Summary
The interaction of binary cyclonic vortices is investigated using the nondivergent barotropic model of Chan and Williams (1987) under two situations: a quiescent environment and a linearly-sheared background flow. It is found that the mutual interaction between the vortices results from a combination of two processes: the advection of symmetric vorticity by the asymmetric flow and the advection of asymmetric vorticity by the symmetric flow. The latter contribution is rather significant. Whether the vortices in a binary system attract or repel each other depends on the asymmetric vorticity distribution associated with the two vortices. Such a distribution is governed by the structure (size) of and the separation between the vortices. In the presence of a sheared flow, the contribution from the advection of asymmetric vorticity by the symmetric flow may also become appreciable depending on the structure and magnitude of the shear. Furthermore, the geographical locations of the vortices in relation to the sheared flow are also important in determining the relative movement of the vortices.
In the presence of β, the movements of the vortices are modified by the northwestward β-drift However, the relative motion between the vortices is almost identical to that on an f-plane. In other words, the mutual interaction between the vortices is largely independent of β. Alternatively, the two vortices can be considered to be one system which drifts towards the northwest under the influence of β while they interact with each other within the system. Physically, this independence arises because the two relative vorticity advection terms have much larger magnitudes than the planetary vorticity advection term. However, the β-effect is still important in that it modifies the asymmetric flow associated with each vortex and hence the asymmetric vorticity. Such modifications change the advection patterns compared with the β=0 case and hence lead to different vortex movements. The presence of a linear shear causes the binary system to move as if it was a large (for a cyclonic shear) or smaller (for an anticyclonic shear) vortex under the influence of β.
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Chan, J.C.L., Law, A.C.K. The interaction of binary vortices in a barotropic model. Meteorl. Atmos. Phys. 56, 135–155 (1995). https://doi.org/10.1007/BF01022526
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DOI: https://doi.org/10.1007/BF01022526