J. Fluid Mech. (2000), vol. 423, pp. 127–154. Printed in the United Kingdom c  2000 Cambridge University Press 127 Finite-core hetons: stability and interactions By M. A. SOKOLOVSKIY 1 AND J. VERRON 2 1 Institute of Water Problems of the Russian Academy of Sciences, 3 Gubkina Str., 117735, Moscow, GSP-1, Russia 2 Laboratoire des Ecoulements G´ eophysiques et Industriels, UMR 5519 CNRS, BP53 X, 38041 Grenoble Cedex, France (Received 19 January 1999 and in revised form 8 June 2000) The dynamics of vertically compensated two-layer vortices (hetons) with finite cores are examined within the context of the quasi-geostrophic approximation on the f -plane. The two-layer version of the contour dynamics method is used, and com- plemented by the so-called contour surgery technique. Special attention is paid to two-heton interactions when the initial locations of the vortex patches are symmetri- cal. A classification of the different regimes observed is made according to external parameters, namely geometrical parameters and stratification. In this parameter space, novel quasi-stationary states resulting from collisions between two hetons may be ob- served: (i) formation of a configuration consisting of two-layer vortices moving in opposite directions and, as a special case, a configuration analogous to the ‘klapstoss’ billiard shot, (ii) absorption of one heton by the other and subsequent movement of a new dipole, (iii) formation of two-layer dipoles, larger than the original hetons, as- sociated with rotating peripheral satellite eddies in their wakes. Some of these results may have implications for the analysis of mesoscale vortices in the ocean. 1. Introduction Mesoscale vortices are now recognized as ubiquitous features of ocean circulation. They most often arise from barotropic and baroclinic instabilities in the strong cur- rents (Gulf Stream, Kuro Shio, Aghulas current, etc.), but they can also appear in the open ocean as a result of local instability, local constraints (e.g. topography), specific forcing features, etc. These coherent structures have a lengthy life and are believed to play a significant role in the redistribution of momentum, heat and salt in the ocean. As a result of their dynamical coherence, the typical distance separating oceanic vortices is often considerable in relation to their own scale (e.g. McWilliams 1984). The question of the stability of an isolated vortex is of interest per se and an unstable structure of this kind can form new coherent vortex structures. Interaction between individual vortices is also of interest as it may result in merging, that is, the appearance of new vortex structures. Interaction between vortices that are initially far apart is possible because of their ability to propel themselves, even in the absence of external influences. For example, Gryanik (1983), Hogg & Stommel (1985a, b) and Young (1985) have successfully modelled the simplest mechanisms of vortex interaction in the framework of the theory of discrete geostrophic vortices. Moreover, the notion of a baroclinic vortex pair (Gryanik 1983) and a heton (Hogg & Stommel 1985a) – a vortex pair (or dipole) which is formed from discrete eddies located in different layers of a two-layer liquid – appeared to be fruitful when studying trajectories of real vortices in atmosphere and ocean (Gryanik & Tevs 1989, 1997).