Motion of three geostrophic Bessel vortices

초록

This study investigates the dynamics of geostrophic vortices (described by modified Bessel functions). We focus on the three-vortex case, where the possibility of self-similar motion and general dynamics for arbitrary strengths is studied. It is found that self-similar motions are limited to rigid rotations and self-similar triple collapse is essentially impossible. For a general description, trilinear coordinates are adopted and extended to the model of geostrophic vortices. The similarities and differences with the point-vortex model are emphasized. The physical regions in the phase plane cannot be directly identified, unlike the point-vortex case where the physical regions are identified as conic sections. The boundary of the physical region approaches the vertices of the triangle in trilinear coordinates in geostrophic vortices, while making a tangent with the sides of the triangle in point vortices. For positive values of the three vortex strengths, the boundary of the physical region is a closed concave curve, whereas it is a circle or ellipse in the case of the point vortex. Importantly, we find a new type of the phase trajectory: an open curve not intersecting with the physical region boundary. We also demonstrate the physical motions and trajectories of vortices for several representative cases of vortex strengths from numerical computations. © 2022 The Author(s)

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