On the Critical Separation Distance of Binary Vortices in a Nondivergent Barotropic Atmosphere

Abstract

The motion of binary cyclonic vortices with equal structure and strength in no environmental flow is investigated with a focus on what determines their merger or separation. For this, proposals in previous studies on the critical separation distance of binary vortices are validated using a nondivergent barotropic model on an f-plane.
Results from numerical experiments indicate that the sign of the initial relative vorticity in the mid-region between two vortices largely determines their merger or separation. This is consistent with the proposal of Falkovich et al. When the initial relative vorticity in the mid-region between two vortices is negative, the two vortices separate. However, it is found that an initial positive relative vorticity between the two vortices does not guarantee their merger. Only when the initial positive relative vorticity exceeds a certain threshold value, the two vonices merge. Based upon the results of numerical experiments, it is suggested that the critical separation distance of binary vortices is slightly smaller than twice the radius at which the relative vorticity of one vortex becomes zero. The merger or separation of binary vortices can be conceptually explained by the advection of the symmetric relative vorticity of one vortex by the symmetric tangential flow of the other vortex. This relative vorticity advection produces vorticity anomalies with different magnitudes to the north and south of each vortex and results in net eastward or westward secondary flow near its center when the two vortices are initially placed in the east-west direction.