Vortex Dipole Research Articles

Anisotropic dipolar vortex quantum droplets in an annular potential

Two-dimensional dipolar Bose–Einstein condensates confined within an annular potential are investigated. Stable ring-shaped anisotropic dipolar vortex quantum droplets are discovered in this configuration. These droplets remain stable under the influence of the annular potential, even with embedded vorticity up to 11. The stability regions of dipolar vortex droplets with varying embedded vorticity are confirmed through long time evolution. The characteristic parameters of the dipolar vortex droplets are systematically studied, and their existence curves are shown to contradict the well-known V–K criterion. Additionally, the shape transformation of dipolar vortex droplets induced by the strength of the mean-field interaction is examined. Finally, the behavior of dipolar vortex droplets confined within a wake-depth annular potential is also discussed.

Abundant vortex dynamics in spin-1 Bose–Einstein condensates induced by Rashba spin–orbit coupling

The paper studies the dynamics of vortices evolved from the ring dark solitons (RDSs) in spin-1 Bose–Einstein condensates with Rashba spin–orbit coupling (SOC). We find that the SOC induces abundant vortex dynamic phenomena, and the numbers of vortex dipoles and lump-like solitons are all determined by the initial depths’ weighted average of the three components of RDSs. For a shallow RDS, the ring first expands and then contracts into a mini RDS, eventually evolving into late vortex dipoles. For the RDS with a moderate initial depth, during the contraction of the ring, it evolves into early vortex dipoles or lump-like solitons, and they evolve back into the mini RDS, which then evolves into late vortex dipoles during the expansion process. For the deep and black RDSs, the early vortex dipoles continue to transform between vortex dipoles and lump-like solitons without forming mini RDS. The motions of vortices mentioned above have a higher disorder degree than that in the system without SOC, because the SOC breaks the mirror symmetry of the condensate. Finally, we reveal that the SOC strength only influences the number of late vortex dipoles, while it does not affect the number of early vortex dipoles and lump-like solitons. Stronger SOC intensity results in a shallower critical depth, and vortices form only at or beyond this depth.

Modon solutions in an N-layer quasi-geostrophic model

Modons, or dipolar vortices, are common and long-lived features of the upper ocean, consisting of a pair of counter-rotating monopolar vortices moving through self-advection. Such structures remain stable over long times and may be important for fluid transport over large distances. Here, we present a semi-analytical method for finding fully nonlinear modon solutions in a multi-layer quasi-geostrophic model with arbitrarily many layers. Our approach is to reduce the problem to a multi-parameter linear eigenvalue problem which can be solved using numerical techniques from linear algebra. The method is shown to replicate previous results for one- and two-layer models and is applied to a three-layer model to find a solution describing a mid-depth propagating, topographic vortex.

Two-dimensional vortex dipole, tripole, and quadrupole solitons in nonlocal nonlinearity with Gaussian potential well and barrier.

In this work, we investigate the dynamics and stability of two-dimensional (2D) vortex dipole, tripole, and quadrupole solitons with fundamental topological charge (m = 1) and higher topological charge (m > 1) in nonlocal nonlinearity with Gaussian potential well and barrier. Both analytical and numerical methods are applied to explore these vortex solitons. The analytical expressions are derived by utilizing the variational approach. The numerical simulations show that nonlocality cannot stabilize the vortex dipole, tripole, and quadrupole beams with topological charge m = 1. Interestingly, it is found that these vortex solitons remain stable during propagation only when the topological charge is m = 2 and when the propagation constants are below specific thresholds, where the vortex beams can maintain their profile no matter whether the nonlocality is weak, intermediate, or strong or how the Gaussian potential barrier height (well depth) increases. Furthermore, for the solitons with higher topological charge (m = 4), another consistent pattern emerges, that is, vortex dipole, tripole, and quadrupole solitons split into stable petal solitons and fundamental solitons with the number of petal solitons corresponding to the number of vortex solitons present. The analytical results are verified by numerical simulations.

Impingement of vortex dipole on heated boundaries and related thermal plume dynamics

The profound influence of an externally induced vortex dipole on thermal plume dynamics is numerically studied for varying Rayleigh numbers (Ra) employing the Bhatnagar–Gross–Krook collision model-based lattice Boltzmann method with a double distribution function approach. This study is extended to vortex dipole impingement with different types of heated bottom boundaries of two-dimensional domain, such as flat, “V-shaped,” and “inverted-V-shaped.” The vortex dipole impingement with the heated boundaries generates secondary vortices, which in turn produce vortex-driven thermal plumes, thereby advancing plume generation. The subsequent merging of the plumes enhances heat transport and leads to a continuous plume ascent. The presence of convex corners facilitates flow separation and also gives rise to the formation of secondary vortex dipoles, thereby significantly impacting the continuous generation of jet-like plumes when compared to concave configurations. The lack of an external vortex in pure buoyancy-driven flows produces less pronounced jet-like plumes and a relatively low Nusselt number. The boundary types and Ra significantly influence the vorticity production, resulting in higher enstrophy and palinstrophy for convex boundaries compared to flat and concave ones. A lower Prandtl number increases secondary vortices and corner rolls, leading to larger velocity gradients, higher thermal diffusivity, resulting in increased kinetic energy and thermal dissipation rates. The increased cell height enhances heat transfer at the top boundary due to improved heat convection from the slanted boundary and influence of early dipole impingement. Furthermore, kinetic energy dissipates in the dipole-driven flows and increases in the buoyancy-dominated flows.

On the Role of the Meridional Jet and Horizontal Potential Vorticity Dipole in the Iowa Derecho of 10 August 2020

Abstract On 10 August 2020, a derecho caused widespread damage across Iowa and Illinois. Des Moines station data show that the arrival of the gust front was characterized by an abrupt shift to northerly flow, exceeding 22 m s−1 for ∼20 min. To test the hypothesis that this northerly jet is associated with a horizontal potential vorticity (PV) dipole in the lower troposphere, we investigated the structure of PV in the University of Wisconsin Nonhydrostatic Modeling System (UWNMS) and of absolute vorticity in High-Resolution Rapid Refresh (HRRR) forecast analyses. This structure is described here for the first time. The negative PV member coincides with the downdraft, while the positive PV member coincides with the updraft, with a northerly jet between. The westerly inflow jet descends anticyclonically in the downdraft, joining with northerly flow from the surface anticyclone. The resulting northerly outflow jet creates the trailing comma-shaped radar echo. The speed of propagation of the derecho is similar to the westerly wind maximum in the 3–5-km layer associated with the approaching synoptic cyclone, which acts as a steering level for resonant amplification. Idealized diagrams and 3D isosurfaces illustrate the commonality of the PV dipole/northerly jet structure. Differences in this structure among the three model states are related to low-level wind shear theory. The PV dipole coincides with the pattern of diabatic stretching tendency, which shifts westward and downward relative to the updraft/downdraft with increasing tilt. The PV dipole can contribute toward dynamical stability in a derecho. Significance Statement The purpose of this work is to investigate the structure of potential vorticity (PV) in the lower troposphere in a derecho. It is found that a northerly outflow jet occurs between an east–west-oriented horizontal PV dipole, which is described here for the first time. The negative PV member coincides with the downdraft and is inertially unstable, while the positive PV member coincides with the updraft. This work contributes toward the theory of resonant structures and longevity. The 3–5-km westerly inflow layer constitutes a steering level, which controls propagation speed despite differences in structure. The degree of westward tilt with height is related to the pattern of forcing by diabatic stretching in producing the PV dipole.

The quantum perfect fluid in 2D

We consider the field theory that defines a perfect incompressible 2D fluid. One distinctive property of this system is that the quadratic action for fluctuations around the ground state features neither mass nor gradient term. Quantum mechanically this poses a technical puzzle, as it implies the Hilbert space of fluctuations is not a Fock space and perturbation theory is useless. As we show, the proper treatment must instead use that the configuration space is the area preserving Lie group {S\mathrm{Diff}}SDiff. Quantum mechanics on Lie groups is basically a group theory problem, but a harder one in our case, since {S\mathrm{Diff}}SDiff is infinite dimensional. Focusing on a fluid on the 2-torus T^2T2, we could however exploit the well known result {S\mathrm{Diff}}(T^2)\sim SU(N)SDiff(T2)∼SU(N) for N\to ∞N→∞, reducing for finite NN to a tractable case. SU(N)SU(N) offers a UV-regulation, but physical quantities can be robustly defined in the continuum limit N\to∞N→∞. The main result of our study is the existence of ungapped localized excitations, the vortons, satisfying a dispersion \omega \propto k^2ω∝k2 and carrying a vorticity dipole. The vortons are also characterized by very distinctive derivative interactions whose structure is fixed by symmetry. Departing from the original incompressible fluid, we constructed a class of field theories where the vortons appear, right from the start, as the quanta of either bosonic or fermionic local fields.

Вихрова октупольна мода у кінетичній моделі колективних збуджень в ядрах

The nature of a new isoscalar octupole resonance found within a kinetic model based on the Vlasov equation for finite Fermi systems with moving surfaces is studied. It is shown that this octupole resonance is due to dynamic effects of the nuclear surface, like the low-energy isoscalar dipole resonance (vortex dipole mode) observed in heavy nuclei. It is found that the velocity field associated with the new octupole resonance has a vortex character in the surface region of the nuclear liquid and, moreover, the vortex motion of nucleons is fragmented into three areas near the nuclear surface. At the same time, the velocity field associated with the high-energy octupole resonance found within our kinetic model displays an octupole deformation form and includes a compression within the nuclear fluid, which is consistent with the corresponding quantum calculations in the random phase approximation.

Dynamics of Ring Dark Solitons and the Following Vortices in Spin-1 Bose–Einstein Condensates

Abstract This work focuses on the evolution behaviors of ring dark solitons (RDSs) and the following vortices after the collapses of RDSs in spin-1 Bose-Einstein condensates. We find that the weighted average of the initial depths of three components determines the number and motion trajectories of vortex dipoles. For the weighted average of the initial depths below the critical depth, two vortex dipoles form and start moving along the horizontal axis. For the weighted average depth above the critical depth, two or four vortex dipoles form, and all start moving along the vertical axis. For the RDS with weighted average depth at exactly the critical point, four vortex dipoles form, half of the vortex dipoles initiate movement vertically, and the other half initiate movement horizontally. Our conclusion is applicable to the two-component system studied in earlier research, indicating its universality.

Taking inspiration from the natural tubular sponge to enhance momentum exchange in marine environments

Coral reefs consist of various alive elements with specific biological functions. Tubular sponges, as the main coral reefs' constituents, have a marvelous mechanism. They receive nutrients by suctioning from the perforated body (Ostia) and pumping the un-digested materials through the water column from the top mouth (Osculum). This mechanism can be an inspiration for making a device to control or improve sediment/pollutant transport. In the current study, an attempt has been made to evaluate an inspired concept's effects on flow hydrodynamics. In this regard, OpenFOAM® V. 1812 (interFOAM solver) and image processing technique were deployed. The perforated finite-height cylinders (height to diameter ratio of 2.5) with various suction/pump discharges (i.e., J = 150, 300, 350, 400, 450, and 600 lit/h) were considered. The results indicated that increasing the outflow discharge (J ≥ 600 lit/h) could widen the wake by flapping the shear layer. In the vertical plane, the results showed that dipole vortices turned into quadrupole vortex. On the free surface, tip-vortices and counter-rotating vortex pairs (CRVP) generated saw-toothed vortices on two sides of the cylinder. Generating these unique vortices is proof of enhancing the momentum exchange through the water column.

Numerical simulation of 3D vorticity dynamics with the Diffused Vortex Hydrodynamics method

In this paper the three-dimensional extension of the Diffused Vortex Hydrodynamics (DVH) is discussed along with free vorticity dynamics simulations. DVH is a vortex particle method developed in-house and widely validated in a 2D framework. The DVH approach has been embedded in a new frontend to the open-source code PEPC, the Pretty Efficient Parallel Coulomb solver. Within this parallel Barnes–Hut tree code, a superposition of elementary heat equation solutions in a cubic support is performed during the diffusion step. This redistribution avoids excessive clustering or rarefaction of the vortex particles, providing robustness and high accuracy of the method. An ascending vortex dipole at various resolutions is selected as a test-case and heuristic convergence measurements are performed, taking into account the conservation of prime integrals and the energy–enstrophy balance.

Hydrodynamics and propulsion of a hydrofoil undergoing leading-edge pitching and traveling wave-based surface undulation

We numerically study the fluid–structure interaction of a free-stream flow across a hydrofoil pitching at its leading edge with superimposed traveling wave-based surface undulations. We utilize an in-house code that employs the sharp interface immersed boundary method and consider a constant pitching amplitude θ0 = 5°, a constant local amplitude-to-thickness ratio AL=0.15, and wave number K = 20 of surface undulation. We compare the effect of surface undulation on a pitching hydrofoil with that of a hydrofoil undergoing pure pitching or experiencing pure surface undulation. The findings reveal that surface undulation on the pitching hydrofoil increases thrust on the hydrofoil. The onset of asymmetry in the vortex street occurs at a lower pitching Strouhal number (St) due to the early formation of a vortex dipole. In addition to the presence of an asymmetric inverse von Kármán vortex street, higher pitching frequencies reveal re-deflection of the asymmetric inverse von Kármán vortices. We quantified dynamics of vortex dipole to explain the occurrence of asymmetric and re-deflected reverse von Kármán vortex street. Furthermore, the analysis reveals an optimum combination of St and phase speed that yields higher propulsive efficiency, as both motions compete in generating thrust. A linearly superimposed scaling analysis for the time-averaged thrust of the combined motion is also presented. The computations and scaling are found to be in good agreement.

Kármán vortex street in a spin–orbit-coupled Bose–Einstein condensate with PT symmetry

The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while ‘the half-quantum vortex street’ is observed in the other component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence, and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately 0.18, which is less than the stability condition 0.28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin–orbit coupling disrupts the symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize the Kármán vortex street in a system.

Fourth-order modon in a rotating self-gravitating fluid

We present a two-dimensional nonlinear equation to govern the dynamics of disturbances in a rotating self-gravitating fluid. The nonlinear term of the equation has the form of a Poisson bracket (Jacobian), and the linear part contains, along with the Laplacian, a biharmonic operator. A solution was found in the form of a dipole vortex (modon). The solution and all its derivatives up to the fourth order are continuous on the separatrix.

Linear instability and weakly nonlinear effects in eastward dipoles

The linear instability and weakly nonlinear dynamics of eastward-propagating, steady-state Larichev–Reznik vortex dipoles are explored in terms of two-dimensional normal-mode analysis. To extract the fastest growing normal modes, we apply both breeding methodology based on solving the initial-value problem, as well as a direct-solution approach through the full-spectrum eigenproblem involving large matrices. We find that the amplification rate of dipole instability decreases with respect to increase in dipole intensity. In our study, both approaches yield consistent results and are systematically compared to provide guidance for further studies of vortex structures.We consider nonlinear self-interaction of the fastest growing mode, along with the induced eddy fluxes, their divergence and mechanical energy balance. Through this analysis, we find that the unstable mode leads to weakening of the dipole by extracting its energy and exchanging potential vorticity content in the down-gradient sense, thus, providing a nonlinear physical mechanism for the dipole destruction. In particular, we highlight the fundamental importance of the west-east asymmetry of the normal mode for destruction to be realized. In summary, we consider this work to be a foundational demonstration of useful methodology for future studies of dynamics and stability of isolated vortices without simplifying spatial symmetries, such as ubiquitous vortices in geophysical fluids.

Asynchronous quantum Kármán vortex street in two-component Bose-Einstein condensate with PT symmetric potential

The dynamics of a miscible two-component Bose-Einstein condensate (BEC) with PT (parity-time) symmetric potential are investigated numerically. The dynamical behaviors of the system is described by Gross-Pitaevskii (GP) equations under the mean-field theory. Firstly, the ground state of the system is obtained by the imaginary-time propagation method. Then dynamical behaviors are numerically simulated by the time-splitting Fourier pseudo-spectral approach under periodic boundary conditions. By adjusting the width and velocity of the obstacle potential, various patterns such as no vortex, oblique drifting vortex dipole, V-shaped vortex pairs, irregular quantum turbulence and combined modes are studied. It is noted that the shedding vortex pairs in components 1 and 2 are staggered, which is called “the asynchronous quantum Kármán vortex street”. Here, the ratio of the distance between two vortex pairs in one row to the distance between vortex rows is approximately 0.18, which is less than the stability criterion 0.28 of classical fluid. We calculated the drag force acting on the obstacle potential during generation of the asynchronous quantum Kármán vortex street. It is found that periodical oscillation of the drag force is generated via drifting up or down of the vortex pairs. Meanwhile, we analyzed the influence of the imaginary part of the PT symmetric potential with gain-loss for wake. The trajectory and frequency of the vortex are changed, due to the imaginary part breaks the local symmetry of the system. In addition, the imaginary part affects the stability of the asynchronous quantum Kármán vortex street. Lots of numerical simulations are carried out to determine the parameter regions of various vortex shedding modes. We also proposed an experimental protocol to realize the asynchronous quantum Kármán vortex street in the miscible two-component BEC with PT symmetric potential.

Statistical analysis of vortex condensate motion in two-dimensional turbulence

An inverse turbulent cascade in a periodic square box produces a coherent system-sized vortex dipole. We study the statistics of its motion by carrying out direct numerical simulations performed for various bottom friction α, pumping intensity ε, and fluid hyperviscosity ν. In the main approximation, coherent vortices can be considered as point vortices, and within this model, they drift at the same dipole velocity, which is determined by their circulation and mutual arrangement. The characteristic value of the dipole velocity is more than an order of magnitude smaller than the polar velocity inside coherent vortices. Turbulent fluctuations give rise to a relative velocity between the vortices, which changes the distance between them. We found that for a strong condensate, the probability density function of the vector ρ, describing the difference in the mutual arrangement of coherent vortices from half the diagonal of the computational domain, has the form of a ring. The radius of the ring weakly depends on control parameters and its width is proportional to parameter δ=ϵ−1/3L2/3α, where ϵ is the inverse energy flux and L is the system size. The random walk around the ring, caused by turbulent fluctuations, has superdiffusion behavior at intermediate times. It results in a finite correlation time of the dipole velocity, which is of the order of turnover time τK=L2/3ϵ−1/3 of system-size eddies produced by an inverse turbulent cascade. The results obtained deepen the understanding of the processes governing the motion of coherent vortices.

The Importance of Being Asymmetric for Geophysical Vortices

Several types of spatial symmetry in vortex structures within rotating stratified fluids are examined by looking at self-propagating configurations in the quasigeostrophic model. The role of symmetry breaking in the dynamics of geophysical waves, vortices and instabilities is highlighted. In particular, the energy exchange of the large-scale vertical shear with monopolar and dipolar vortices is analyzed. Various coupled vortex-wave structures are described in terms of wavy and evanescent modes. The Rossby wave radiation is shown to induce a zonal asymmetry, which is needed for the energy support and self-amplification of vortices in large-scale flow. The consequences for the evolution of the most long-lived vortices in the subtropical westward flows are discussed.

Scattering of swell by currents

The refraction of surface gravity waves by currents leads to spatial modulations in the wave field and, in particular, in the significant wave height. We examine this phenomenon in the case of waves scattered by a localised current feature, assuming (i) the smallness of the ratio between current velocity and wave group speed, and (ii) a swell-like, highly directional wave spectrum. We apply matched asymptotics to the equation governing the conservation of wave action in the four-dimensional position–wavenumber space. The resulting explicit formulas show that the modulations in wave action and significant wave height past the localised current are controlled by the vorticity of the current integrated along the primary direction of the swell. We assess the asymptotic predictions against numerical simulations using WAVEWATCH III for a Gaussian vortex. We also consider vortex dipoles to demonstrate the possibility of ‘vortex cloaking’ whereby certain currents have (asymptotically) no impact on the significant wave height. We discuss the role of the ratio of the two small parameters characterising assumptions (i) and (ii) above, and show that caustics are significant only for unrealistically large values of this ratio, corresponding to unrealistically narrow directional spectra.

Deformation and destruction of north-eastward drifting dipoles

We systematically study the evolution of Larichev–Reznik dipoles in an equivalent-barotropic quasi-geostrophic beta-plane model in high-resolution numerical simulations. Our results shed light on the self-organization and rich dynamics of dipolar vortices, which are ubiquitous in geophysical flows. By varying both dipole strength and initial angle α0 of dipole tilt to the zonal direction, we discover new breakdown mechanisms of the dipole evolution. The dipoles are quickly destroyed by Rossby wave radiation, if initial tilt is too large or the dipole is too weak; otherwise, via damped oscillations, the dipoles tend to adjust themselves to different states drifting eastward. Two competing physical mechanisms that govern dipole transformations are found: (1) spontaneous dipole instability due to a growing critical linear mode and (2) meridional separation of dipole partners that accumulates over the adjustment period and prevents the above instability. Which mechanism prevails depends on the initial tilt and dipole strength, and the details of this are discussed.