A stable tripole vortex model in two-dimensional Euler flows

11 pages, 5 figures, 1 appendix, supplementary movies https://doi.org/10.1017/jfm.2019.730An exact solution of a stable vortex tripole in two-dimensional (2-D) Euler flows is provided. The stable tripole is composed of an inner elliptical vortex and two small-amplitude lateral vortices. The non-vanishing vorticity field of this tripole, referred to as here as an embedded tripole because of the closeness of its vortices, is given in elliptical coordinates (,) by the even radial and angular order-0 Mathieu functions Je0 () ce0 () truncated at the external branch of the vorticity isoline passing through the two critical points closest to the vortex centre. This tripole mode has a rigid vorticity field which rotates with constant angular velocity equal to 0 Je0 (1) ce0 (0)/ 2, where 1 is the first zero of Jef0 () and 0 is a constant modal amplitude. It is argued that embedded 2-D tripoles may be conceptually regarded as the superposition of two asymmetric Chaplygin–Lamb dipoles, separated a distance equal to 2R, as long as their individual trajectory curvature radius R is much shorter than their dipole extent radiusPartial supportfor this study was obtained through project CTM2014-56987-P (Spanish Ministry of Science and Innovation