On the existence and evolution of a spanwise vortex in laminar shallow water dipoles

Abstract

The 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=U0D0/ν∈[90,470] and the aspect ratio α = h/D0∈[0.075,0.7],associated with the shallowness of the flow, are varied, where U0 is the initial velocity of the vortex dipole, D0 is the initial diameter, h is the water depth, and v 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 α2Re. By contrast, for large values of α2Re and α≲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 α2Re 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 α≳0.6, a third regime is observed, where the spanwise vortex is replaced by a vorticity tongue