Three-dimensional Quasi-geostrophic Staggered Vortex Arrays

We determine and characterise relative equilibria for arrays of point vortices in a three-dimensional quasi-geostrophic flow. The are equally spaced along two horizontal rings whose centre lies on the same vertical axis. An additional vortex may be placed this Depending parameters defining array, equal or opposite sign. address linear stability arrays. find both stable unstable equilibria, depending geometry array. For arrays, instability lead to quasi-regular chaotic motion vortices. depends number radius ratio between rings, offset central vortex, when latter is present. In case also strength vortex. non-linear evolution selection cases presented exhibiting examples motion.