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 ␦. By quantifying the strength of the secondary motions ͑vertical motions and nonzero horizontal divergence͒ with respect to the swirling motions of the primary vortex cores, it was found that the three-dimensionality of a shallow ͑␦ Ӷ 1͒ dipolar vortex only depends on a single parameter: ␦ 2 Re. Depending on the value of this parameter, three flow regimes are observed for shallow dipolar vortices: ͑1͒ a quasi-two-dimensional regime where the structure of the dipolar vortex remains almost unchanged throughout its lifetime, ͑2͒ a transitional regime where the structure presents some three-dimensional characteristics but remains coherent, and ͑3͒ 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.

Conditional vorticity budget of coherent and incoherent flow contributions in fully developed homogeneous isotropic turbulence Phys. Fluids 24, 035108 (2012) Flow visualization of a vortex ring interaction with porous surfaces Phys. Fluids 24, 037103 (2012) Boundary layer turbulence in transitional and developed states Phys. Fluids 24, 035105 (2012) Energy exchange between a vortex ring and an ionic polymer metal composite Appl. Phys. Lett. 100, 114102 (2012) Strain-vorticity induced secondary motion in shallow flowsThe present work investigates the existence and evolution of a spanwise vortex at the front of shallow dipolar vortices. The vortex dipoles are experimentally generated using a double flap apparatus. Particle image velocimetry measurements are performed in a horizontal plane and in the vertical symmetry plane of the flow. The dynamics of such vortical structures is investigated through a parametric study in which both the Reynolds number Re ¼ U 0 D 0 = 2 90; 470 ½ and the aspect ratio a ¼ h=D 0 2 0:075; 0:7 ½ , associated with the shallowness of the flow, are varied, where U 0 is the initial velocity of the vortex dipole, D 0 is the initial diameter, h is the water depth, and is the kinematic viscosity of the fluid. The present experiments confirm the numerical results obtained in a companion paper by Duran-Matute et al. [Phys. Fluids 22, 116606 (2010)], namely that the flow remains quasi parallel with negligible vertical motions below a critical value of the parameter a 2 Re. By contrast, for large values of a 2 Re and a . 0:6, a three-dimensional regime is observed in the shape of an intense spanwise vortex generated at the front of the dipole. The present study reveals that the early-time motion and dynamics of the spanwise vortex do not scale on the unique parameter a 2 Re but is strongly influenced by both the aspect ratio and the Reynolds number. A mechanism for the generation of the spanwise vortex is proposed. For a & 0:6, a third regime is observed, where the spanwise vortex is replaced by a vorticity tongue.

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