. (2008). The three-dimensional structure of an electromagnetically generated dipolar vortex in a shallow fluid layer. Physics of Fluids, 20(11), 116601-1/15. [116601]. DOI: 10.1063/1.3005452 General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. The three-dimensional structure of an electromagnetically generated dipolar vortex in a shallow fluid layer Many experiments have been performed in electromagnetically driven shallow fluid layers to study quasi-two-dimensional ͑Q2D͒ turbulence, the shallowness of the layer commonly is assumed to ensure Q2D dynamics. In this paper, however, we demonstrate that shallow fluid flows exhibit complex three-dimensional ͑3D͒ structures. For this purpose we study one of the elementary vortex structures in Q2D turbulence, the dipolar vortex, in a shallow fluid layer. The flow evolution is studied both experimentally and by numerical simulations. Experimentally, stereoscopic particle image velocimetry is used to measure instantaneously all three components of the velocity field in a horizontal plane, and 3D numerical simulations provide the full 3D velocity and vorticity fields over the entire flow domain. It is found that significant and complex 3D structures and vertical motions occur throughout the flow evolution, i.e., during and after the forcing phase. We conclude that the bottom friction is not the main mechanism leading to three-dimensionality of the flow but rather the impermeability of the boundaries. It is further shown that free-surface deformations, i.e., gravity waves, are of minor importance too as a mechanism to generate 3D motion. Furthermore, it is demonstrated that the observations are not due to three-dimensionality introduced by the forcing mechanism but intrinsically due to the flow dynamics itself. The flow evolution is analyzed with respect to its quasi-two-dimensionality by adopting the ratio of "horizontal" to "vertical" kinetic energies, the normalized horizontal divergence, and a measure of the relaxation to a Poiseuille-like profile. An important observation is that, although the relative magnitude of the vertical velocity as compared to the horizontal flow components decreases for decreasing fluid depth, the vertical profile of the horizontal flow relaxes rather slowly to a Poiseuille-like profile, i.e., not faster than the b...

Decaying turbulence in a shallow flow is shown to be characterized by the emergence of long-lived meandering currents, which are closely related to pronounced vertical flows inside the shallow layer. These vertical flows are concentrated in regions that are dominated either by vorticity or by strain of the flow field. Upwelling of fluid is observed in patch-like domains near elliptic points. Downward flow takes place close to hyperbolic points where the hyperbolic nature of the streamlines leads to thin, elongated regions of intense downwelling. The latter results in long, contracting regions in the free-surface flow. Particles that float on the liquid surface will congregate in these strain-dominated regions, thus lining out the large-scale meandering streams.

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