Vorticity Field Research Articles

High-resolution PIV measurement over wind-generated waves

The interaction between wind and waves plays a significant role in the exchange of heat, aerosols and gases, thereby influencing our understanding of climate dynamics and air–sea interaction. Particle image velocimetry (PIV) has emerged as a valuable tool for investigating the intricate effects of small-scale waves on airflow characteristics in laboratory settings. However, previous PIV experiments have exhibited notable variability in spatial resolution, potentially affecting the accuracy of turbulence statistics, particularly in relation to small-scale waves such as capillary ripples. To systematically explore the impact of PIV spatial resolution on airflow characteristics over multi-scale wind-generated waves, we conducted high-resolution planar PIV experiments near the wave surface. We adjusted the spatial resolution of the results by modifying the spatial filter. Additionally, recognising the limitations of the high-resolution PIV system in terms of wall-normal and streamwise extent, we conducted larger field-of-view experiments to capture consecutive waveforms and achieve spatial averaging across the boundary layer. Consistent with existing literature, our findings illustrate the formation of a horizontal shear layer leading to airflow separation on the lee side of the wave, accompanied by a pronounced vorticity field and circulation region. Notably, analysis of the high-magnification dataset reveals localised airflow separation caused by small-scale capillary waves, phenomena not resolved by the large field-of-view set-up, underscoring the importance of adequate spatial resolution. Further analysis indicates that a spatial resolution larger than the size of the capillary waves leads to significant attenuation of the spanwise vorticity imposed by the small-scale waves. In this study, we also introduce a novel method relying to identify wave surfaces solely on PIV images, demonstrating its effectiveness in detecting capillary-scale waves.

2-битные метаповерхности Патчаратнама-Берри с генерацией, интерференцией и гашением орбитального углового момента для широкополосного снижения ЭПР

The radar cross-section (RCS) reduction using non-absorbing digital Patcharatnam-Berry (PB) metasurfaces (MSs), consisting of 2-bit modules with generation, interference and cancellation of vortex electromagnetic waves with orbital angular momentum (OAM) is studied. Each module has a helical PB-phase profile and possesses vortex scattering. Module unit cells contain a shielded dielectric substrate and meta-particles in the form of triple-coupled split-ring resonators. The modules are distinguished by 2-bit coding of the initial tilt angle of the meta-particles 0º, 45º, 90º and 135º. The purpose of the work is to numerically analyze the generation of antiphase vortex beams (VBs) by OAM-modules and to assess the influence of interference and cancellation of antiphase vortices on the structure and order of OAM in the resulting field and the RCS reduction of three digital MSs in the form of 2´2 lattice of 2-bit OAM-modules of different sizes with different topological charges. The scattering characteristics are studied using HFSS for normally incident circularly polarized waves using of the finite element method. The simulation showed that the interference of phase vortices of four OAM-modules forms the main axial vortex and N additional interference side near and far vortices (N depends on the size of the MS). Interference vortex beams create phase singularities and zero the resulting far field in N side directions over the entire forward hemisphere. The intense OAM modes of the main vortex beams are of the fourth or eighth order. The OAM modes of adjacent interference VBs, as a rule, differ in sign. The proposed 2-bit MSs provide wider-angle phase cancellation of vortex fields (compared to 1-bit MSs) and, as a consequence, wider-angle diffuse scattering of the resulting field of the MS, which is important for RCS reduction.

Impact of the biological fouling on the hydrodynamic characteristics of nets under different current and attack angle conditions

The impact of biological fouling on the hydrodynamic performance of nets is examined in this paper. Since the safety and reliability of the net are threatened by biological fouling, particularly in the context of drag forces and flow characteristics. The drag forces exerted on clean nets and those affected by biological fouling under different attack angles (90° and 45°) are compared. The results highlight that biological fouling increases drag significantly, with 26.2 % to 65.8 % higher drag compared to clean nets within specific solidity ranges. As such, traditional drag coefficient formulas may not accurately predict the drag for biofouling nets. Aside from this, it is found that biological fouling enhances the shielding effect behind net twines, particularly at the 45° attack angle. Notably, significant velocity attenuation and fluctuation behind the aperture center of biofouling nets are observed, especially at the 45° attack angle. Furthermore, how the attack angle affects the vorticity field of biofouling nets on different characteristic planes are also assessed in this paper, aiming to provide insights into understanding how biological fouling alters the flow dynamics around the net structure, potentially affecting its performance and susceptibility to excitations such as currents/waves.

Vortex in superconducting thin-film strips of arbitrary width

The currents and field distributions of a vortex in a thin superconducting strip of a width W are considered. It is shown that unlike infinite films where the vortex field crosses the film only in one direction (say, from the half-space under the film to the half-space above it), in strips (as well as in finite size film samples of any shape) the field lines go back to the lower half-space not only out of the sample but also through certain strip parts. The strip patches where the magnetic lines ‘dive’ back to the space under the strip are situated mostly near the strip edges, at the strip and out of it. The magnetic flux through the strip associated with the vortex is shown to be less than the flux quantum and depends on the vortex position. The suppression of the vortex flux is strong in narrow strips with W<<Λ=2λ2/d where λ is the bulk London penetration depth and d is the film thickness. The vortex energy scales roughly with W/Λ and depends on vortex position.

Laminar flow and convective heat transfer characteristics of plain and wavy wall cross confined circular cylinder

An attempt is made to identify the convective heat transfer characteristics of the plain wall (Pw) and wavy wall (Ww) cross confined circular cylinder in the laminar flow regime (20 ≤ Re ≤ 100). The study has been extended to identify the wake heat transfer characteristics for various confinements (L = 0.5D, 1D, 1.5D and 2D), such that the weaker and stronger heat transfer region in the downstream of cross-confined cylinder has been investigated. CFD solver Ansys Fluent (Version 18.0) is used for assessing the field variables, the results are analyzed using streamline plots, λ 2-criterion vortex identification method, Nusselt number and field synergy method. The wall confinement is highly significant on heat transfer, the maximum Nusselt number is observed at high confinement (L = 0.5D) for all the Reynolds number studied. The changes in Nusselt number with respect to confinements is more significant at high confinements (L = 0.5D and L = 1D), become less significant at low confinements (L = 1.5D, 2D). It is found around 73% and 50% rise in Nusselt number for the confinement height, L = 0.5D as compared to L = 1D at Reynolds number 20 and100, respectively. Besides, in order to identify the heat stagnation region in the wake, contour of zero temperature gradient along the flow direction is observed. From the contour, it is identified that more heat stagnation region in the wake of Pw confined cylinder as compared to Ww confinement which is due to the three-dimensional behavior of flow in the wake.

Time-Averaged Parameters of the Circular Synthetic Jet for Different Dimensionless Stroke Length

Abstract The circular synthetic jet (SJ) for different dimensionless stroke lengths and at Reynolds number Re = 5000 was investigated in this paper. Particle image velocimetry (PIV) was used. The flow was measured at a distance of 240 mm from the orifice, and this area was divided into two fields of view (FOV). The parameter fields were created by the injunction of these two FOVs. The time-averaged velocity, turbulent kinetic energy (TKE), turbulence intensity, vorticity field, centerline, and profiles of SJ were presented and discussed. Additionally, the jet half-width of SJ was investigated. The data discontinuity at a line of the FOVs was discussed. The impact of the dimensionless stroke lengths on the parameters of SJ at Re = 5000 was discussed.

Derivation of “Double-Loop” Theory and Mechanism of Cavitation-Vortex Interaction in Turbulent Cavitation Boundary Layer

Abstract “Double-loop” theory was determined by deriving a correlation between turbulent fluctuating kinetic energy and water vapor volume fraction from the momentum equation, which further logically revealed the mystery of cavitation breaking around a three-dimensional symmetry hydrofoil based on the numerical results of large eddy simulation and Zwart–Gerber–Belamri cavitation model. When the second-order fluctuation moment Vx′Vx′ and the streamwise velocity Vx are depleted, a vortex is generated, leading to alternating cavitation interface fluctuations. In one state, cavitation naturally breaks outward from the inner zone, triggering an up-and-down fluctuation in the normal velocity in the gap vortex and transferring external energy to the inner zone. In another state, cavitation collapse caused by a reentrant jet stagnates the reverse Vx so that Vx′Vx′ tends to zero. It triggers a rise in an upward normal velocity in the attached vortex, creating an exchange of energy through the wake. The pressure implosion resulting from the Shrinkage of the “Like-Rayleigh–Plesset” cavity at the cavitation onset is stronger than the pressure implosion created by the vortex field during cavitation breaking.

Turbulence Closure With Small, Local Neural Networks: Forced Two‐Dimensional and β‐Plane Flows

AbstractWe parameterize sub‐grid scale (SGS) fluxes in sinusoidally forced two‐dimensional turbulence on the β‐plane at high Reynolds numbers (Re ∼25,000) using simple 2‐layer convolutional neural networks (CNN) having only O(1000) parameters, two orders of magnitude smaller than recent studies employing deeper CNNs with 8–10 layers; we obtain stable, accurate, and long‐term online or a posteriori solutions at 16× downscaling factors. Our methodology significantly improves training efficiency and speed of online large eddy simulations runs, while offering insights into the physics of closure in such turbulent flows. Our approach benefits from extensive hyperparameter searching in learning rate and weight decay coefficient space, as well as the use of cyclical learning rate annealing, which leads to more robust and accurate online solutions compared to fixed learning rates. Our CNNs use either the coarse velocity or the vorticity and strain fields as inputs, and output the two components of the deviatoric stress tensor, Sd. We minimize a loss between the SGS vorticity flux divergence (computed from the high‐resolution solver) and that obtained from the CNN‐modeled Sd, without requiring energy or enstrophy preserving constraints. The success of shallow CNNs in accurately parameterizing this class of turbulent flows implies that the SGS stresses have a weak non‐local dependence on coarse fields; it also aligns with our physical conception that small‐scales are locally controlled by larger scales such as vortices and their strained filaments. Furthermore, 2‐layer CNN‐parameterizations are more likely to be interpretable.

Coherence analysis of geophysical wakes in flow past a three-dimensional hill

Wakes generated by topographies are ubiquitous in nature. The formation and evolution mechanism of wake-generated eddies is essential to understanding the effect of topography on oceanic bottom flow. In this study, we analyze the temporally resolved numerical database [1] of stratified wakes past an isolated three-dimensional hill, via proper orthogonal decomposition (POD) of the vertical vorticity field. We study the dynamics of the near wake (x/D < 3) and the far wake (x/D ≥ 3) separately, where x is the downstream distance from the center of the hill. The aim is to understand how rotation influences the change of coherence from the near to the far wake and also the coherence across heights.

High-speed photography and particle image velocimetry of cavitation in a Venturi tube

This article details the construction of an experimental visualization platform for observing cavitation. The platform uses high-speed photography and particle image velocimetry (PIV) techniques to conduct experimental research into the flow pattern and vortex field of cavitation in Venturi tubes. Dynamic mode decomposition is employed to extract the energy distribution characteristics of the cavitation flow field. Cavitation occurs at an exit-to-inlet pressure ratio of 0.595, and the length of the cavitation zone increases as this ratio decreases. When the pressure ratio reaches 0.280, the flow rate remains almost constant and the flow becomes chocked. The cavitation shape evolves periodically in the chocking flow, and the cavitation zone can be divided into three parts: an initiation and development area, a fusion area, and a collapse area. The fusion area exhibits periodic changes in the form of contraction, expansion, and re-contraction. Near the wall, the collapse area exhibits complex boundary conditions, with re-entrant jet causing bubble aggregation, rolling, and shedding. PIV and energy extraction reveal that vortices primarily appear near the wall, where they undergo a periodic process of fragmentation and fusion. The strength of the vortices exhibits a small–large–small pattern that is related to the cloud aggregation, rolling, and shedding caused by the re-entrant jet.

Slip topology of steady flows around a critical point: Taking the linear velocity field as an example

The flow of viscous fluids is considered as the aggregation of the motion of fluid particles when the fluid is conceived to be made up by an infinite number of particles. As an alternative of this conventional model, fluid motion could be understood as the slip of fluid layers with a molecular scale over each other, where the slip structures of fluid and their associated small-scale motion are characterized by an axial-vector-valued differential 1-form, called the vortex field. In this paper, in the case of steady flows we define the swirling degree of the velocity field at a point, and further the swirl field of the steady flow, to study the slip topology of fluid or the local streamline pattern around the critical point. The linear velocity field in the right real Schur form is used to carry out detailed analyses around the isolated critical point. Theoretical deduction and numerical test unveil the connection between the swirling degree and the swirl field, greatly make clear the topological property of slip structures of fluid in steady flows, especially in three-dimensional space.

Структура вихревых полей в волноводе пекериса с учетом дислокаций

Vortex fields are the most complex and least studied objects in the acoustics of layered media. They significantly complicate the structure of the sound field due to the appearance of nodal and saddle points in it, in the vicinity of which the concept of the phase of the sound wave becomes uncertain. Therefore, such special points of the sound field are usually called phase front dislocations. In turn, the dislocation structure of the vortex field is most complex in waveguides, which play an extremely important role in theoretical and applied hydroacoustics. In this work, the vortex structure of the sound field and the corresponding dislocation structure of the vortex field are analyzed using the example of a Pekeris waveguide, the sound field in which is constructed within the framework of a non-self-adjoint model formulation of the corresponding boundary value problem.

Tunable Near and Mid-Infrared (1.3–5 µm) Picosecond Pulsed Optical Vortex Parametric Oscillator

In this paper, we present a picosecond pulsed, synchronously pumped optical parametric oscillator producing vortex beam output with tunable wavelengths in the near- to mid-infrared range. The system utilizes a Nd:YVO4 picosecond pulsed solid-state laser emitting at a wavelength of 1.064 µm to pump a Z-shaped, singly resonant OPO which contains a MgO:PPLN crystal with a fan-shaped grating. The wavelength tuning characteristics of the OPO output are examined both as a function of the MgO:PPLN grating period and crystal temperature. The orbital angular momentum of the pump field can be selectively transferred to either the signal or idler fields by appropriately adjusting the location of the MgO:PPLN crystal within the OPO cavity. The maximum output power of the signal and idler vortex fields are 5.12 W and 3.46 W, respectively, for an incident pump power of 19 W.

2D asymmetric diffraction grating controlled by vortex light in double-Λ-type atomic system

A two-dimensional (2D) asymmetric diffraction grating controlled by vortex light in a double-Λ-type atomic system is studied. Such an atomic system is driven by a weak traveling-wave probe field and a signal field, a position-dependent strong standing-wave (SW) control field, and a Laguerre–Gaussian (LG) vortex field. Due to the asymmetric properties of the LG vortex field, the probe photons can be asymmetrically diffracted into four different domains after passing through the atomic media. The Diffraction patterns and intensities of the 2D asymmetric diffraction grating can be manipulated by the detuning of the probe field, the interaction length, and the intensity of SW control field. In addition, the relative phase and the azimuth parameter which is closely related to the vortex light also can be used to regulate the asymmetric diffraction grating effectively. This work may provide useful reference for optical information processing, especially for the design of optical beam dividers with desired intensities and novel quantum devices requiring asymmetric optical transmission.

Numerical Analysis of Water–Sediment Flow Fields within the Intake Structure of Pumping Station under Different Hydraulic Conditions

The vortices, backflow, and siltation caused by sediment-laden flow are detrimental to the safe and efficient operation of pumping stations. To explore the effects of water–sediment two-phase flow on the velocity field, vorticity field, and sediment distribution within intake structures, field tests and numerical simulations were conducted in this study with consideration for the sediment concentration, flow rate, and start-up combination. We applied a non-contact laser scanner and ultrasonic Doppler velocimetry to obtain the field data and reverse modeling of the three-dimensional model of the intake structure under siltation. A multiphase flow model based on the Euler–Euler approach combined with the k-ε turbulence model was adopted for numerical simulation under 10 working conditions, and the reliability was verified with field data. The results indicate that sediment promotes the evolution of coaxial vortices into larger-scale spiral vortices along the water depth, and the process of sediment deposition is controlled by the range, intensity, and flow velocity of the backflow zone. Furthermore, the maximum volume fraction of the near-bottom sediment increased by 202.01% compared to the initial state. The increase in flow rate exacerbates the turbulence of the flow field. Although the increase in sediment concentration benefits the flow diffusion, it further promotes sediment deposition. This study provides a new idea for modeling complex surfaces and considers different operating conditions. It can serve as a scientific reference for the structural optimization and anti-siltation design of similar water-conservancy projects.

Analytical solution for the submerged free jet

Laminar submerged free jet theory still falls short in the near-nozzle region and transition to Schlichting's self-similar jet. The author's recent solution, based on mass conservation, is found lacking beyond the near-nozzle jet-core region. Instead, it is here constrained to conserve momentum, resulting in a locally linearized convection-diffusion equation, valid over jet width and up to self-similarity, when compared to simulations. This new solution leads to profile-specific values of virtual-origin correction to Schlichting's solution. Additionally, extensive jet characteristics are examined: (1) curvature core, (2) radial inflection location, (3) radial velocity, (4) vorticity field, (5) issuing mass, and (6) jet width. All are well predicted, and new insights are gained for a variety of issuing profiles: from uniform, through a non-monotonous profile and up to fully developed. The issuing mass of all non-uniform profiles undergoes an initial contraction proportional to the profile's level of development. Interestingly, the submerged jet contracts identically to the free-surface jet in the very near-nozzle region, before significant influence of their differing boundary conditions. Moreover, unless the issuing profile contains a radial inflection point, the inflection always occurs in the entrained fluid, just beyond the bounds of the issuing mass. It also follows an initial contraction and only later a widening toward the self-similar trend. Despite this contraction, the entrained fluid causes monotonous total jet-widening, at a rate inversely proportional to the level of development. Finally, this new solution correctly captures additional jet features, such as the local radial velocity and decay of the primary vorticity.

Fluid–structure interaction for mechanical filament valve mimicking a biological leaflet valve

The biological leaflet valve is a structure found in blood vessels and the cardiac system, designed to maintain a unidirectional flow within the vessels. Two filaments inspired by the biological leaflet are installed inside the channel, and behavior of two filaments is explored by using immersed boundary method. It is observed that the filaments serve as a valve, maintaining the unidirectional flow inside the channel depending on the length (L) and the initial inclined angle (θ) of the filaments. The behavior of the filaments is classified into three modes based on the flow characteristics around the filaments. The pressure and vorticity fields in the vicinity of the filaments are examined to investigate the influence of the surrounding flow on the behavior of filaments. The present study reveals the time sensitivity of valve response, the power consumption, and hydrodynamic efficiency (ηV,steady) of the filament valve, noting that the response speed of the filament valve can vary up to 2.5 times depending on L and θ. The dynamic behavior of the filament valve is analyzed with respect to changes in the properties of the filaments, observing a monotonic decrease in hydrodynamic efficiency with an increase in the bending rigidity (γ) of the filaments. As a result, the present study will be employed as a cornerstone in the development of a mechanical system that emulate biological structures through biomimetics.

A theory for the emission of infrasound from Tornadoes

Tornadoes have been shown to radiate infrasound to great distances, however convincing fundamental sound mechanisms are still absent. After using vortex sound theory to study sound generated by two numerical tornadoes, we found that there is a significant low-frequency signal between 0.1 Hz and 1 Hz. The sound is closely related to rotation of the non-axisymmetric vorticity field and its frequency depends on the rotational frequency. The non-axisymmetric vorticity field is represented by a Kirchhoff vortex-like flow in baseline tornado model and by multiple-vortex flow in eddy injection tornado model. Interestingly, there also exist high-frequency components in the later model which are hypothesized to originate from vortex merging process. Field detection data of tornado infrasound provides some support for the low-frequency sound.

An Algorithm for Solving the Problem of Phase Unwrapping in Remote Sensing Radars and Its Implementation on Multicore Processors

The problem of the interferometric phase unwrapping in radar remote sensing of Earth systems is considered. Such interferograms are widely used in the problems of creating and updating maps of the relief of the Earth’s surface in geodesy, cartography, environmental monitoring, geological, hydrological and glaciological studies, and for monitoring transport communications. Modern radar systems have ultra-high spatial resolution and a wide band, which leads to the need to unwrap large interferograms from several tens of millions of elements. The implementation of calculations by these methods requires a processing time of several days. In this paper, an effective method for equalizing the inverse vortex field for phase unwrapping is proposed, which allows solving a problem with quasi-linear computational complexity depending on the interferogram size and the number of singular points on it. To implement the method, a parallel algorithm for solving the problem on a multi-core processor using OpenMP technology was developed. Numerical experiments on radar data models were carried out to investigate the effectiveness of the algorithm depending on the size of the source data, the density of singular points and the number of processor cores.

Mathematical Simulation of the Influence of Acoustic on the Efficiency of PM 2.5 Coagulation

The particles of micron and submicron sizes (PM 2.5 and less) in gas environments pose a significant danger to humanity due to the emergence of specific and very dangerous diseases of the cardiovascular, respiratory, and immune systems of the human body. Such particles are the most difficult to detect; therefore, their effects on human health have only been discovered in recent decades. Classical ultrasonic coagulation by sinusoidal action turns out to be ineffective for PM 2.5 due to the peculiarities of the physical mechanisms of hydrodynamic and orthokinetic interaction realized in gaseous media. This article presents a theoretical justification for choosing ways to increase the efficiency of ultrasonic coagulation of PM 2.5 by creating special conditions under which nonlinear disturbances of the velocity and pressure of the gas phase in the ultrasonic field occur. The authors performed simulations of ultrasonic coagulation under nonlinear disturbances of the velocity (vortex) and the pressure (shock waves), which has numerical difficulties due to the instability of existing methods. As a result of the numerical analysis, the possibility of increasing the coagulation rate of particles in the submicron size range up to limit values (13 times due to nonlinear pressure disturbances, and an additional increase of at least 2 times due to aerosol compaction in the vortex field of gas velocity) was shown.