Formation Of Vortex Dipoles Research Articles

Asymmetric wake, origin, generation, and suppression behind asymmetrically pitching hydrofoil

The wakes behind a symmetrically and a quasi-symmetrically pitching hydrofoil are numerically studied. To understand the generation mechanism of the asymmetric wake behind a symmetrically pitching hydrofoil, we shed light on the timing of vortex shedding and convection velocity of vortices in the wake. The centers of the vortices in the wake are tracked using a method based on the critical point theory. The tracks of the vortex centers reveal crucial insights into the dependence of the vortex convection velocity on pitching frequency and pitching amplitude. The vortex strength and the spatial separation between the vortices embody the wake deflection. We find the inherent inability of the shear-layer rolling up at par with the pitching motion results in an uneven temporal separation (Δtʹ) between two consecutive vortices, which dictates the spatial separation between the vortices. The uneven temporal separation facilitates formation of vortex dipoles, which gives rise to the asymmetric wake formation. To substantiate the hypothesis of the uneven temporal generation of vortices, we used quasi-symmetric pitching of the hydrofoil, which can even the timing of vortex shedding and can metamorphose the asymmetric wake into a symmetric wake. On the contrary, relaxing the shear-layer roll-up can transmute a symmetric wake to an asymmetric wake. The detailed analysis of symmetrically pitching hydrofoil, quasi-symmetrically pitching hydrofoil, flexible hydrofoil, and asymmetrically pitching hydrofoil reveals that Δtʹ = 0.5, Δtʹ < 0.5 and Δtʹ > 0.5 correspond to a symmetric wake, an upward deflected wake and a downward deflected wake, respectively.

Long Josephson junctions with exciton-polariton condensates

We demonstrate the possibility to build stable Josephson $\pi$-junction stripes with exciton-polariton condensates. The stability of the $\pi$-junction between arbitrary long polariton stripes is achieved at low pumping by balancing the snaking instability with counter-propagating flows towards the junction. Not dissimilar from a dark soliton, the instability becomes relevant at high pumping leading to formation of vortex dipoles. The resulting structures can be stabilised to produce static lattices of Josephson vortices in straight and ring geometries. Our results build towards realization of quantum technological applications based on the Josephson effect at room temperature.

Experiments on tip vortices interacting with downstream wings

The interaction of meandering tip vortices shed from a leading wing with a downstream wing was investigated experimentally in a water tunnel using flow visualization, particle image velocimetry measurements, and volumetric velocity measurements. Counter-rotating upstream vortices may exhibit sudden variations of the vortex core location when the wing-tip separation is within approximately twice the vortex core radius. This is caused by the formation of vortex dipoles near the wing tip. In contrast, co-rotating upstream vortices do not exhibit such sensitivity. Large spanwise displacement of the trajectory due to the image vortex is possible when the incident vortex is further inboard. For both co-rotating and counter-rotating vortices, as long as there is no direct impingement upon the wing, there is a little change in the structure of the time-averaged vortex past the wing, even though the tip vortex shed from the downstream wing may be substantially weakened or strengthened. In the absence of the downstream wing, as well as for weak interactions, the most energetic unsteady modes represent the first helical mode |m| = 1, which is estimated from the three-dimensional Proper Orthogonal Decomposition modes and has a very large wavelength, on the order of 102 times the vortex core radius, λ/a = O(102). Instantaneous vorticity measurements as well as flow visualization suggest the existence of a smaller wavelength, λ/a = 5–6, which is not among the most energetic modes. These two-orders of magnitude different wavelengths are in agreement with the previous measurements of tip vortices and also exhibit qualitative agreement with the transient energy growth analysis. The very long wavelength mode in the upstream vortex may persist during the interaction, and reveal coupling with the trailing vortex as well as increased meandering.

Numerical study on the hydrodynamics of thunniform bio-inspired swimming under self-propulsion.

Numerical simulations are employed to study the hydrodynamics of self-propelled thunniform swimming. The swimmer is modeled as a tuna-like flexible body undulating with kinematics of thunniform type. The wake evolution follows the vortex structures arranged nearly vertical to the forward direction, vortex dipole formation resulting in the propulsion motion, and finally a reverse Kármán vortex street. We also carry out a systematic parametric study of various aspects of the fluid dynamics behind the freely swimming behavior, including the swimming speed, hydrodynamic forces, power requirement and wake vortices. The present results show that the fin thrust as well as swimming velocity is an increasing function of both tail undulating amplitude Ap and oscillating amplitude of the caudal fin θm. Whereas change on the propulsive performance with Ap is associated with the strength of wake vortices and the area of suction region on the fin, the swimming performance improves with θm due to the favorable tilting of the fin that make the pressure difference force more oriented toward the thrust direction. Moreover, the energy loss in the transverse direction and the power requirement increase with Ap but decrease with θm, and this indicates that for achieving a desired swimming speed increasing θm seems more efficiently than increasing Ap. Furthermore, we have compared the current simulations with the published experimental studies on undulatory swimming. Comparisons show that our work tackles the flow regime of natural thunniform swimmers and follows the principal scaling law of undulatory locomotion reported. Finally, this study enables a detailed quantitative analysis, which is difficult to obtain by experiments, of the force production of the thunniform mode as well as its connection to the self-propelled swimming kinematics and vortex wake structure. The current findings help provide insights into the swimming performance and mechanisms of self-propelled thunniform locomotion.

A DPIV study on the effects of separation distance upon the vortical behaviour of jet–cylinder impingements

An experimental investigation based on laser-induced fluorescence (LIF) and digital particle image velocimetry (DPIV) was conducted to provide a better understanding into the effects of jet–cylinder separation distance on the vortical structures and dynamic behaviour resulting from jet impingements upon convex cylinders. Separation distances of 1, 2 and 4 jet diameters were investigated, while cylinder–jet diameter ratio was maintained at 2 throughout. LIF and DPIV results show that jet ring-vortex initiation, wall-separated vortex initiation, vortex dipole formation and vortex separation occur further away from the impingement point as the separation distance decreases. Varying the separation distance also influences the recirculating wake region size at the cylinder lee sides, as well as producing two distinct flow modes between adjacent vortex dipoles along the cylinder straight edges. Mean and instantaneous skin friction coefficient distributions determined from DPIV results not only showcase the different effects of separation distance on the wall shear stress, but also illustrate how the flow dynamics influence the local wall shear stress levels. On the other hand, wall-separated vortex initiation, vortex dipole formation and separation events incur little distinctive changes upon the local wall shear stress distributions that may ease their unique identification.

Dynamics of laminar circular jet impingement upon convex cylinders

Flow dynamics associated with a laminar circular jet impinging upon a convex cylinder has been investigated by laser-induced fluorescence and digital particle-image velocimetry techniques. Cylinder-to-jet diameter ratios of 1, 2, and 4 were investigated, while the jet-to-cylinder separation distance was kept at four jet diameters throughout. Flow visualization and λ2 criterion results show that once the jet ring-vortices impinge upon the cylindrical surface, they move away from the impingement point by wrapping themselves partially around the surface. As the cylinder diameter increases, wall boundary layer separation, vortex dipole formation, and separation locations are initiated earlier along the cylindrical surface, producing significantly larger wakes. Along the cylinder straight-edges, ring-vortex cores are significantly smaller after impingement. This is due to accentuated vortex-stretching caused by partial wrapping around the cylindrical surface by the ring-vortices, on top of their movement away from the impingement point. Interestingly, vortex dipoles demonstrate a strong tendency to travel upstream and interact with other upstream vortex dipoles, instead of moving downstream gradually seen for flat-surface jet-impingements. Wall shear stress results are also presented to quantify the effects of cylinder diameter-ratio on surface skin friction distribution. Finally, these preceding observations are corroborated and explained in a three-dimensional flow dynamics model presented here.

Vortex Dipole Formation by Baroclinic Instability of Boundary Currents

Abstract In situ data of the Mediterranean Water undercurrents and eddies south of Portugal indicate that the undercurrents have a tubelike structure in potential vorticity and that dipole formation can occur when the lower undercurrent extends seaward below an offshore upper countercurrent. A two-layer quasigeostrophic model is used to determine the dynamical conditions under which dipole formation is possible. With piecewise-constant potential vorticity, the flow exhibits two linear modes of instability comparable to those found in the Phillips model with topography. Weakly nonlinear analysis and fully nonlinear simulations of the flow evolution agree on the regimes of either finite-amplitude perturbation saturation, corresponding to filamentation, or amplification, corresponding to vortex or dipole formation. This latter regime is more specifically studied: vortex dipole formation and ejection from the coast is obtained for long waves, with opposite-signed but similar amplitude layer potential vorticities. A simple point vortex model reproduces this phenomenon under the same conditions. It is then shown that dipole formation occurs for minimal wave dispersion, and hence for weak horizontal velocity shears. As observed at sea, dipoles are formed when the lower potential vorticity core extends seaward below a countercurrent.

Transition from deep to shallow water layer: formation of vortex dipoles

In this paper we study the transition from a deep to a shallow water layer and the formation of quasi-two-dimensional vortex dynamics. Vortices are experimentally generated by a circular horizontal turbulent pulsed jet. The dimensional analysis gives two relevant dimensionless parameters: the jet Reynolds number Re and a number C which characterizes the vertical confinement. They are respectively defined by Re= Q /ν and C=( Q /H 2)t inj ( H is the water depth, ν is the kinematical viscosity, Q the injected momentum flux and t inj the injection duration). Experimental results show a strong influence of C on the flow: when C<1, the evolution is a typical three-dimensional turbulence decay, while when C>2 we observe the formation of large vortex dipoles. However these dipoles are not strictly two-dimensional because of the presence of a vertical circulation in the front of the dipole. Results are independent of the jet Reynolds number in the range 1000< Re<1800. In addition, a comparison between experimental shallow water dipoles and theoretical model is exposed.

Simulations of Spatially Developing Two-Dimensional Shear Layers and Jets

A computational study of spatially evolving two-dimensional free shear flows has been performed using direct numerical simulation of the Navier–Stokes equations in order to investigate the ability of these two-dimensional simulations to predict the overall flow-field quantities of the corresponding three-dimensional “real” turbulent flows. The effects of inflow forcing on these two-dimensional flows has also been studied. Simulations were performed of shear layers, as well as weak (large co-flow and relatively weak shear) and strong (small co-flow and relatively strong shear) jets. Several combinations of discrete forcing with and without a broadband background spectrum were used. Although spatially evolving direct simulations of shear layers have been performed in the past, no such simulations of the plane jet have been performed to the best of our knowledge. It was found that, in the two-dimensional shear layers, external forcing led to a strong increase in the initial growth of the shear-layer thickness, followed by a region of decreased growth as in physical experiments. The final downstream growth rate was essentially unaffected by forcing. The mean velocity profile and the naturally evolving growth rate of the shear layer in the case of broadband forcing compare well with experimental data. However, the total and transverse fluctuation intensities are larger in the two-dimensional simulations with respect to experimental data. In the weak-jet simulations it was found that symmetric forcing completely overwhelms the natural tendency to transition to the asymmetric jet column mode downstream. It was observed that two-dimensional simulations of “strong” jets with a low speed co-flow led to a fundamentally different flow with large differences even in mean velocity profiles with respect to experimental data for planar jets. This was a result of the dominance of the two-dimensional mechanism of vortex dipole ejection in the flow due to the lack of spanwise instabilities. Experimental studies of planar jets do not show vortex dipole formation and ejection. A three-dimensional “strong”-jet simulation showed the rapid evolution of three-dimensionality effectively preventing this two-dimensional mechanism, as expected from experimental results.