Abstract
Motion of point vortices is analysed numerically by use of the potential flow theory in order to investigate some features of vortex merger in the two-dimensional mixing layer. Merging vortices are replaced by two groups of point vortices and the other vortices by an effective background field. Parameters in the calculation are the distance between the two vortices and their size. A quadrupole moment of the point vortex distribution, which is defined in this paper, is calculated at each step of the motion. This quantity is shown to describe process of merger well. Calculation shows that the two vortices rotate around their center along a nearly elliptical path and merge when they come close to each other. The unified vortex continues to deform even after that. Value of the quadrupole moment changes according to these motions. Time scale of merger is estimated by two ways, one from a motion of each vortex and the other from a decrease of the quadrupole moment. The estimated time scale is proportional to the square of the distance, and depends little on the vortex size if it is within a certain range. This result is consistent with the assumption made by Takaki & Kovasznay (1978). An area increase and an oscillatory deformation of the unified vortex are observed and discussed based upon a variation of the quadrupole moment.
