Vortex Dynamics Research Articles

Vertical bending and aerodynamic performance in flying snake-inspired aerial undulation.

This paper presents a numerical investigation into the aerodynamic characteristics and fluid dynamics of a flying snake-like model employing vertical bending locomotion during aerial undulation in steady gliding. In addition to its typical horizontal undulation, the modeled kinematics incorporates vertical undulations and dorsal-to-ventral bending movements while in motion. Using a computational approach with an incompressible flow solver based on the immersed-boundary method, this study employs Topological Local Mesh Refinement (TLMR) mesh blocks to ensure the high resolution of the grid around the moving body. Initially, we applied a vertical wave undulation to a snake model undulating horizontally, investigating the effects of vertical wave amplitudes (ψ_m). The vortex dynamics analysis unveiled alterations in leading-edge vortices (LEV) formation within the midplane due to changes in the effective angle of attack resulting from vertical bending, directly influencing lift generation. Our findings highlighted peak lift production at ψ_m=2.5° and the highest lift-to-drag ratio at ψ_m=5°, with aerodynamic performance declining beyond this threshold. Subsequently, we studied the effects of the dorsal-ventral bending amplitude (ψ_DV), showing that the tail-up/down body posture can result in different fore-aft body interactions. Compared to the baseline configuration, the lift generation is observed to increase by 17.3% at ψ_DV = 5°, while a preferable lift-to-drag ratio is found at ψ_DV = -5°. This study explains the flow dynamics associated with vertical bending and uncovers fundamental mechanisms governing body-body interaction, contributing to the enhancement of lift production and efficiency of aerial undulation in snake-inspired gliding.

How does vortex dynamics help undulating bodies spread odor?

In this paper, we examine the coupling between odor dynamics and vortex dynamics around undulating bodies, with a focus on bio-inspired propulsion mechanisms. Utilizing computational fluid dynamics simulations with an in-house immersed boundary method solver, we investigate how different waveform patterns, specifically carangiform and anguilliform, influence the dispersion of chemical cues in both water and air environments. Our findings reveal that vortex dynamics significantly impact the overall trajectory of odor spots, although the alignment between odor spots and coherent flow structures is not always precise. We also evaluate the relative contributions of diffusion and convection in odor transport, showing that convection dominates in water, driven by higher Schmidt numbers, while diffusion plays a more prominent role alongside convection in air. Additionally, the anguilliform waveform generally produces stronger and farther-reaching chemical cues compared to carangiform swimmers. The critical roles of Strouhal number and Reynolds number in determining the efficiency of odor dispersion are also explained, offering insights that could enhance the design of more efficient, adaptive, and intelligent autonomous underwater vehicles by integrating sensory and hydrodynamic principles inspired by fish locomotion.

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.

Enhancing Aerodynamic Performance of Double Rectangular Cylinders through Numerical Analysis at Varying Inclinations

In the present work, numerical simulations are conducted for external flow through a double rectangular cylinder with different inclinations at Reynolds number (Re) 50 to 200 based on free stream velocity. The cylinder aspect ratio is considered to be fixed at 0.25. During the numerical simulations, one cylinder is kept fixed, and the other cylinder is inclined at ‘θ = 20o’ first clockwise and then in an anticlockwise direction alternatively for both cylinders. Because of the inclined cylinder, the vortex dynamics lead to significant changes in flow-induced forces. In this article, the focus is given to how Re and inclination in the cylinder influence the flow structures and associated aerodynamic properties. It is shown that when any of the cylinders are inclined, a significant decrease in the average drag coefficient is noticed as compared to the parallel cylinder case. In a similar manner, the lift coefficient also decreases when any one of the cylinders is inclined at θ = 20o either clockwise or counterclockwise as compared to the parallel cylinder case.

Effect of sweep angle on three-dimensional vortex dynamics over plunging wings

The effects of sweep angle and reduced frequency on the leading-edge vortex (LEV) structure over flapping swept wings in the Reynolds number (Re) range of O(104) are yet to be completely understood. With increasing interest in designing bio-inspired micro-air-vehicles, understanding LEV dynamics in such scenarios is imperative. This study investigates the effects of three different sweep angles (Λ=0°, 30°, and 60°) on LEV dynamics through high-fidelity improved delayed detached eddy simulation to analyze the underlying flow physics. Plunge ramp kinematics at two different reduced frequencies (k = 0.05 and 0.4) are studied to investigate the unsteady motion effects on LEV characteristics. The leading-edge suction parameter concept is applied to determine LEV initiation, and the results are verified against flow field visualization for swept-wing geometries. The force partitioning method is used to investigate the spanwise lift distribution resulting from the LEV. Distinct peaks in the lift coefficient occur for the high reduced frequency case due to the impulse-like plunging acceleration. This causes the LEV to detach from the leading edge more quickly and convect faster, significantly affecting the lift generated by the wing. As reduced frequency increases, the LEV breakdown mechanism switches from vortex bursting to LEV leg-induced instabilities. These results provide insights into the complex vortex structures surrounding swept wings at Re = 20 000, and the impact both sweep angle and reduced frequency have on the lift contribution of these flow features.

Magnetic Memory Effects in BaFe2(As0.68P0.32)2 Superconducting Single Crystal.

Among many iron-based superconductors, isovalently substituted BaFe2(As1-xPx)2 displays, for x ≈ 0.3, apart from the quite usual Second Magnetization Peak (SMP) in the field dependence of the critical current density, an unusual peak effect in the temperature dependence of the critical current density in the constant field, which is related to the rhombic-to-square (RST) structural transition of the Bragg vortex glass (BVG). By using multi-harmonic AC susceptibility investigations in three different cooling regimes-field cooling, zero-field cooling, and field cooling with measurements during warming up-we have discovered the existence of a temperature region in which there is a pronounced magnetic memory effect, which we attributed to the direction of the structural transition. The observed huge differences in the third harmonic susceptibility at low and high AC frequencies indicates the difference in the time-scale of the structural transition in comparison with the timescale of the vortex excitations. Our findings show that the RST influence on the vortex dynamics goes beyond the previously observed influence on the onset of the SMP.

Onset of global instability in a premixed annular V-flame

We investigate self-excited axisymmetric oscillations of a lean premixed methane–air V-flame in a laminar annular jet. The flame is anchored near the rim of the centrebody, forming an inverted cone, while the strongest vorticity is concentrated along the outer shear layer of the annular jet. Consequently, the reaction and vorticity dynamics are largely separated, except where they coalesce near the flame tip. The global eigenmodes corresponding to the linearised reacting flow equations around the steady base state are computed in an axisymmetric setting. We identify an arc branch of eigenmodes exhibiting strong oscillations at the flame tip. The associated eigenvalues are robust with respect to domain truncation and numerical discretisation, and they become destabilised as the Reynolds number increases. The frequency of the leading eigenmode is found to correspond to the Lagrangian disturbance advection time from the nozzle outlet to the flame tip. The essential role of this convective mechanism is also supported by resolvent analysis, which finds that the same flame-tip disturbance structure and frequency are optimally amplified when the flame is subjected to external white noise forcing. Strong non-modal effects in the form of pseudo-resonance are not found. Nonlinear time-resolved simulation further reveals notable hysteresis phenomena in the subcritical regime prior to instability. Hence, even when the flame is linearly stable, perturbations of sufficient amplitude can trigger limit-cycle oscillations and higher-dimensional dynamics sustained by nonlinear feedback. A Monte Carlo simulation of passive tracers in the unsteady flame suggests a nonlinear non-local instability mechanism. Notably, linear analysis of the subcritical time-averaged limit-cycle state yields eigenvalues that do not match the nonlinear periodic oscillation frequencies. This mismatch is attributed to the fundamentally nonlinear dynamics of the subcritical V-flame instability, where the dichromatic, non-local interaction between the heat release rate along the flame surface and the vortex dynamics in the jet shear layer cannot be approximated as a simple distortion of the mean flow.

Analysis of Wind Power Fluctuation in Wind Turbine Wakes Using Scale-Adaptive Large Eddy Simulation

In large wind farms, the interaction of atmospheric turbulence and wind turbine wakes leads to complex vortex dynamics and energy dissipation, resulting in reduced wind velocity and subsequent loss of wind power. This study investigates the influence of vortex stretching on wind power fluctuations within wind turbine wakes using scale-adaptive large eddy simulation. The proper orthogonal decomposition method was employed to extract the most energetic contributions to the wind power spectra. Vertical profiles of mean wind speed, Reynolds stresses, and dispersive stresses were analyzed to assess energy dissipation rates. Our simulation results showed excellent agreement when compared with wind tunnel data and more advanced numerical models, such as the actuator line model and the actuator line model with hub and tower effects. This highlights the important role of coherent and energetic flow components in the spectral behavior of wind farms. The findings indicate a persistent energy cascading length scale in the wake of wind turbines, emphasizing the vertical transport of energy to turbine blades. These results complement existing literature and provide new insights into the dynamics of wind turbine wakes and their impact on wind farm performance.

Turbulent flow around convex curved tandem cylinders

Turbulent flow around curved tandem cylinders has been studied for the first time, by means of direct numerical simulation. The convex configuration was used, with a nominal gap ratio of $L/D = 3$ and a Reynolds number of 3900. Along the span, the flow regimes vary from alternating overshoot/reattachment to co-shedding. Three distinct Strouhal numbers coexist in the flow that are tied directly to different tandem cylinder flow regimes. This result differs substantially from convex curved tandem cylinders at a transitional Reynolds number, where only a single dominant frequency is found. All regimes exhibit some degree of instability, so that the flow can be considered multistable. A mode switch from alternating overshoot/reattachment to symmetric reattachment is found. Complex interactions are observed between the primary instability, the shear layer instability and the flow mode alterations. As opposed to previous investigations with single and tandem straight cylinders in the subcritical flow regime, our results indicate that there may be direct feedback from the primary instability to the shear layer instability. The downdraft region in the gap exhibits slow meandering, and may travel upstream and amplify the shear layer instability, causing early transition in the gap shear layer. This downdraft is governed by the slow modulations of the vortex formation region in the lower gap, meaning that the vortex dynamics of this region may indirectly influence the shear layer instability higher up in the gap.

A penta-hybrid approach for modeling the nanofluid flow in a spatially dependent magnetic field

Abstract The penta-hybrid nanofluid is a nanofluid that contains five different types of nanoparticles. It can achieve higher heat transfer rates than conventional hybrid nanofluids due to the synergistic effects of the nanoparticles. It also has more diverse physical and thermal properties, which make it more adaptable for various applications. Therefore, this research examines the influence of localized magnetic fields on the vortex dynamics in a penta-hybrid nanofluidic flow in a vertical cavity with an aspect ratio of 1:10, driven by a top and bottom lid moving in the opposite direction. The stream-vorticity formulation is used to solve the dimensionless governing partial differential equation. A confined magnetic field in the form of horizontal and vertical strips has been applied instead of a uniform magnetic field throughout the flow domain, which is more realistic. Moreover, MATLAB codes developed by the authors are used to investigate how these parameters affect the flow and thermal properties of the nanofluids. The results suggest that magnetic fields have an impact on how stress, flow patterns, and temperature are distributed. Moreover, the presence of a magnetic field influences the spacing of isotherms, indicating a more even temperature distribution. It has also been observed that stress distribution is affected by the magnetic field, with higher stress levels near walls and regions with velocity-induced stress. However, in certain areas, the magnetic field can decrease shear stress depending on its strength and orientation. These study findings have implications for designing and operating nanofluidic devices. For instance, utilizing a magnetic field can help regulate flow patterns, temperature distribution, and stress distribution within nanofluidic channels. This capability could prove beneficial for a range of applications, such as cell separation, drug delivery, and nanofluidic heat exchange systems.

On the linear response theory of vortex meandering and its statistical verification in experiments

Meandering designates the main manifestation of unsteady vortex dynamics observed in experiments. This study has the twofold objective to (i) develop a theoretical model describing vortex meandering and (ii) conduct a quantitative and objective evaluation of the model against experimental data. Based on an analogy with Brownian motion, we derive the theoretical model in the framework of linear response theory. Taking the form of a Langevin equation, our model explains meandering as the competition between external excitation by free-stream perturbations, counteracted by stabilising intrinsic vortex dynamics. As such, it contains the previous approaches to explaining the phenomenon as limiting cases, and clearly highlights their shortcomings. The statistical identification of characteristic regularities in experimental data as well as the assessment of their consistency with theoretical models are important problems in physics. For samples obtained from finite-length records of correlated data, these statistical characteristics are not unique and may show spurious behaviour merely induced by the finiteness of the sample. Statistical inference provides a systematic and quantitative methodology to objectively assess the reproducibility of statistical characteristics and to evaluate their consistency with theoretical models. Their systematic application to the analysis of vortex meandering has not been done before and provides statistical evidence for our proposed Brownian-motion-like model. That is, experimental vortex meandering constitutes the manifestation of a stationary Gauss–Markov random process, which implies that the dynamics admits an ergodic probability measure.

Chiral active systems near a substrate: Emergent damping length controlled by fluid friction

Chiral active fluids show the emergence of a turbulent behaviour characterised by multiple dynamic vortices whose maximum size varies for each experimental system, depending on conditions not yet identified. We propose and develop an approach to model the effect of friction close to a surface in a particle based hydrodynamic simulation method in two dimensions, in which the friction coefficient can be related to the system parameters and to the emergence of a damping length. This length is system dependent, limits the size of the emergent vortices, and influences other relevant system properties such as the actuated velocity, rotational diffusion, or the cutoff of the energy spectra. Comparison of simulation and experimental results of a large ensemble of rotating colloids sedimented on a surface shows a good agreement, which demonstrates the predictive capabilities of the approach, which can be applied to a wider class of quasi-two-dimensional systems with friction.

Entropy generation and thermal behavior of microchannel fitted with punched curved vortex generators

Utilizing curved vortex generators (VGs) has emerged as a promising way to improve heat transfer in heat exchangers. However, research on the placement of punched rectangular curved winglet VGs on two opposing heat transfer surfaces of microchannel heat exchangers is limited. Through experiments and simulations, the effects of five perforation positions and three pitches on fluid flow and heat transfer were examined. This analysis is performed in the turbulent flow regime (2500 < Re < 3500) and the governing equations are solved by using SST k-ω model, assuming that the fluid is incompressible, has constant thermal properties, and ignores the effects of thermal radiation and gravity. Metrics such as the Nusselt number ratio, friction coefficient ratio, secondary flow intensity, thermal enhancement factor, and entropy generation are used to analyze the flow dynamics of mixed vortices. The results indicate that different perforation positions significantly affect the vortex characteristics, altering heat transfer and pressure loss. Furthermore, the pitch of the VGs plays a crucial role in governing heat transfer and frictional losses. Specifically, the heat transfer rate increased by 12.1 % to 61.1 % compared to empty tubes, accompanied by a rise in pressure loss ranging from 50.6 % to 115.1 %. To validate the findings, the principle of entropy generation was utilized. Notably, under conditions of a Re of 2500, a perforation position proximal to the VG's leading edge (θ = +12°), and a pitch of 15 mm, a remarkable thermal enhancement factor of 1.29 was achieved.

Free energy formulae for confined nematic liquid crystals based on analogies with Kirchhoff–Routh theory in vortex dynamics

Active nematics are influenced by alignment angle singularities called topological defects. The localization of these defects is of major interest for biological applications. The total distortion of alignment angles due to defects is evaluated using Frank free energy, which is one of the criteria used to determine the location and stability of these defects. Previous work used the line integrals of a complex potential associated with the alignments for the energy calculation (Miyazako and Nara 2022 R. Soc. Open Sci . 9 , 211663 (doi: 10.1098/rsos.211663 )), which has a high computational cost. We propose analytical formulae for the free energy in the presence of multiple topological defects in confined geometries. The formulae derived here are an analogue of Kirchhoff–Routh functions in vortex dynamics. The proposed formulae are explicit with respect to the defect locations and conformal maps, which enable the explicit calculation of the energy extrema. The formulae are applied to calculate the locations of defects in so-called doublets and triplets by solving simple polynomial formulae. A stability analysis is also conducted to detect whether defect pairs with charges ± 1 / 2 are stable or unstable in triplet regions. Our numerical results are shown to match the experimental results (Ienaga et al. 2023 Soft Matter 19 , 5016–5028. (doi: 10.1039/d3sm00071k )).

Numerical investigations of aerodynamic characteristics in highly loaded tandem cascades with end-bend

Tandem cascades and end-bend blades can reduce compressor losses and promote energy conservation. In this study, a vortex model tailored for tandem cascades is proposed. Numerical investigations are conducted to elucidate the influence of end-bend heights and angles on aerodynamic characteristics. A quantitative assessment of the loss contribution for each vortex is provided based on loss weight coefficients. The findings demonstrate that end-bend angles exert a more pronounced impact on aerodynamic characteristics than end-bend heights. Although the implementation of end-bend increases the loss of the front blade trailing edge shedding vortex, it reduces losses by weakening the passage vortex and the rear blade trailing edge shedding vortex, resulting in a net decrease of the total loss. The end-bend blade optimizes the loading profile near the endwall, characterized by an expanded low-pressure zone behind the gap. A comparative analysis is performed among four tandem cascades: straight, curved, end-bend, and combined curved-end-bend. The correlation between losses, vortices, and topological structures is established by using topological analysis together with the vortex model. It is a crucial research methodology for elucidating the mechanisms of loss generation and vortex dynamics in tandem cascades with end-bend.

Numerical simulation on the interaction of median fins for enhancing vortex dynamics and propulsion performance in fish self-propelled swimming

Studies have shown that fish can enhance propulsion performance by utilizing the interaction between median fins (dorsal, anal, and caudal fins), compared to fish with only caudal fin. However, most of the current studies are based on the fish oscillating in-place, and the analysis of median fins interaction to improve swimming propulsion performance is still insufficient, and the mechanism needs further study. This study applied three-dimensional numerical simulation methods to solve the process of grass carp accelerating from a stationary state to cruising state under different body and median fins combination, as well as different motion parameter models. A comparative quantitative analysis of different models was conducted to assess the impact of median fins interactions on enhancing swimming performance, with a detailed analysis of the hydrodynamic mechanisms and their relationship with vortex dynamics. The results indicated that interactions between median fins could generate significant hydrodynamic benefits, with the fish's average swimming speed increasing up to 4.6 times, thrust up to 33.47%, and swimming efficiency up to 25.48%. This study found that the enhancement of propulsion performance was due to the formation of high-intensity and persistent posterior body vortices by the movements of the dorsal and anal fins, which were captured by the leading-edge of the caudal fin, greatly enhancing the strength of the leading-edge vortex. This study elucidates the hydrodynamic mechanisms of the interaction between median fins and could provide new insights into the efficient swimming mechanism of fish in nature.

Excitation of the Gyrotropic Mode in a Magnetic Vortex by Time-Varying Strain.

We demonstrate the excitation of the gyrotropic mode in a magnetostrictive vortex by time-varying strain. The vortex dynamics is driven by a time-varying voltage applied to the piezoelectric substrate and detected electrically by spin rectification at subthreshold values of rf current. When the frequency of the time-varying strain matches the gyrotropic frequency at a given in-plane magnetic field, the strain-induced in-plane magnetic anisotropy leads to a resonant excitation of the gyration dynamics in the magnetic vortex. We show that nonlinear gyrotropic dynamics can be excited already for moderate amplitudes of the time-varying strain.

The nonlinear behavior of generic tail fins for small wind turbines

This paper describes analysis and measurements of the yaw response of tail fins for small wind turbines. It is based on an extension of unsteady slender body theory (USBT) to cover non-slender fins and high angles of incidence, both of which make the theory nonlinear. We provide three main additions to the substantial literature on linearized USBT for tail fins. First, USBT is extended to high angles by modeling the nonlinear vortex dynamics. Second, the restriction to slender bodies is removed by modeling the chordwise load variation. Third, we consider the effect of time-varying wind speed. The extended theory is compared to wind tunnel measurements of the yaw behavior of delta, elliptical, and rectangular tail fins without a rotor and nacelle. The fins were released from initial yaw angles of −40° and −80°; the latter is of sufficient magnitude to show the importance of the nonlinear yaw dynamics. Generally good agreement was found between the theory and measurements, and the theory was shown to be more accurate than a “polar” or quasi-steady model which uses only the lift and drag of a delta planform. Of the three planforms, the rectangular one showed the lowest accuracy in terms of frequency but the damping was accurately predicted. Overall, the results demonstrate the importance of nonlinearity in the response of a yawing tail fin, particularly for the higher aspect ratio fins at large yaw angles.

Numerical investigation of the collision of a vortex pair upon a solid wavy wall

The vortex dynamics produced by the collision of a vortex pair with a solid wavy wall are examined numerically using a proposed high-order vortex particle method. The influences of the Reynolds number (ReΓ) of the vortex pair, the wavelength (λw), and the wave amplitude (Aw) of the wall on the induced vortex structures, interactions among vortices, and the instability and reconnection of secondary vortices are discussed. The boundary layers at the top of ripples separate first to form the secondary vortices moving around the primary tubes. Meanwhile, the boundary layers at the bottom of ripples detach late, move vertically upward, and then form incomplete vortex loops due to an unsuccessful reconnection of the secondary vortices. The ReΓ effects cause the appearance of various vortex structures, such as incomplete primary vortex loops from the bottom of ripples at ReΓ=1000, secondary vortex loops due to interactions of the first loops with the wall at ReΓ=2000, and hairpin vortices at ReΓ=4000. The wavelength of the wall induces instability in the secondary vortex tubes. This instability on the secondary tubes appears at the top of ripples at λw=2r0, while it spreads over the whole secondary vortices at λw=4r0, where r0 is the initial spacing between the primary vortex tubes. This instability results in various wavy tubes that robustly interact with the primary tubes. Due to the effects of Aw, the primary vortex tubes significantly decay with time compared to those in the flat wall case.

Flux dynamics, anisotropy in Jc and vortex phase diagram of H+-intercalated FeSe single crystal

This paper investigates the superconductivity, pinning, and vortex dynamics of FeSe before and after protonation. The study shows that, after being protonated, FeSe's superconducting critical temperature Tc has been increased to more than 40 K and the critical current density Jc has also been increased from 2.1 × 104 A/cm2 to 1.2 × 106 A/cm2, with significantly larger magnetic relaxation rates (Q). Meanwhile, the critical current density anisotropy (γ) decreases substantially while the upper critical field Hc2 increases from 13 T to 91 T after protonation. In addition, the reasons for the absence of the second peak effect in Hx-FeSe were explored. This investigation also reveals the existence of the vortex phase transition associated with the pinning behavior in protonated FeSe, demonstrated by the foot-like characteristics of resistivity. Based on these results, the vortex phase diagrams of FeSe before and after protonation were established. These findings provide important insights for exploring new high-temperature superconductors and their magnetic flux dynamics through protonation.