ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
Two motion of two interacting vortices in the presence of a background gradient of potential vorticity due to the β-effect is considered. The vortices, and their interaction, are modeled using a two-layer, quasigeostrophic model. The paper extends that of McDonald [Philos. Trans. R. Soc. London, Ser. A 456, 1029 (2000)] who, using a similar model, considered only steady configurations of zonally aligned vortices, i.e., lying along the same parallel of latitude. Here Green's function techniques are used to calculate the velocity of one vortex due to the presence of the Rossby wave wake of the other. This enables consideration of the more general case of vortices having arbitrary relative location, the only requirement being that the vortices are well-separated (i.e., several Rossby radii apart). An additional quasisteady approximation enables the time evolution of vortices to be studied. Of particular interest is the existence of equilibrium configurations in which the vortices do not move relative to each other and maintain their orientation with respect to the direction defined by the gradient of the background potential vorticity field. It is shown that necessary conditions for equilibrium are that the vortices are (a) of equal strength, or (b) aligned zonally. The stability of equilibria to small perturbations in the relative location of the vortices is investigated and the equilibria found to be weakly unstable in that the vortex trajectories drift slowly (but not exponentially fast) from their equilibrium paths. This is verified by numerical computation of the trajectories near equilibrium. For equal strength vortices not in equilibrium the distance between the vortices remains constant, but the line joining the two vortices rotates with constant angular velocity. For this case, examples of the trajectories of the individual vortices and the center of mass are given. For vortices of differing strength and arbitrary initial configurations, the motion is, in general, complicated. Some examples are presented. © 2001 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.1351858
