A novel laboratory experiment for investigating statistically steady rotating turbulence is presented. Turbulence is produced nonintrusively by means of electromagnetic forcing. Depending on the rotation rate the Taylor-based Reynolds number is found to be in the range of 90Շ Re Շ 240. Relevant properties of the turbulence, both with and without rotation, have been quantified with stereoscopic particle image velocimetry ͑SPIV͒. This method enables instantaneous measurement of all three velocity components in horizontal planes at a distance H from the bottom. The root-mean-square turbulent velocity decreases inversely proportional to H in the nonrotating experiments and is approximately constant when background rotation is applied. The integral length scale shows a weak H-dependence in the nonrotating experiments which is presumably due to the spatial extent of the forcing. Based on the behavior of the principal invariants of the Reynolds stress anisotropy tensor, the rotating turbulence has been characterized as a three-dimensional two-component flow. Furthermore, these SPIV measurements provide supporting evidence for ͑i͒ reduction of the dissipation rate, ͑ii͒ suppression of the vertical velocity as compared to the horizontal velocity, and ͑iii͒ increased spatial and temporal correlation of the horizontal velocity components, with the temporal correlation growing ever stronger as the rotation rate is increased. A less commonly known feature of rotating turbulence, quantified here for the first time in a laboratory setting, is the reverse dependence on the rotation rate of the spatial horizontal velocity correlation functions. Another interesting result concerns the linear ͑anomalous͒ scaling of the longitudinal spatial structure function exponents in the presence of rotation, consistent with a study by Baroud et al. ͓Phys. Rev. Lett. 88, 114501 ͑2002͔͒.

. (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...

Previous high-resolution contour dynamics calculations ͓Dritschel and Waugh, Phys. Fluids A 4, 1737 ͑1992͔͒ have shown that in two-dimensional inviscid flow the interaction of two unequal corotating vortices with uniform vorticity is not always associated with vortex growth and may lead to vortices smaller than the original vortices. In the present study, we investigate whether these results also hold for two-dimensional vortices with continuous vorticity distributions. Similar flow regimes are found as for uniform vorticity patches, but the variation of the flow regimes with the initial vortex radii and peak vorticities is more complicated and strongly dependent on the initial shape of the vorticity profile. It is found that the "halo" of low-value vorticity, which surrounds the cores of continuous vortices, significantly increases the critical distance at which the weaker vortex is destroyed. The halo also promotes the vortex cores to merge more efficiently, since it accounts for a substantial part of the loss of circulation into filaments. Simple transformation rules and merger criteria are derived for the inviscid interaction between two Gaussian vortices. The strong dependence of the flow regimes on the initial vorticity distribution partly explains why previous laboratory experiments in an electron plasma ͓Mitchell and Driscoll, Phys. Fluids 8, 1828 ͑1996͔͒ show complete merger of two unequal vortices in a range of parameter space where contour dynamics simulations with uniform vorticity patches predict partial merger or partial straining-out of the smaller vortex. It is shown that the measured times for complete merger are in reasonable agreement with inviscid dynamics when the vortices are very similar. For more distinct vortices the weaker vortex is often observed to be destroyed on a time scale much smaller than expected from inviscid numerical simulations. An explanation for this discrepancy is given by the combined effects of vortex stripping and viscous diffusion, which leads to an enhanced erosion of the weaker vortex. These results are verified by laboratory experiments in a conventional ͑rotating͒ fluid.

The strain-induced evolution of shielded monopolar vortices has been investigated in a stratified fluid. A steady strain flow was generated by an arrangement of four rotating horizontal discs, whereas the monopolar vortex was created by a small spinning sphere. Quantitative information about the flow field was obtained by tracking passive tracer particles. The vortex was observed to deform into a tripolar-like structure, followed by the shedding of the accompanying satellites. During this stage, the remaining vortex core evolved quasi-steadily, which was evident from the functional relationship between the vorticity and the stream function. Furthermore, it was shown that the removal of the surrounding ring of oppositely signed vorticity induces an accelerated horizontal growth of the vortex core. Owing to the diffusive decay of vorticity, the vortex was finally torn apart along the horizontal strain axis. The dynamics of the vortex core appeared to be very similar to that of an elliptic patch of uniform vorticity. The instantaneous vorticity contours at high vorticity levels were close to ellipses with nearly the same aspect ratios and orientations. Moreover, the observed vortex evolution was in qualitative agreement with the calculated motion of an elliptic patch of uniform vorticity. As a second approach, the full two-dimensional vorticity equation was solved numerically by a finite-difference method in order to account for both the non-uniform spatial vorticity distribution of the laboratory vortex and the diffusion of vorticity in the horizontal directions. The numerically obtained vortex evolution was in good agreement with that observed in the laboratory.

The dynamics of two identical vortices in linear shear was studied both numerically and experimentally. Numerical simulations based on the technique of contour dynamics reveal that the vortex evolution in adverse shear is significantly different from that in cooperative shear. Vortices in adverse shear predominantly separate, whereas vortices in cooperative shear predominantly merge. In addition, adverse shear may destruct the vortices much in the same way as a single vortex in adverse shear, whereas cooperative shear stabilizes the vortices and thus enhances the possibility of vortex merger. The critical distance for vortex merger depends strongly on both the sign and the strength of the linear shear and, to a lesser extent, on the initial vorticity distribution. A simple vortex merger criterion is derived based on the interaction of two point vortices in linear shear. The different behavior of vortices in adverse and cooperative shear was confirmed by rotating-tank experiments.

The Northern Current is a slope current in the northwest Mediterranean that shows high mesoscale variability, generally associated with meander and eddy formation. A barotropic laboratory model of this current is used here to study the role of the bottom topography on the current variability. For this purpose, a source–sink setup in a cylindrical tank placed on a rotating table is used to generate an axisymmetric barotropic current. To study inviscid topographic effects, experiments are performed over a topographic slope and also over a constant-depth setup, the latter being used as a reference for the former. With the aim of obtaining a fully comprehensive view of the vorticity balance at play, the flow may be forced in either azimuthal direction, leading to a “westward” prograde current (similar to the Northern Current) or an “eastward” retrograde current. For slow flows, eastward and westward currents showed similar patterns, dominated by Kelvin–Helmholtz-type instabilities. For high-speed flows, eastward and westward currents showed very different behavior. In eastward currents, the variability is observed to concentrate toward the center of the jet and shows strong meandering formation. Westward currents, instead, showed major variability toward the edges of the jet, together with a strong variability over the uppermost slope, which has been associated here with a topographic Rossby wave trapped over the shelf break. The differences between eastward and westward jets are explained through the balance between shear-induced and topographically induced vorticity at play in each case. Moreover, a model of jets over a beta plane is successfully applied here, allowing its extension to any ambient potential vorticity gradient caused either by latitudinal or bottom depth changes.

Magnetic actuation of microscopic beads is a promising technique for enhancement and manipulation of scalar transport in micro-fluidic systems. This implies laminar and essentially three-dimensional (3D) unsteady flow conditions. The present study addresses fundamental transport phenomena in such configurations in terms of 3D coherent structures formed by the Lagrangian fluid trajectories in a 3D time-periodic flow driven by a rotating sphere. The flow field is represented by an exact Stokes solution superimposed by a nonlinear closed-form perturbation. This facilitates systematic “activation” and exploration of two fundamental states: (i) invariant spheroidal surfaces accommodating essentially 2D Hamiltonian dynamics; (ii) formation of intricate 3D coherent structures (spheroidal shells interconnected by tubes) and onset to 3D dynamics upon weak perturbation of the former state. Key to the latter state is emergence of isolated periodic points and the particular foliation and interaction of the associated manifolds, which relates intimately to coherent structures of the unperturbed state. The occurrence of such fundamental states and corresponding dynamics is (qualitative) similar to findings on a realistic 3D lid-driven flow subject to weak fluid inertia. This implies, first, a universal response scenario to weak perturbations and, second, an adequate representation of physical effects by the in essence artificial perturbation. The study thus offers important new insights into a class of flow configurations with great practical potential.

This study employs three-dimensional particle-tracking velocimetry (3D-PTV) for experimental investigation of the existence and properties of periodic lines in 3D lid-driven time-periodic flows inside a cylindrical cavity. These periodic lines, consisting of material points that periodically return to their initial position, play a central role in the transport properties of laminar flows, yet their existence has so far been demonstrated only in numerical simulations. The formation and characteristics of periodic lines are inextricably linked with spatiotemporal symmetries of the flow. 3D-PTV measurements determined that relevant symmetries, identified with previous symmetry analyses, are satisfied within experimental error bounds. These measurements subsequently isolated periodic lines in the designated symmetry planes, thus offering first experimental evidence of their physical existence and their fundamental reliance on symmetries. Experimental periodic lines are topologically equivalent to those in simulated flows with identical symmetries and exhibit the same response to changes in forcing conditions. The laboratory experiments by these observations bridge the gap from theoretical and numerical predictions on periodic lines to real 3D flows.