MULTIPOLAR VORTICES IN 2-DIMENSIONAL INCOMPRESSIBLE FLOWS

In a two-dimensional incompressible fluid, the barotropic instability of isolated circular vortices can lead to multipole formation. The mul tipoles we study here are composed of a core vortex surrounded by two or more identical satellite vortices, of opposite-sign vorticity to th e core, and the total circulation is zero. First, we present the gener ation of multipoles from unstable piecewise-constant monopoles perturb ed on a monochromatic azimuthal mode. The stationary multipoles formed by this nonlinear evolution retain the same energy, circulation and a ngular momentum as the original monopoles, but possess a lower enstrop hy. These multipolar steady states are then compared to multipolar equ ilibria of the Euler equation, obtained either analytically by a pertu rbation expansion or numerically via a relaxation algorithm. Finally t he stability of these equilibria is studied. Quadrupoles (one core vor tex bound to three satellites) prove relatively robust, whether initia lly perturbed or not, and resist severe permanent deformations (mode-2 shears or strains of amplitude up to 0.1zeta(max)). Amplification of the mode-3 deformation proves more destructive. More complex multipole s degenerate in less than a turnover period into end-products of a les ser complexity, via vortex splitting, pairing or merging. We use the c onservation of integral properties to classify the large variety of in stability mechanisms along physical guidelines. To conclude, we synthe tize the connections between these various vortex forms.