. In the non-uniform shear flow, partial merger occurs, where the vortex sheds off a filament, but the remaining part of the vortex resumes its natural rotation. (C) 1997 Elsevier Science B.V.