THE LIFE-CYCLE OF TRIPOLES IN 2-DIMENSIONAL INCOMPRESSIBLE FLOWS

The mechanisms of coherent tripole formation from unstable shielded ci rcular vortices are analysed in the context of two-dimensional incompr essible flows. Three stages are identified during the transformation p rocess: 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 influen ce 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 asy mmetric 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 diffus ion. Finally the influence of bottom topography on tripole formation i s considered, providing a rich phenomenology when the height of the to pography is varied.