We consider the interaction between two quasi-geostrophic vortices of height-to-width aspect ratio h/r, lying at two different vertical levels. We investigate whether such structures naturally align. In the case the vortices occupy distinct yet contiguous vertical levels, such an alignment can contribute to the growth in volume of oceanic mesoscale vortices. The other growth mechanism is the merger of vortices sharing common vertical levels. We show that there exist titled equilibrium states where vortices nearly align slantwise. Most equilibria for prolate vortices ( ) are stable apart in a very narrow region of the parameter space. The instability is however normally non-destructive. Pairs of oblate vortices may also be in an unstable equilibria if they are moderately offset in the horizontal direction. In this case, the instability may result in the shedding of filamentary potentially vorticity away from the vortices. This shedding of potential vorticity may result in the further alignment of the main structures.

中文翻译：

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两个三维准地转涡的排列

我们考虑位于两个不同垂直高度的高宽比 h/r 的两个准地转涡旋之间的相互作用。我们调查这些结构是否自然对齐。在涡流占据不同但连续的垂直水平的情况下，这种排列可能有助于海洋中尺度涡旋体积的增长。另一种增长机制是共享公共垂直水平的漩涡合并。我们表明存在标题平衡状态，其中涡流几乎倾斜对齐。长涡旋 ( ) 的大多数平衡在参数空间的一个非常狭窄的区域内是稳定的。然而，不稳定性通常是非破坏性的。如果成对的扁涡在水平方向上适度偏移，它们也可能处于不稳定的平衡状态。在这种情况下，不稳定性可能导致丝状潜在涡度从涡流中脱落。这种潜在涡度的脱落可能导致主要结构的进一步对齐。