Non-Self-Similar Collapse of a Geostrophic Vortex Model

초록

We consider a geostrophic vortex model, relevant to large-scale horizontal atmospheric motion, and focus on the dynamics of three point vortices. The fixed and relative equilibria of the model are obtained. Compared with the pointvortex model in Euler flows, the equilibrium states are similar, but the conditions for their formation differ. We investigate the collapse of solutions for three geostrophic vortices and show that the collapse is non-self-similar. The conditions leading to collapse are examined in the phase space, and the non-self-similar collapse of vortices is validated numerically. This result differs remarkably from the classical point-vortex model, in which collapse is always self-similar.

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