Dynamics and structure of decaying shallow dipolar vortices

The current work reports on a numerical and experimental study of the evolution of decaying dipolar vortices in a shallow fluid layer. The dynamics and the structure of such vortices are investigated as a function of both their Reynolds number Re and the aspect ratio of vertical and horizontal length scales d. By quantifying the strength of the secondary motions (vertical motions and nonzero horizontal divergence) with respect to the swirling motions of the primary vortex cores, it was found that the three-dimensionality of a shallow (d¿1) dipolar vortex only depends on a single parameter: d2¿Re. Depending on the value of this parameter, three flow regimes are observed for shallow dipolar vortices: (1) a quasi-two-dimensional regime where the structure of the dipolar vortex remains almost unchanged throughout its lifetime, (2) a transitional regime where the structure presents some three-dimensional characteristics but remains coherent, and (3) a three-dimensional regime where the structure of the dipolar vortex acquires a complicated three-dimensional shape with a persistent spanwise vortex at its front.