Rr Ruben Trieling

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 (Q2D) 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 (3D) 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 l...

Interaction of two unequal corotating vortices

Previous high-resolution contour dynamics calculations [Dritschel and Waugh, Phys. Fluids A 4, 1737 (1992)] 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 t...

Experiments on rapidly rotating turbulent flows

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 90≲Reλ≲240. Relevant properties of the turbulence, both with and without rotation, have been quantified with stereoscopic particle image velocimetry (SPIV). 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 characteriz...

The Behavior of Jet Currents over a Continental Slope Topography with a Possible Application to the Northern Current

Abstract 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 flo...

Dipolar vortices in a strain flow

The evolution characteristics of dipolar vortices in a strain flow were investigated both experimentally and theoretically. The laboratory experiments were performed in a stratified fluid, the strain flow being generated by four rotating horizontal discs, whereas the dipolar vortex was created by a pulsed injection of a small amount of fluid. Dye-visualization studies and particle-tracking techniques were used to obtain qualitative and quantitative information about the horizontal flow field. Depending on the initial orientation of the dipole, either a head–tail structure or a pair of elliptic-like monopolar vortices was formed. In the former case, the distance between the vortex centers was observed to remain nearly constant due to the opposing effects of strain and lateral diffusion, while in the latter case, the vortex centers were passively advected by the ambient flow. The head–tail formation could be explained kinematically by a simple point-vortex model. Full-numerical simulations based on the quasi-two-dimensional vorticity equation revealed a very good agreement with the laboratory observations.

Decay of monopolar vortices in a stratified fluid

The decay of monopolar vortices in a stratified fluid has been investigated experimentally, and the observations have been compared with an analytical decay model that accounts for both the increasing vertical thickness and the radial expansion of these pancake-like structures. The monopolar vortices were generated by two different forcing techniques, and the corresponding horizontal velocity field was measured by tracking passive tracer particles. It was found that the monopolar vortices are characterized by a core of single-signed vorticity and a ring of oppositely signed vorticity, and that their net circulation is zero. The observations are in good agreement with the theoretical model, which provides a better description of the vortex evolution than the diffusion models presented in earlier studies.

Influence of initial conditions on decaying two-dimensional turbulence

A numerical study of freely decaying two-dimensional turbulence is presented to show how the time evolution of characteristic flow quantities is influenced by the initial conditions. The numerical method adopted is a standard two-dimensional (2D) Fourier pseudospectral algorithm with Newtonian viscosity. Vortex statistics are extracted using a vortex census method. Several characteristic initial vorticity distributions analogous to those employed in previous laboratory experiments are considered. Some of the initial vorticity distributions have in common a dominant subset of vortices. Reliable statistics are obtained for each characteristic distribution by ensemble averaging. For the dominant subset, the time evolutions of the global enstrophy and the number density, respectively, are found to collapse confirming the self-similarity of 2D turbulence, one of the starting points for the scaling theory proposed by Carnevale et al. [Phys. Rev. Lett. 66, 2735 (1991)]. The relationship between the relevant scal...

Monopolar vortices in an irrotational annular shear flow

The evolution characteristics of monopolar vortices in an irrotational annular shear flow were investigated both experimentally and theoretically. The background flow was generated in a rotating tank by an appropriate source–sink configuration, while the monopolar vortex was created by withdrawing fluid for a short time. Dye-visualization studies demonstrated the gradual destruction of the vortex through a process called ‘vortex stripping’, i.e. long filaments of passive tracers were being shed from the edge of the vortex. In contrast to uniform shear flows, these filaments were asymmetrically attached to the vortex core. Furthermore, the vortex was observed to evolve in a quasi-stationary manner until its final indefinite breaking. The asymmetric stripping process could be explained by modelling both the monopolar vortex and the ambient flow simply by point vortices, and by adopting the method of contour kinematics to trace material contours in the velocity field induced by the point vortices. Furthermore, the effect of a continuous spatial vorticity distribution was investigated by applying the contour dynamics technique, in which the vortex is represented by a stack of uniform vorticity patches. The observed vortex evolution could be well captured by this latter approach.

Laboratory experiments on multipolar vortices in a rotating fluid

The instability properties of isolated monopolar vortices have been investigated experimentally and the corresponding multipolar quasisteady states have been compared with semianalytical vorticity-distributed solutions to the Euler equations in two dimensions. A novel experimental technique was introduced to generate unstable monopolar vortices whose nonlinear evolution resulted in the formation of multipolar vortices. Dye-visualization and particle imaging techniques revealed the existence of tripolar, quadrupolar, and pentapolar vortices. Also evidence was found of the onset of hexapolar and heptapolar vortices. The observed multipolar vortices were found to be unstable and generally broke up into multipolar vortices of lesser complexity. The characteristic flow properties of the quadrupolar vortex were in close agreement with the semianalytical model solutions. Higher-order multipolar vortices were observed to be susceptible to strong inertial oscillations.

Dynamics of monopolar vortices in a strain flow

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.