Stability and transitions of hetonic quartets and baroclinic modons

Ziv Kizner

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24 Scopus citations


A new concept, a hetonic quartet, is presented. A hetonic quartet is a two-layer ensemble of four synchronously translating quasigeostrophic discrete vortices aligned perpendicularly to the axis of their translation. On the f-plane, a hetonic quartet is made up of conventional point vortices (confined to either the upper or the lower layer) with specially fitted circulations and distances between each other, the upper- and lower-layer vortices being opposite in sign and located symmetrically about the translation axis. On the β-plane, a two-layer version of the modulated point vortex model [Phys. Fluids 25, 2175 (1982)] is applied. A necessary and sufficient condition for the stability of f-plane hetonic quartets to perturbations that do not violate the above-mentioned symmetry is established using the analytical methods of Hamiltonian dynamics, whereas on the β-plane, a necessary (linear) stability condition is determined. As distinct from hetons, a stable hetonic quartet is not rigid: when slightly moved off equilibrium it undergoes elastic oscillations. Periodically or continuously acting small perturbations force a stable hetonic quartet to split up into two pairs of hetons, each traveling at different speeds along the same axis. The separation in the faster heton is generally greater than that between the "centers of mass" of the upper- and lower-layer vortices of the original hetonic quartet. The similarity between baroclinic modons and hetonic quartets is traced, and a plausible scenario of the transitions observed in smooth circular baroclinic modons with moderate riders [J. Fluid Mech. 468, 239 (2002)] is suggested, with the substantial stability of the ultimate elliptical modon state being attributed to the lack of overlap of the main upper and lower vorticity chunks in the modon. The splitting of finite-core hetons (two-layer f-plane vortical pairs composed of two circular patches of constant vorticity) [J. Fluid Mech. 423, 127 (2000)] is linked with the transitions in baroclinic modons and hetonic quartets.

Original languageEnglish
Article number056601
JournalPhysics of Fluids
Issue number5
StatePublished - May 2006

Bibliographical note

Funding Information:
The author is indebted to R. Khvoles for his assistance with preparation of the illustrations, and to G. M. Reznik, M. A. Sokolovskiy, and V. M. Gryanik for helpful discussions. The support of BSF Grant No. 2002392 is gratefully acknowledged.


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