Tripolar coherent vortices are shown to emerge from the unstable evolution of perturbed two-dimensional axisymmetric flows, They are obtained from the nonlinear equilibration of barotropically linearly unstable normal modes, as well as from more general initial perturbations. This instability is proposed as an important mechanism for the generation of both dipolar and tripolar coherent vortex structures.

The mechanisms of coherent tripole formation from unstable shielded circular vortices are analysed in the context of two-dimensional incompressible flows. Three stages are identified during the transformation process: the linear growth of the initial normal mode perturbation, its nonlinear amplification and the finite-amplitude saturation under the tripolar form. We give a geometrical discussion of the mutual influence of the core vortex and of the satellites generated from the shield. The role of the angular momentum in determining the finite amplitude saturation is demonstrated using a simple elliptical model of the core vortex associated with two point-vortex satellites. The long-time asymmetric breaking of the tripole into a dipole and a monopole is shown to be driven by the erosion of the core vortex by stripping and diffusion. Finally the influence of bottom topography on tripole formation is considered, providing a rich phenomenology when the height of the topography is varied.

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International audienceIn this study, the authors first show that it is difficult to reconstruct the vertical structure of vortices using only surface observations. In particular, they show that the recent surface quasigeostrophy (SQG) and interior and surface quasigeostrophy (ISQG) methods systematically lead to surface-intensified vortices, and those subsurface-intensified vortices are thus not correctly modeled. The authors then investigate the possibility of distinguishing between surface- and subsurface-intensified eddies from surface data only, using the sea surface height and the sea surface temperature available from satellite observations. A simple index, based on the ratio of the sea surface temperature anomaly and the sea level anomaly, is proposed. While the index is expected to give perfect results for isolated vortices, the authors show that in a complex environment, errors can be expected, in particular when strong currents exist in the vicinity of the vortex. The validity of the index is then analyzed using results from a realistic regional circulation model of the Peru–Chile upwelling system, where both surface and subsurface eddies coexist. The authors find that errors are mostly associated with double-core eddies (aligned surface and subsurface cores) and that the index can be useful to determine the nature of mesoscale eddies (surface or subsurface intensified) from surface (satellite) observations. However, the errors reach 24%, and some possible improvements of the index calculations are discussed

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In a two-dimensional incompressible fluid, the barotropic instability of isolated circular vortices can lead to multipole formation. The multipoles we study here are composed of a core vortex surrounded by two or more identical satellite vortices, of opposite-sign vorticity to the core, and the total circulation is zero. First, we present the generation of multipoles from unstable piecewise-constant monopoles perturbed on a monochromatic azimuthal mode. The stationary multipoles formed by this nonlinear evolution retain the same energy, circulation and angular momentum as the original monopoles, but possess a lower enstrophy. These multipolar steady states are then compared to multipolar equilibria of the Euler equation, obtained either analytically by a perturbation expansion or numerically via a relaxation algorithm. Finally the stability of these equilibria is studied. Quadrupoles (one core vortex bound to three satellites) prove relatively robust, whether initially perturbed or not, and resist severe permanent deformations (mode-2 shears or strains of amplitude up to 0.1ζ(max). Amplification of the mode-3 deformation proves more destructive. More complex multipoles degenerate in less than a turnover period into end-products of a lesser complexity, via vortex splitting, pairing or merging. We use the conservation of integral properties to classify the large variety of instability mechanisms along physical guidelines. To conclude, we synthetize the connections between these various vortex forms.