Wave - vortex dynamics

Numerical studies of two-dimensional turbulence show the importance of localised structures, both in the small scales where intermittent transfers occur and in the large scales dominated by coherent vortices. This work is an attempt to establish a more appropriate theoretical framework than the usual Fourier representation. We present a dual representation, mixing continuous field and point vortices. The difficulties arising from the redundancy of the representation are solved through a hypothesis of mutual advection. The resulting equations conserve the natural invariants of the system. As a first application, we show that introducing a weakly charged point vortex in a continuous field with quasiperiodic behaviour induces a purely Lagrangian chaos. As the point vortex grows in intensity, it becomes quasistationary and the induced phase mixing dominates the behaviour of the continuous field.