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The paper proposes a theory of similarity of quasi-geostrophic vortices against the background of large-scale flows. This information is useful when planning laboratory and numerical experiments to study mesoscale and submesoscale vortex dynamics of vortices interacting with currents. Special attention is paid to studying geometric similarity of phenomena. It is revealed that the complete set of dimensionless similarity numbers of baroclinic vortices includes four dimensionless parameters: the dimensionless intensity of the vortex, the geometric similarity of the background flow (the ratio of the relative vorticity to the deformation coefficient of the background flow), the coefficient of horizontal stretching of the vortex core, and the coefficient of vertical oblateness of the vortex core coinciding with the Burger number. To describe the similarity of barotropic vortices against the background of barotropic flows, the number of necessary dimensionless parameters is reduced by one number: the coefficient of vertical oblateness of the vortex core is eliminated from consideration. When studying axisymmetric vortices or vortex structures close to axisymmetric, another geometric parameter of the vortex is eliminated from consideration—the coefficient of horizontal stretching of the vortex core. As a result, the maximum possible set of similarity parameters includes four dimensionless numbers, and the minimum is two. [ABSTRACT FROM AUTHOR]

The evolution of unforced and weakly damped two-dimensional turbulence over random rough topography presents two extreme states. If the initial kinetic energy E is sufficiently high, then the topography is a weak perturbation, and evolution is determined by the spontaneous formation and mutual interaction of coherent axisymmetric vortices. High-energy vortices roam throughout the domain and mix the background potential vorticity (PV) to homogeneity, i.e., in the region between vortices, which is most of the domain, the relative vorticity largely cancels the topographic PV. If E is low, then vortices still form but they soon become locked to topographic features: Anticyclones sit above topographic depressions and cyclones above elevated regions. In the low-energy case, with topographically locked vortices, the background PV retains some spatial variation. We develop a unified framework of topographic turbulence spanning these two extreme states of low and high energy. A main organizing concept is that PV homogenization demands a particular kinetic energy level E#. E# is the separator between high-energy evolution and low-energy evolution. [ABSTRACT FROM AUTHOR]

Here we consider a model of an isolated vortex to understand the vertical dynamics induced by mesoscale eddies in the ocean. We use the analytical solutions to a balanced model for an ellipsoid of uniform potential vorticity to examine how the vertical motions induced depend on the vortex shape and its orientation, i.e. whether the vortex is vertically upright or tilted with respect to the vertical axis. The motion induced by the vortex can be divided into two kinds: (1) the interior flow which acts on the vortex itself and (2) the exterior flow which acts on its surroundings. For an upright ellipsoid, there are no self-induced vertical motions and the vortex rotates steadily about the vertical axis. However, for a tilted ellipsoid we find solutions exist where the vortex rotates about the vertical axis, while the vertical motions cause the tilt angle of the vortex to oscillate. This effect is stronger as the tilt angle is increased. Considering the exterior flow, there exists an exterior vertical velocity for the upright and tilted ellipsoids. However, the dynamics induced by the exterior vertical velocity is very different for the upright and tilted cases. We find that for an upright ellipsoidal vortex, the vertical motions are largest for vortices with high horizontal eccentricity and a vertical height-to-width aspect ratio near unity, vanishing as the horizontal cross-section of the vortex becomes circular. Instead for the tilted case, the vertical motions are largest when the horizontal cross section is circular, and for strongly prolate vortices, with the largest vertical motions occurring when the tilt angle is 45 ∘ . [ABSTRACT FROM AUTHOR]

The Liutex vector is new quantity introduced to represent the rigid-body rotation part of fluid motion and thus to define and identify vortices in various flows. In this work, the intermittency and power-law similarity of the Liutex vector in homogeneous, isotropic turbulence and a turbulent channel are explored. First, we found that the Liutex vector is more intermittent than the vorticity vector in the considered turbulent flows, which indicates that an iso-surface of a Liutex magnitude with an appropriate threshold could capture the major rotating motions or vortical motions of the flow. Second, the three-dimensional energy spectrums of velocity, vorticity (enstrophy spectrum) and the Liutex vector in homogeneous isotropic turbulence are shown to exhibit power laws of −5/3, 1/3 and 1/3 in the inertial subrange, respectively, whilst the Liutex energy spectrum particularly satisfies an additional −10/3 power law in the viscous subrange. This viscous similarity of the Liutex vector is the only power law that survived from the wall presence and is argued to originate from the fact that the Liutex vector represents the rigid part of fluid motion and is free from any shear contamination. The existence of such a viscous similarity law indicates a certain coherence of the small scales of turbulence and could possibly help understand and model turbulence. [ABSTRACT FROM AUTHOR]

To effectively analyses the flame propagation of premixed hydrogen-air explosion, this paper carries out a numerical study on the dynamics of flame propagation during hydrogen explosions in a closed duct under different blocking rates. The study shows that flame structure is roughly the same when the flame passes through an obstacle under different blocking rates. The difference in blocking rates only shows a slight difference in the degree of flame deformation. When the flame passes through the obstacle, Rayleigh -Taylor (R-T) instability accompanies the entire flame propagation process and corresponds to each stage flame acceleration. Kelvin-Helmholtz(K-H) instability has a more prominent influence on the tip flame propagation. When the explosion flame propagates, instabilities lead to difference in density gradient and pressure gradient in the duct. Interaction between density gradient and pressure gradient leads to formation of baroclinic torque, which is the main cause of the vorticity. During the flame propagation, the vorticity at the front of the flame is roughly zero, whereas the vorticity formed at the obstacle or in the burned gases is more apparent. The larger the blocking rate, the more prominent the turbulence intensity during the flame propagation. • Flame structure is roughly same under the different blocking rates obstacles. • Rayleigh -Taylor (R-T) instability accompanies the entire flame propagation. • Kelvin-Helmholtz(K-H) instability influence on the tip flame propagation. • Baroclinic torque is the main cause of the vorticity. [ABSTRACT FROM AUTHOR]

This paper presents the results of experimental and numerical investigations on synthetic jet actuators with various arrangements. First, an actuator with one membrane in the cavity is a standard, reference arrangement; and second, one novel modified arrangement has two membranes in the cavity. Authors use constant temperature-anemometry measurements to identify the characteristic frequencies in which the output jet velocity reaches a maximal value, namely, the resonant frequency of the actuator (Helmholtz frequency) and of the membrane (structural resonance). A numerical model of a synthetic jet actuator has been validated using experimental data for the case with one membrane in a cavity. The simulation results confirm the existence of a toroidal vortex at the actuator exit for the frequencies determined in the experiment. Numerical results of a modified actuator with two membranes in the cavity give promising results in the context of separation control by synthetic jet devices, i.e., increase of output velocity and vorticity from the same occupied space is obtained. Numerical simulations show that in the modified actuator with two membranes in the cavity, the jet output velocity and vorticity of a created toroidal vortex at the actuator outlet can be increased by 80%, compared to the case with one membrane. The new geometry of a synthetic jet actuator with perpendicular membranes is to be implemented into the wind tunnel measurements to prove the use of a modified synthetic jet actuator as a device applicable for active flow control. [ABSTRACT FROM AUTHOR]

The runaway condition is unsteady and is of significant importance in pump turbines. In this research, the shear-stress transport (SST) k - ω turbulence model is used to simulate the unsteady flow in the vaneless region and the runner of a prototype pump turbine. The characteristics of pressure fluctuations, vortex identification based on Q criterion and local entropy generation rate (LEGR) in the pump turbine under runaway condition are studied, and the relationships of these physical quantities in the vaneless region are determined. Internal flow research reveals the motion and transmission characteristics of vortices in the vaneless region and the runner. The results show that the vortices that move clockwise in the vaneless region are responsible for the flow separation, the increase of LEGR, and the generation of the characteristic frequency 1.4 f n of these physical quantities (pressure fluctuations, Q criterion and LEGR). In runner, it is found that the characteristic frequency of pressure fluctuation is 3.6 f n , which satisfies a linear relationship with the characteristic frequency 1.4 f n in the vaneless region. The vortices, moving in the vaneless and runner region, interact with the blades of runner and mainly contribute to the pressure fluctuation characteristic frequency in the runner. • Unsteady flow and fluctuations of a pump turbine under runaway condition are studied. • Flow separation and vortices cause energy dissipation in vaneless region and runner. • Vortex motion greatly affects pressure fluctuation in vaneless region. • Interaction between blade and vortex causes pressure fluctuation frequency in runner. [ABSTRACT FROM AUTHOR]

Unsteady cavitating turbulent flow around a NACA66 hydrofoil was simulated using a mass transfer cavitation model and a modified filter-based turbulence model in this paper. The modified filter-based turbulence model can accurately predict the pressure coefficient in midplane and shedding frequency of the unsteady cloud cavitation than standard κ – 𝜀 model and filter-based turbulence model. The time evolution of transient cavitation cloud structure predicted by the three-turbulence model was compared. The result which was predicted by the modified filter-based turbulence model is in good agreement with the experimental results. The time evolution of re-entrant jet had been analyzed. The instantaneous wall-pressure evolution on the suction surface (SS) predicted by the modified filter-based turbulence model had been analyzed. The cavitation-vortex interaction had been analyzed in this study. The different effects on the cavitation-vortex interaction of the vortex stretching term, vortex dilatation term and baroclinic torque term in the transport equation of vorticity had been discussed. [ABSTRACT FROM AUTHOR]

Concentration-compactness is used to prove compactness of maximising sequences for a variational problem governing symmetric steady vortex-pairs in a uniform planar ideal fluid flow, where the kinetic energy is to be maximised and the constraint set comprises the set of all equimeasurable rearrangements of a given function (representing vorticity) that have a prescribed impulse (linear momentum). A form of orbital stability is deduced. [ABSTRACT FROM AUTHOR]

In the framework of two-dimensional ideal hydrodynamics, we define a vortex system as a smooth vorticity function with a few local positive maximums and negative minimums separated by curves of zero vorticity. We discuss the invariants of such structures that follow from the vorticity conservation law and the invertibility of Lagrangian motion. Introducing new functional variables diagonalizing the original noncanonical Poisson bracket, we develop a Hamiltonian formalism for vortex systems. [ABSTRACT FROM AUTHOR]

By using the Stereo Particle Image Velocimetry (PIV) technique we observe the secondary flow of second kind in a corner of a channel of square cross-section. The boundary layer thickness is much lower than the channel size. Therefore, the flow is still developing, not filling the entire channel cross-section, which is the case more widely reported in literature studied in a very long channel. The non-linear secondary effects of interacting boundary layers are observed as a single stream-wise vortex close to the channel corner in case of laminar boundary layers. In the case of turbulent boundary layers, the secondary flow takes shape of a symmetric pair of counter-rotating vortices. This pattern is observable only in the average velocity field, while the instantaneous ones display large amount of vortices, whose spatial distribution close to the corner in dependence on their orientation leads to statistically emergent net vorticity. At the same time, this pattern is reproduced by using a numerical simulation. • Secondary flow of second kind in a short channel observed by Stereo PIV • For R e L ≤ 1. 0 ⋅ 1 0 5 , the secondary flow is laminar in shape of single vortex in the corner. • The size of laminar secondary flow vortex decreases with R e L as R ∼ R e L − 1 ∕ 2 . • At R e L ≥ 1. 3 ⋅ 1 0 5 , a pair of counter-rotating vortices appears in the averaged sense. • This pattern develops also in a "steady-state" numerical simulation. [ABSTRACT FROM AUTHOR]

Barotropic geostrophic flows are investigated using rectangular and polar coordinate systems. It is shown that, for the analysis of geostrophic flows with radial symmetry, the use of a polar coordinate system is preferable. Relations between the hydrodynamic characteristics, including the expressions of the fluid particle velocity components and vorticity through pressure, are obtained. It is established that, in the case of stationary barotropic flows, isobaths coincide with current lines. Stationary radially symmetric geostrophic flows are considered. [ABSTRACT FROM AUTHOR]

Taking advantage of alternative expressions for potential vorticity (PV) in divergence forms, we derive balances between volume integral of PV and boundary conditions, that are then applied to practical computations of PV: • We propose a new method for diagnosing the Ertel potential vorticity from model output, that preserves the balances; • We show how the expression of PV can be derived in general coordinate systems. This is here emphasised with isopycnic coordinates by generalising the PV expression to the general Navier-Stokes equations; • We propose a generalised derivation for the Haynes-McIntyre impermeability theorem, which highlights the role of the bottom boundary condition choice (e.g. no-slip vs free-slip) and mixing near the bottom boundary for the volume integral of PV. The implications of balances between volume integral of PV and boundary conditions are then analysed for specific processes at various scales: • At large scale, we show how an integral involving surface observations (derived from satellite observations) is linked to the integral of PV within a layer (between two isopycnals). This surface integral can be calculated for models and observations and can be used for validation; • At mesoscale or sub-mesoscale, we analyse the relationship between net PV anomalies and net surface density anomalies for idealised vortices and 2D fronts. This can help determining vortex or jet structures for idealised studies or empirical methodologies; • We also confirm and integrate previous results on the modification of PV within a bottom boundary layer into a single diagnostic taking into account the effect of density and velocity modifications by diabatic processes along the topography and diapycnal mixing within the boundary layer. • Ertel potential vorticity (PV) expressions in divergence form improve PV diagnostics in models. • Balances are derived between volume integral of PV and boundary conditions. • Practical numerical computations of PV, preserving balances, are proposed. • The implications of balances are examined for selected processes. [ABSTRACT FROM AUTHOR]

Highlights • A new method is proposed to analyze the vortex. • A new iso-vortex surface is done according to Q criterion. • Tendency of vortex structure is intuitive according to the iso-vortex surface. • Vorticity magnitude has a sudden change near the wall. Abstract This study presents a new method to analyze the vortex of cyclone separator by using the vortex identification of Q criterion. The Phase Doppler Particle Analyzer (PDPA) is used to measure the flow, and the numerical simulation is done by using the Reynolds stress model (RSM). In addition, a new conception of iso-vortex surface according to Q criterion is proposed for identifying the vortex structure. Since the model is validated by agreement between the numerical results and experimental data, and then is used to analyze the flow field. The results show that the tendency of the vortex structure is intuitive according to the new iso-vortex surface. Equivalent diameter of the iso-vortex surface is large in the upper region of the cylinder and decreases along the axis downward. The carrier energy of vortex decay gradually. In the process, vortex develops rapidly, even ruptures. Meanwhile, the vorticity magnitude has a sudden change near r /R = 0.93, and then vorticity magnitude rises up sharply. The vortex line of relative stable region is almost circular distribution, while the vortex line is complex at the upper region of cylinder, which has a hierarchical trend. The trend of the vortex center deviating from the geometric center firstly increases, reaches a peak value, and then reduces gradually. The axial position of peak value increases with the increase of velocity. Furthermore, the vortex structure can be appropriately adjusted to improve the flow instability, which is highly significant. [ABSTRACT FROM AUTHOR]

Abstract The rotary-type energy recovery device (RERD) is a promising energy recovery device which can significantly reduce the energy consumption of the Reverse Osmosis system in seawater desalination. A two-dimensional particle image velocimetry (PIV) measurement has been carried out in our previous study to visualize and understand the flow dynamics in the duct of the RERD. Based on the PIV experimental results, a computational fluid dynamics (CFD) method was applied to study flow characteristics and mixing process in the RERD. Three different turbulence modeling approaches (standard k - ε , RNG k - ε , and Realizable k - ε) were compared and validated by PIV experimental data. As a result, the simulation method was able to capture major features of the flow characteristic in the duct, such as the jet flow and the vortex structure. The Realizable k - ε turbulence model, presenting a good agreement with the experimental data, was recommended for analyzing the detailed information of flow characteristics. The simulation results revealed a swirling flow formed in the duct. This three-dimensional flow structure caused high flow turbulence and significant mass transfer in the mixing zone. These results would be beneficial to researchers in better understanding the mixing process in the duct of the RERD. Highlights • Three different k - ε turbulence model results were compared with experimental data. • Numerical results enriched the finding of the "entrance effect" observed by PIV method. • The Realizable k - ε model showed better predictions of vortex structures in the duct center. • A high concentration gradient and a swirling flow were in the duct transverse plane. [ABSTRACT FROM AUTHOR]

The importance of type-II superconductors with strong pinning comes from their ability to carry large transport currents in the presence of a magnetic field. We report on the results of the bulk magnetization measurements in the superconducting state in clean single crystals of NdFeAsO 0.9 F 0.1 at various temperatures. The zero-temperature superconducting critical current density, J c , where the superconducting transition temperature T c reaches a maximum of 45(1) kelvin, displays a remarkable high value. The field dependence of the critical current density was analyzed within the collective pinning model. A remarkably good agreement between the experimental results and theoretical δ1 pinning curve is obtained. This indicates that pinning in NdFeAsO 0.9 F 0.1 crystal originates from spatial variation of the mean free path. Additionally, the normalized pinning force density, F p , curves verses H/H irr (H irr is the irreversibility field) were scaled using the Dew-Hughes model. Our analysis suggests that point pinning alone cannot explain the observed field variation of F p . [ABSTRACT FROM AUTHOR]

We apply the modulation theory to study the vortex and radiation solution in the 2D nonlinear Schrödinger equation. The full modulation equations which describe the dynamics of the vortex and radiation separately are derived. A general algorithm is proposed to efficiently and accurately find vortices with prescribed values of energy and spin index. The modulation equations are solved by accurate numerical method. Numerical tests and simulations of radiation are given. [ABSTRACT FROM AUTHOR]

The vortex motion of a dust cloud was experimentally observed in unmagnetized cogenerated dusty plasma in different experimental parameters. Particle image velocimetry analysis demonstrated that several vortex zones exist in the dust cloud at relatively low pressures (0.06 mbar (or 6 Pa)–0.08 mbar (or 8 Pa)) and low discharge voltages (peak‐to‐peak voltage 540–560 V), whereas in relatively high pressure (0.4 mbar (or 40 Pa)–0.7 mbar (or 70 Pa)) and high discharge voltage (peak‐to‐peak voltage 690–740 V), dust vortices formed in dense dust cloud with background plasma fluctuation. [ABSTRACT FROM AUTHOR]

Mixing is an essential operation in many microfluidic devices. Droplet-based micromixers utilize droplets for mixing enhancement. In the present study, a novel three-dimensional simulation is conducted which has the ability to capture not only the mixing process, but also the chemical reactions inside liquid droplets. This two-phase model is used for simulating the reacting flow inside a serpentine microchannel and explores the effects of droplet size and reaction rate on the production and consumption of species in droplets. It is observed that the chemical reaction in each droplet, begins from its front area. Furthermore, it is shown that the production of species does not depend on water fraction (ratio of water flow rate to total flow rate) and for all droplet sizes, only depends on the reaction rate. Moreover, different transient generated vortices and secondary flows are studied in the presence and absence of droplets and explained in details based on the position of droplets. It is found that during the passage of droplets through a microchannel bend, the number of cross-sectional vortices changes and the velocity magnitude in these secondary flows increases dramatically. [ABSTRACT FROM AUTHOR]

The concepts and methods of the visual representation of fluid dynamics computations of vortical flows are studied. Approaches to the visualization of vortical flows based on the use of various definitions of a vortex and various tests for its identification are discussed. Examples of the visual representation of solutions to some fluid dynamics problems related to the computation of vortical flows in jets, channels, and cavities and of the computation of separated flows occurring in flows around bodies of various shapes are discussed. [ABSTRACT FROM AUTHOR]

We did a numerical study of the internal flow field of a vortex pump. Five operating points were considered and validated through a measured characteristic curve. The internal flow pattern of a vortex pump was analyzed and compared to the Hamel-Oseen vortex model. The calculated flow field was assessed with respect to the circumferential velocity, the vorticity and the axial velocity. Whereas the trajectories of the circumferential velocity were largely in line with the Hamel-Oseen vortex model, the opposite was true for vorticity. Only the vorticity at strong part load was in line with the predictions of the Hamel-Oseen vortex model. We therefore compared the circumferential velocity and vorticity for strong part load operation to the analytical predictions of the Hamel-Oseen vortex model. The simulated values were below the analytical values. The study therefore suggests that a vortex similar to the Hamel-Oseen vortex is only present at the strong part load operation. [ABSTRACT FROM AUTHOR]

This paper presents flow-structure interaction between a sphere wake and a free water surface for different submerged elevations in an open water channel for Reynolds numbers in the range of 2.5×103 ⩽Re⩽1×104 based on the diameter of the sphere. [ABSTRACT FROM AUTHOR]

The design of turbine blades is a critical issue in the performance of vertical-axis wind-turbines (VAWTs). In a previous study, it is discovered that a loss of thrust in VAWT blades with a wave-like leading edge can be attributed primarily to vortex distribution. This finding prompted us to apply the wave-like blade design to the trailing edge rather than the leading edge. In this study, computational fluid dynamics was used to observe the flow field on straight and tubercle blades in order to predict the resulting thrust and power performance. Increasing the amplitude and wavelength of the tubercle was shown to increase the maximum thrust by as much as 2.31% and the power coefficient by 16.4%, compared to a straight blade. Furthermore, the overall and maximum thrust performance of blades with a modified trailing edge was shown to exceed those of blades with a wave-like leading edge, due to a shift in the location of the vortices by the induced flow. [ABSTRACT FROM AUTHOR]

Through-silicon via (TSV) technology has been quickly improved, however, there are challenges in reducing electrodeposition time. In this research, new conical TSVs, 3 μm diameter and 27 μm depth (3 × 27 μm), were made. The flow pattern of the electrolyte inside a conical TSV and a cylindrical TSV is simulated with a TSV chip attached on a rotating disk electrode (RDE) rotating at 1000 rpm in the electrolyte. The flow pattern inside conical TSVs confirmed advantages of the conical shape over the cylindrical shape. The conical shape forms deeper vortexes and shows higher velocities at the same depth than the cylindrical shape. A character of electrolyte bases on anodic area charge was used to optimize electrolyte bath composition for the extreme fast filling. Without additives, the anodic area charge at 1000 rpm was larger than that at 10 rpm, however, the reverse obtained in the presence of additives. D-optimal designs for quantitative multilevel of additives were applied to create an experiment plan. The result confirmed a strong effect of Cl − concentration and interactions of Cl − with polyethylene glycol (PEG) and bis-(3-sodiumsulfopropyl)-disulfide (SPS) with sulfonated diallyl dimethyl ammonium chloride copolymer (SDDACC) which bring to anodic area charge at 1000 rpm was smaller than that at 10 rpm. In an optimal concentration of SDDACC, the 3 × 27 μm conical TSV was filled within 3 minutes. A new additive acceleration mechanism was proposed from the accumulation of Cu(I) thiolate inside vortexes. [ABSTRACT FROM AUTHOR]

The static and dynamic properties of vortices in a nanosized superconducting strip with one central weak link (weakly superconducting region or normal metal) are investigated in the presence of external magnetic and electric fields. The time-dependent Ginzburg-Landau equations are used to describe the electronic transport and have been solved numerically by a finite element analysis. Anisotropy is included through the spatially dependent anisotropy coefficient $$\zeta $$ in different layers of the sample. Our results show that the energy barrier for vortices to enter a weak link is smaller than that for vortices to enter the superconducting layers. The magnetization shows periodic oscillations. With the introduction of the weak link, the period of oscillations decreases. [ABSTRACT FROM AUTHOR]

Water vapor in natural gas often leads to the decrease of gas calorific value per unit volume; it also reduces the flow area of pipeline. Moreover, the CO2 and H2S will corrode the pipeline when dissolved in liquid water. According to the containing water problems in high pressure natural gas during development, a roof-mounted type supersonic cyclone flow natural gas dehydration unit was designed in combination with the fluid mechanics and engineering thermodynamics principle. Based on the research status at home and abroad, the supersonic natural gas condensate flow numerical model was built, including multicomponent two-phase expansion flow model and water vapor condensing model. The flow characteristics of each work section of supersonic natural gas dehydration unit were numerical analyzed, and the device internal pressure, temperature, Mach number, vapor nucleation rate, moisture distribution were obtained. According to the results of numerical simulation, optimization design was carried out to improve the efficiency of separation. [ABSTRACT FROM AUTHOR]

We calculate the relaxation of Brinkman-Smith mode via Leggett-Takagi relaxation in the presence of an isolated vortex in superfluid $$^{3}$$ He-B. The calculation is based on an analytical solution of the order parameter far from the vortex axis. We obtain an expression for the dissipated power per vortex length as a function of the tipping angle of the magnetization and the orientation of the static magnetic field with respect to the vortex. [ABSTRACT FROM AUTHOR]

We construct a class of self-similar 2d incompressible Euler solutions that have initial vorticity of mixed sign. The regions of positive and negative vorticity form algebraic spirals. [ABSTRACT FROM AUTHOR]

The coherent secondary flow structures (i.e., swirling motions) in a curved artery model possess a variety of spatio-temporal morphologies and can be encoded over an infinitely-wide range of wavelet scales. Wavelet analysis was applied to the following vorticity fields: (i) a numerically-generated system of Oseen-type vortices for which the theoretical solution is known, used for bench marking and evaluation of the technique; and (ii) experimental two-dimensional, particle image velocimetry data. The mother wavelet, a two-dimensional Ricker wavelet, can be dilated to infinitely large or infinitesimally small scales. We approached the problem of coherent structure detection by means of continuous wavelet transform (CWT) and decomposition (or Shannon) entropy. The main conclusion of this study is that the encoding of coherent secondary flow structures can be achieved by an optimal number of binary digits (or bits) corresponding to an optimal wavelet scale. The optimal wavelet-scale search was driven by a decomposition entropy-based algorithmic approach and led to a threshold-free coherent structure detection method. The method presented in this paper was successfully utilized in the detection of secondary flow structures in three clinically-relevant blood flow scenarios involving the curved artery model under a carotid artery-inspired, pulsatile inflow condition. These scenarios were: (i) a clean curved artery; (ii) stent-implanted curved artery; and (iii) an idealized Type IV stent fracture within the curved artery. [ABSTRACT FROM AUTHOR]

Right ventricular diastolic dysfunction (RVDD) is an important prognostic indicator in pulmonary arterial hypertension (PAH). RV vortex rings have been observed in healthy subjects, but their significance in RVDD is unknown. Vorticity, the local spinning motion of an element of fluid, may be a sensitive measure of RV vortex dynamics. Using four-dimensional (4D) flow cardiac magnetic resonance imaging (CMR), we investigated the relationship between right heart vorticity with echocardiographic indexes of RVDD. Thirteen (13) PAH subjects and 10 controls underwent same-day 4D flow CMR and echocardiography. RV diastolic function was assessed using trans-tricuspid valve (TV) early (E) and late (A) velocities, E/A ratio, and e’ and a’ tissue Doppler velocities. RV and right atrial (RA) integrated mean vorticity was calculated for E and A-wave filling periods using 4D datasets. Compared with controls, A-wave vorticity was significantly increased in RVDD subjects in both the RV [2343 (1,559 –3,295) vs. 492 (267-2,649) 1/s, P = 0.028] and RA [30 (27– 44) vs. 9 (5–27) 1/s, P = 0.005]. RA E vorticity was significantly decreased [13 (7–22) vs. 28 (15–31) 1/s, P = 0.038] in RVDD. E-wave vorticity correlated TV e’, E-,and TV E/A (P < 0.05), and A-wave vorticity associated with both TV A and E/A (P < 0.02). RVDD is associated with alterations in E- and A-wave vorticity, and vorticity correlates with multiple echocardiographic markers of RVDD. Vorticity may be a robust noninvasive research tool for the investigation of RV fluid and tissue mechanical interactions in PAH. [ABSTRACT FROM AUTHOR]

The accuracy, robustness, dissipation characteristics and efficiency of several structured and unstructured grid methods are investigated with reference to the low Mach double vortex pairing flow problem. The aim of the study is to shed light into the numerical advantages and disadvantages of different numerical discretizations, principally designed for shock-capturing, in low Mach vortical flows. The methods include structured and unstructured finite volume and Lagrange-Remap methods, with accuracy ranging from 2nd to 9th-order, with and without applying low-Mach corrections. Comparison of the schemes is presented for the vortex evolution, momentum thickness, as well as for their numerical dissipation versus the viscous and total dissipation. The study shows that the momentum thickness and large scale features of a basic vortical structure are well resolved even at the lowest grid resolution of 32×32 provided that the numerical schemes are of a high-order of accuracy or the numerical framework is sufficiently non-dissipative. The implementation of the finite volume methods in unstructured triangular meshes provides the best results even without low Mach number corrections provided that a higher-order advective discretization for the advective fluxes is employed. The compressible Lagrange-Remap framework is computationally the fastest one, although the numerical error for the momentum thickness does not reduce as fast as for other numerical schemes and computational frameworks, e.g., when higher-order schemes are utilized. It is also shown that the low-Mach number correction has a lesser effect on the results as the order of the spatial accuracy increases. [ABSTRACT FROM AUTHOR]

Wall deposition is one of the most conventional problems in the spray drying process. The operation of a spray dryer is affected by the wall deposition fluxes inside the equipment. In this study, computational fluid dynamic (CFD) simulation was used to investigate the effect of spray dryer geometry on wall deposition. A CFD model was developed for different geometries of spray dryer with a conical (case A) or a parabolic (cases B and C) bottom. The results implied that the parabolic geometry resulted in a lower deposition rate on the spray dryer walls. A comparison of results using the P-values (F-test) of the air velocity, in the conical and parabolic geometries, showed that there was a significant difference in air stability between them. The flow field in conical geometry case A was significantly more unstable, and parabolic geometry case C produced the most uniform airflow patterns. Moreover, the higher wall shear stress in case C, with lower values of the vorticity, would result in less wall deposition. [ABSTRACT FROM PUBLISHER]

This paper focuses on the multi-scale wake structures of a new asymmetric side mirror of a race car, which can generate the aerodynamic downforce. The turbulent wake generated by symmetric bluff bodies of triangle and semi-cylinder and an asymmetric bluff body (called CT-cylinder) were experimentally investigated and were compared. Firstly, the instantaneous velocity and vorticity were quantitatively measured by high-speed PIV at a Reynolds number of 14,440 in the circulating water channel. Then a one- and two-dimensional wavelet multi-resolution techniques were used to analyze the instantaneous velocity and vorticity in order to decompose turbulent structures into a number of subsets based on their central frequencies. It is found that the CT-cylinder wake generates the asymmetric flow structures and separation region that is smaller than that of the triangle wake. The contribution to vorticity concentration comes from the large-scale structure of CT-cylinder wake in the ( x , y )-plane, and the intermediate-scale structure of the CT-cylinder wake dominates the flow structure in the ( x , z )-plane. There is no evident difference among the three wakes in the relatively small-scale structures. The large-scale structures of three wakes exhibit the main contributions to the Reynolds shear stress, accounting for almost 82–92%. However, the small-scale structures make less contribution to Reynolds shear stresses. The phase-averaging and spectral analyses indicate that the CT-cylinder wake generates the relatively smaller vortices and smaller separation region and the CT-cylinder wake exhibits lower fluctuation in the shear layer. [ABSTRACT FROM AUTHOR]

Vortex merging is a basic fluid phenomenon which has been much studied for two-dimensional flows. Here we extend such a study to a specific class of three-dimensional flows, namely to vortices possessing a helical symmetry. In addition to the standard Reynolds number, this introduces another dimensionless control number, the pitch, which quantifies the periodicity length along the helix axis. Helical vortices with large pitches merge very much as in a two-dimensional setting. However, their rotation speed is reduced and the merging period is delayed. These effects, caused by the presence of a self-induced velocity in curved three-dimensional vortices, are understood by computing the streamfunction in the frame of reference rotating with the two vortices, and by inspecting the locations of its hyperbolic points. At intermediate pitch values, only viscous diffusion acts, resulting in a slow viscous type of merging. Finally for small pitches, the system is unstable resulting, at the nonlinear stage, in a different type of merging which breaks the initial central symmetry. [ABSTRACT FROM AUTHOR]

Using the nonlinear Ginzburg–Landau equations we study the vortex configurations in a superconducting square with a central square pillar in the presence of a uniform applied magnetic field. The presence of the pillar changes the vortex structure in the superconducting sample considerably. We calculate magnetization, magnetic induction, supercurrent and vorticity, which show different vortex configurations as a function of magnetic field. [ABSTRACT FROM AUTHOR]

An experimental investigation is conducted to study the effect of middle length and inclination angle of an S-shaped channel on adiabatic two-phase flow patterns. To study this effect, three channel lengths of 0.25, 0.50, and 1.00m, and four bends at the angles of 22.5°, 45°, 67.5° and 90° were used along the test section which is 35.83m long. The channel cross section dimensions were 0.05×0.10m and the test fluids were air and water. The observed flow patterns in 12 cases were studied. Each flow pattern was identified by visual observation and recorded with video camera for further analysis of the collected data points. The momentum transfer phenomenon between the phases for passing the upward middle section along the S-shaped channel was closely investigated. Five flow patterns of vortex plug, vortex slug, vortex wavy-annular, churn and mist packet annular were observed. The vortex type flow patterns were recorded with high speed video camera. The physical mechanisms and momentum transfer related to formation of these flow patterns were explained in detail. Flow pattern maps were obtained and then compared for different middle lengths and inclination angles to perform a parametric study on the S-shaped channel. Moreover, effect of upstream/downstream of the S-shaped channel on the maps and transition lines were discussed. It was revealed that upstream effects reflect the interactions and momentum transfer between the phases. Therefore, flow pattern types mainly depend on upstream behavior. On the other hand, the amount of backward flow resulting in the establishment of countercurrent flow and creation of vortexes along middle section is determined by downstream effects. Increasing the middle length or inclination angle causes the transition to vortex plug flow pattern to occur at higher liquid velocities. It also causes the area with churn flow pattern on the map to expand ending in smaller vortex slug flow pattern area. However, increasing middle length or decreasing inclination angle, ends in smaller area of mist packet annular area. It is also observed that for higher middle lengths, increasing the inclination angle shifts the transition lines more remarkably. A dimensionless analysis of obtained flow pattern maps is also carried out. It is shown that effect of geometry changes along S-shaped pipeline on two-phase flow pattern transitions is determined by either inclination angle or elevation difference between two horizontal lines. The explained flow mechanisms, obtained flow pattern maps and the transition lines can be used to predict the particular flow pattern that will be established for a given mass flux, inclined length and angle along pipelines. [ABSTRACT FROM AUTHOR]

The properties of spray-induced vortex-like structures for asymmetric pressure swirl atomizer were studied experimentally with different injection pressures. The high-speed Particle Imaging Velocimetry (PIV) was used to study the spray characteristics such as velocity and vorticity. The vortex centers were identified by velocity weighted vorticity. The translational velocity components of vortex centers were computed from its displacement divided by the time interval. For five different pressure conditions, the motion trajectories of vortex center were the same in an earlier period of spray, but were different in a later period of spray. The normalized translational velocity of vortex center and normalized time were introduced to compare with vortex ring model. The results indicated that the normalized axial translational velocity decreased with increasing normalized time, which converged to the predictions of the model in long time limit where α = -0.75 in the turbulent case. However, the results for the normalized radial translational velocity were different from the predictions of the model. The normalized radial translational velocity decreased with the increase of the normalized time when the injection pressure was lower than a critical value, but it obviously increased with the increase of the normalized time in case of the injection pressure higher than the critical value. Furthermore, the average vorticities at the vortex center were obtained and increased with the increase of the injection pressure. This study provides references for developing spray theory and improving injection technology. [ABSTRACT FROM AUTHOR]

The resistive state of a superconductor in magnetic field has been thoroughly investigated both by experiments and by theoretical simulations. However, a local study of vortex dynamics inducing dissipation was performed only recently by means of scanning Hall probe microscopy (SHPM). In this work we extend this idea and we visualize the oscillatory motion of vortices in NbSe2 using scanning tunneling microscopy (STM). In contrast to previous experiments, sensitive to magnetic fields, the STM probes the local density of states and the local topography. Its ability to resolve vortices is limited by the coherence length. In the case of type-II superconductors this is expected to resolve vortex motion beyond the detection limit of the SHPM. We experimentally verify the enhanced sensitivity by observing vortex motion in a very dense vortex lattice (H=600mT). [ABSTRACT FROM AUTHOR]

In this work we solved the time-dependent Ginzburg-Landau equations, TDGL, to simulate two superconducting systems with different lateral sizes and with an antidot inserted in the center. Then, by cycling the external magnetic field, the creation and annihilation dynamics of a vortex-antivortex pair was studied as well as the range of temperatures for which such processes could occur. We verified that in the annihilation process both vortex and antivortex acquire an elongated format while an accelerated motion takes place. [ABSTRACT FROM AUTHOR]

Highlights: [•] A novel vortex micromixer is proposed comprising an injection channel, a nozzle structure and a double-heart mixing chamber. [•] The double-heart chamber can induce symmetrical rotating vortex structures. [•] The mixing ratio reaches 92% even at Reynolds numbers as low as Re=1 given a nozzle ratio of 0.25. [ABSTRACT FROM AUTHOR]

• Four micromixers with double V-shaped baffles are designed. • All mixers achieve high mixing efficiency at the short distance of 3500 μm. • The visualization of vortex formation is conducted to analyze the mixing mechanism. • Different vortex patterns form in the microchannels as inlet velocity varies. Achieving rapid mixing of different liquids in a short distance is important for biochemical applications. Here, a new type of micromixers consisting of double symmetrical V-shaped baffles (MMA and MMB mixers) and double asymmetrical V-shaped baffles (MMC and MMD mixers) is proposed. Numerical simulations are performed to evaluate their mixing performance when the Reynolds number (Re) ranges from 0.1 to 50. Meanwhile, the visualization of vortex formation is conducted to analyze the mixing mechanism. The results show that the mixing efficiency of all mixers approaches 0.8 for all Re at the short distance of 3500 μm. At relatively low Re =0.5, the MMA and MMB perform better than MMC and MMD due to more adequate molecular diffusion; whereas the unbalanced lateral flows and multidirectional vortices in the MMC and MMD induce stronger chaotic convection at high Re =50, leading to a higher performance. Moreover, the disturbance created by the vortex on the mass transfer surface is not only relying on its vorticity but also correlates with the position of vortex/vortex leg. Lastly, all micromixers are fabricated, tested and compared with the simulation results and both of them show a good agreement. [Display omitted] [ABSTRACT FROM AUTHOR]

In order to study site-selective NMR in chiral p -wave superconductors, we calculate local nuclear relaxation rate T 1 − 1 in the vortex lattice state by Eilenberger theory with and without non-magnetic impurity scattering in the Born limit and unitary limit. The local T 1 − 1 in the NMR resonance line shape is different between two chiral states p ± , depending on whether the chirality is parallel or anti-parallel to the vorticity. In the p − -wave, anomalous suppression of local T 1 − 1 occurs around the vortex core due to the negative coherence term coming from odd-frequency s -wave Cooper pair induced around the vortex. We especially examine the site dependence of the anomalous suppression of local T 1 − 1 , including the applied magnetic field dependence and the impurity effects. [ABSTRACT FROM AUTHOR]

Highlights: [•] Fireline length effects on rate of spread. [•] Rate of spread relationship to fireline shape. [•] Counter-rotating vortices in wildfire. [Copyright &y& Elsevier]

There is a close relationship between jet shear layer and acoustic refraction, but research on the unsteady characteristics between them is relatively inadequate. Firstly, the relationship between the sound ray direction and the vorticity, which is the classical ray tracing method, was simply derived, and the applicable conditions were focused on to extend it to the unsteady conditions. Then, the concept of effective area of sound refraction was proposed for beamforming sound source identification array. Sound propagation experiment was carried out in a 3/4 open-jet acoustic wind tunnel by using microphone array and controllable sound source with low flow resistance and self-noise, and the unsteady acoustic drift of initial source with different frequencies was measured. After that, the flow structure of same wind tunnel, especially the jet shear layer, was simulated and verified, which proved that the shear layer formed by the straight section of one nozzle side is quasi two-dimensional. In the simulation, 30 monitoring areas were divided along the shear layer, and the variation of vorticity integral value in each area was analyzed. Finally, similar to the Amiet method, the volume of the effective region was ignored, and several conditions that could be satisfied in this paper were introduced to establish a linear relationship between regional vorticity and acoustic drift. Through the comparison between the acoustic drift of direct measurement and vorticity calculation, the validity of the linear relationship at the time average and instantaneous levels is proved. The research of this paper show that the relationship between vorticity and acoustic ray is still valid at unsteady level as long as the conditions of low-speed flow and high frequency sound are satisfied. At the same time, it provided a new idea for non-contact flow measurement in shear layer of jet structure. [ABSTRACT FROM AUTHOR]

The testing of the standard and modified SST models of the transfer of shear stresses was carried out on an example of calculating the heat transfer with an intense detached flow around a conical dimple with a slope angle of 45 ° on the heated wall of a narrow channel. It was shown that the standard turbulence model by Menter SST (MSST) of 2003, widely used in the packages Fluent, CFX, StarCCM+, etc., significantly underestimated the intensity of the return flow. A correction of this model was presented that took into account the influence of the curvature of streamlines within the framework of the Rodi-Leshziner-Isaev (RLI) approach for spatial separated flows. It was found that the predictions for the RLI MSST 2003 were close to the predictions for the original standard MSST 1993, in which the eddy viscosity was calculated using the vorticity modulus. At the same time, the predictions based on the modified one, following Smirnov-Menter (SM) MSST 2003, included in the ANSYS model catalog did not differ too much from the standard MSST 2003. The preference of the MSST modified within the RLI 2003 for calculating the heat transfer in intense separated flows was substantiated. [ABSTRACT FROM AUTHOR]

A model is developed to explore fire–atmosphere interactions due to the convective sink and vorticity sources in a highly simplified and idealized form, in order to examine their effect on spread and the stability of various fire front geometries. The model is constructed in a cellular automata framework, is linear, and represents a background flow, convective sink, and vortices induced by the fire plume at every burning cell. We use standard techniques to solve the resulting Poisson equations with careful attention to the boundary conditions. A modified Bresenham algorithm is developed to represent convection. The three basic flow types—large-scale background flow, sink flow, and vortex circulation—interact in a complex fashion as the geometry of the fire evolves. Fire-generated vortex–sink interactions produce a range of fire behavior, including unsteady spread rate, lateral spreading, and dynamic fingering. In this simplified framework, pulsation is found associated with evolving fire-line width, a fire-front acceleration in junction fires, and the breakup of longer initial fire lines into multiple head fires. Fuel is very simply represented by a single burn time parameter. The model fuel is uniform yet patchiness occurs due to a dynamic interaction of diffusive and convective effects. The interplay of fire-induced wind and the geometry of the fire front depends also on the fuel burn time. [ABSTRACT FROM AUTHOR]

For the new sandglass-type floating body with special shape, this paper mainly analyzes the characteristic of the heave damping and its corresponding components by computational fluid dynamics (CFD) method. Firstly, the convergence and accuracy of the CFD method to simulate the heave motion of sandglass-type floating body were validated along with the experimental data. Secondly, the numerical model of the floating body with forced heave motion was created, and then hydrodynamic forces versus different motion amplitudes were calculated and compared to discuss its nonlinear characteristics. Afterwards, based on time-history curves of the hydrodynamic force, heaving added mass and damping of the floating body versus various frequencies were achieved and found to be different from the potential results. In order to analyze the reasons that cause difference, numerical simulations using inviscid and k-ε turbulent models were performed respectively, and the results indicate that the effect of fluid viscosity on the hydrodynamic coefficients is small and not decisive. Then equivalent radiation damping based on CFD wave elevation was deduced to explore the relation between the inviscid CFD and potential models. Finally, local wave field and vorticity field near the body were mainly discussed, and quantitative analysis based on mechanical energy was performed to verify that the vortex due to the body shape is the essential cause of the heave damping for the sandglass-type floating body. • Numerical method to simulate the heave motion of the new sandglass-type FPSO were validated. • Equivalent radiation damping based on CFD solutions was deduced and discussed with the potential results. • Vortex generated by the non-viscous fluid separation was analyzed based on mechanical energy. [ABSTRACT FROM AUTHOR]