The self-similar collapse of three vortices is the motion of three vortices colliding at a single point at finite time. Such a motion has first been shown to exist for two-dimensional, planar, point vortices. In this paper, we show that the concept generalises naturally to three-dimensional quasi-geostrophic vortices as well as to surface quasi-geostrophic vortices. We first determine the conditions that lead to the collapse for these singular vortices. We then show how these conditions precipitate the merger of finite core vortices both in a three-dimensional quasi-geostrophic flow and in a surface quasi-geostrophic flow.

中文翻译：

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三个地球物理涡旋的自相似坍缩

三旋涡的自相似坍缩是三个旋涡在有限时间内单点碰撞的运动。这种运动首先被证明存在于二维平面点涡流中。在本文中，我们表明该概念可以自然地推广到三维准地转涡旋以及表面准地转涡旋。我们首先确定导致这些奇异涡流坍塌的条件。然后我们展示了这些条件如何在三维准地转流和表面准地转流中促成有限核心涡的合并。