Flow Separation and Vortex Dynamics in Waves Propagating over A Submerged Quartercircular Breakwater

The interactions of cnoidal waves with a submerged quartercircular breakwater are investigated by a ReynoldsAveraged Navier–Stokes(RANS) flow solver with a Volume of Fluid(VOF) surface capturing scheme(RANSVOF) model. The vertical variation of the instantaneous velocity indicates that flow separation occurs at the boundary layer near the breakwater. The temporal evolution of the velocity and vorticity fields demonstrates vortex generation and shedding around the submerged quartercircular breakwater due to the flow separation. An empirical relationship between the vortex intensity and a few hydrodynamic parameters is proposed based on parametric analysis. In addition, the instantaneous and time-averaged vorticity fields reveal a pair of vortices of opposite signs at the breakwater which are expected to have significant effect on sediment entrainment, suspension, and transportation,therefore, scour on the leeside of the breakwater.

VORTEX DYNAMICS OF THE ANISOTROPIC GINZBURG-LANDAU EQUATION

In this article, using coordinate transformation and Gronwall inequality, we study the vortex motion law of the anisotropic Cinzburg-Landau equation in a smooth bounded domain Ω （R^2,that is ,Эtuε=j,k=1∑2（ajkЭxkuε）xj＋ε^2^-b（x）（1-｜uε｜^2）uε,x∈Ω,and conclude that each vortex,bj（t）（j=1,2,…,N）satisfies dt^-dbj（t）=-（a（bj（t））^-a1k（bj（t））Эxka（bj（t））,a（aj（t））^-a2k（bj（t））Эxka（bj（t）））,where a（x）=√a11a22-a12^2. We prove that all the vortices are pinned together to the critical points of a（x）. Furthermore, we prove that these critical points can not be the maximum points.

Liutex-based vortex dynamics:A preliminary study

Vortex dynamics,with the possibility of efficient flow control,is explored in this study based on the new introduced vortex definition and identification system of Liutex.With the six core elements of vortex identification,including(1)absolute strength,(2)relative strength,(3)local rotational axis,(4)global rotational axis,(5)vortex core size and(6)vortex boundary,provided by the Liutex system,it is possible to numerically devise strategies,primarily by introducing additional source terms in Navier-Stokes equations,which we call Liutex force field model here,to control the vortex regions.Two methodologies of centripetal force model and counter-rotation force model are preliminarily investigated in a cavitating flow around two-dimensional Clark-Y hydrofoil.It is found that Liutex based models are capable of illustrating the vortex dynamics and possibly strengthening or weakening the vortices.

Vortex dynamics and entropy generation in separated transitional flow over a compressor blade at various incidence angles

The transition process within a Laminar Separation Bubble(LSB)that formed on a compressor blade surface was investigated using Large Eddy Simulations(LESs)at a Reynolds number of 1.5×10;and incidence angles of 0°,+3°,and+5°.The vortex dynamics in the separated shear layers were compared at various incidence angles and its effects on the loss generation were clarified through entropy analysis.Results showed that transition onset,which was accurately identified by the Linear Stability Theory(LST),was significantly promoted at the increased incidence angle.As such,the development of LSB was suppressed and the relative role of viscous instability played in the transition process was weakened.At the incidence angle of 0°,two-dimensional spanwise vortices detached from the blade surface and roiled up periodically,which were further stretched and eventually evolved into large-scale hairpin vortices.As time passed,the fully developed hairpin vortices broke down into small-scale eddies.Meanwhile,the flow near the wall reversely ejected into the outer separated shear layers and a sweeping process happened subsequently,forcing the separated shear layers to reattach and accelerating the generation of turbulent fluctuations.By comparison,the strength of vortex rolling-up was weakened at higher incidence angles,and the vortex pairing and breakdown of large-scale vortices were less pronounced.Therefore,the level of turbulent fluctuations that generated in the separated shear layers was reduced.Detailed entropy analysis showed that the turbulent dissipation effect related to the Reynolds shear stresses determined the largest amount of positive entropy generation,which declined to a lower level as the incidence angle increased from 0°to+5°.Correspondingly,the profile loss was reduced by 50.4%.

The Dynamics of Barotropic Vortex Merging

The merging of multiple vortices is a fundamental process of the dynamics of Earth＇s atmosphere and oceans. In this study, the interaction of like-signed vortices is analytically and numerically examined in a framework of two-dimensional inviscid barotropic flows. It is shown that barotropic vortex interaction turns out to be more intricate than simple merging scenarios often assumed in previous studies. Some particular configurations exist in which the vortex merging process is never complete despite strong interaction of like-signed vortices, regardless of the strengths or distances between the vortices.While the conditions for a complete vortex merging process introduced in this study appear to be too strict for most practical applications, this study suggests that careful criteria for vortex mergers should be properly defined when simulating the interaction of vortices, because the merging may not always result in a final enhanced circulation at the end of the interaction,as usually assumed in the literature.

Cascade excitation of vortex motion and reentrant superconductivity in flexible Nb thin films

High quality Nb films were successfully prepared on both flexible polyimide(PI)and rigid Al2O3substrates and their transport properties were systematically studied at various applied currents,external magnetic fields,and sample orientations.It is found that a curved Nb/PI film exhibits quite different superconducting transition and vortex dynamics compared to the flat Nb/Al2O3film.For the curved Nb/PI film,smooth superconducting transitions were obtained at low currents,while unexpected cascade structures were revealed in theρ(T)curves at high currents.We attribute this phenomenon to the gradient distribution of vortex density together with a variation of superconductivity along the curved film.In addition,reentrant superconductivity was induced in the curved Nb/PI thin film by properly choosing the measurement conditions.We attribute this effect to the vortex pinning from both in-plane vortices and out-of-plane vortices.This work reveals the complex transport properties of curved superconducting thin films,providing important insights for further theoretical investigations and practical developments of flexible superconductors.

On the Dynamics of Vortex Filaments and Their Core Structure

We give a brief review of the asymptotic theory of slender vortex filaments with emphases on (i) the choices of scalings and small parameters characterizing the physical problem,(ii) the key steps in the formulation of the theory and (iii) the assumptions and/or restrictions on the theory of Callegari and Ting (1978).We present highlights of an extension of the 1978 asymptotic theory:the analyses for core structures with axial variation.Making use of the physical insights gained from the analyses,we present a new derivation of the evolution equations for the core structure.The new one is simpler and straightforward and shows the physics clearly.

THE NONLINEAR INTERACTION OF VORTEX RINGS WITH A FREE SURFACE

Nonlinear interactions of vortex rings with a free surface are considered in an incompressible, ideal fluid using the vortex contour dynamics technique and the boundary integral equation method. The flow is axisymmetric and the vorticity is linearly distributed in the vortex. Effects of the gravity and the surface tension as well as the initial geometric parameter of the vortex on the interaction process are investigated in considerable detail. The interaction process may be divided into three major stages: the vortex free-traveling stage, the collision stage, and the vortex stretching and rebounding stage. Time evolutions of both the vortex and free surface under various conditions are provided and analyzed. Two kinds of waves exist on the free surface during interaction. In a special case where the gravity and surface tension are very weak or the vortex is very strong, an electric-bulb-like 'cavity' is formed an the free surface and the vortex is trapped in the 'cavity' for quite a. long time, resulting in a large amount, of fluid above the mean fluid surface.

Move a Tropical Cyclone with 4D-Var and Vortex Dynamical Initialization in WRF Model

Previous studies showed that 4 D-Var technique used for data assimilation could be modified for weather control. This study demonstrates the ability of 4 D-Var to influence the future path of a tropical cyclone by calculating perturbations in WRF simulation. Given the background error covariance matrix, the initial field is improved by the vortex dynamic initialization technique. Our results show that 4 D-Var can be applied to control the trajectory of simulated tropical cyclones by producing "optimal" perturbations. In the numerical simulation experiment of Typhoon Mitag in 2019, after this kind of weather control similar to data assimilation, the tropical cyclone moved obviously,and the damaging wind over the coastline weakened. The prediction results after the initial field modified by 4 D-Var have a great change, and the position of the tropical cyclone moved about 0.5° southeastward after assimilation,which misses the southeast coast of China. Moreover, the damaging wind is also weakened. Since the 4 D-Var is premised on the assumption that the model is perfect and does not consider the model error, then the research plan to consider model error and introduce new methods is discussed in the paper.

Numerical investigation of flow over a two-dimensional square cylinder with a synthetic jet generated by a bi-frequency signal

The flow around a square cylinder with a synthetic jet positioned at the rear surface is numerically investigated with the unsteady Reynolds-averaged Navier-Stokes(URANS)method.Instead of the typical sinusoidal wave,a bi-frequency signal is adopted to generate the synthetic jet.The bi-frequency signal consists of a basic sinusoidal wave and a high-frequency wave.Cases with various amplitudes of the high-frequency component are simulated.It is found that synthetic jets actuated by bi-frequency signals can realize better drag reduction with lower energy consumption when appropriate parameter sets are applied.A new quantity,i.e.,the actuation efficiency Ae,is used to evaluate the controlling efficiency.The actuation efficiency Ae reaches its maximum of 0.2668 when the amplitude of the superposed high-frequency signal is 7.5%of the basic signal.The vortex structures and frequency characteristics are subsequently analyzed to investigate the mechanism of the optimization of the bi-frequency signal.When the synthetic jet is actuated by a single-frequency signal with a characteristic velocity of 0.112 m/s,the wake is asymmetrical.The alternative deflection of vortex pairs and the peak at half of the excitation frequency in the power spectral density(PSD)function are detected.In the bi-frequency cases with the same characteristic velocity,the wake gradually turns to be symmetrical with the increase in the amplitude of the high-frequency component.Meanwhile,the deflection of the vortex pairs and the peak at half of the excitation frequency gradually disappear as well.

Dynamic performance and wake structure of flapping plates with different shapes

The dynamic performance and wake structure of flapping plates with different shapes were studied using multi-block lattice Boltzman and immersed boundary method.Two typical regimes relevant to thrust behavior are identified.One is nonlinear relation between the thrust and the area moment of plate for lower area moment region and the other is linear relation for larger area moment region.The tendency of the power variation with the area moment is reasonably similar to the thrust behavior and the efficiency decreases gradually as the area moment increases.As the mechanism of the dynamic properties is associated with the evolution of vortical structures around the plate,the formation and evolution of vortical structures are investigated and the effects of the plate shape,plate area,Strouhal number and Reynolds number on the vortical structures are analyzed.The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to flapping locomotion.

Identification, characterization and evolution of non-local quasi-Lagrangian structures in turbulence

The recent progress on non-local Lagrangian and quasi-Lagrangian structures in turbulence is reviewed.The quasi-Lagrangian structures, e.g., vortex surfaces in viscous flow, gas-liquid interfaces in multi-phase flow, and flame fronts in premixed combustion, can show essential Lagrangian following properties, but they are able to have topological changes in the temporal evolution. In addition,they can represent or influence the turbulent flow field. The challenges for the investigation of the non-local structures include their identification, characterization, and evolution.The improving understanding of the quasi-Lagrangian structures is expected to be helpful to elucidate crucial dynamics and develop structure-based predictive models in turbulence.

Finite superconducting square wire-network based on two-dimensional crystalline Mo_(2)C

Superconducting wire-networks are paradigms to study Cooper pairing issues,vortex dynamics and arrangements.Recently,emergent low-dimensional crystalline superconductors were reported in the minimal-disorder limit,providing novel platforms to reveal vortices-related physics.Study on superconducting loops with high-crystallinity is thus currently demanded.Here,we report fabrication and transport measurement of finite square-network based on two-dimensional crystalline superconductor Mo_(2)C.We observe oscillations in the resistance as a function of the magnetic flux through the loops.Resistance dips at both matching field and fractional fillings are revealed.Temperature and current evolutions are carried out in magnetoresistance to study vortex dynamics.The amplitude of oscillation is enhanced due to the interaction between thermally activated vortices and the currents induced in the loops.The driving current reduces the effective activation energy for vortex,giving rise to stronger vortex interaction.Moreover,by the thermally activated vortex creep model,we derive the effective potential barrier for vortex dissipation,which shows well-defined correspondence with structures in magnetoresistance.Our work shows that low-dimensional crystalline superconducting network based on Mo_(2)C possesses pronounced potential in studying the modulation of vortex arrangements and dynamics,paving the way for further investigations on crystalline superconducting network with various configurations.

Slat cove dynamics of multi-element airfoil at low Reynolds number

The flow around the slat cove of a two-dimensional 30P30N multi-element airfoil is investigated with time-resolved particle image velocimetry(TR-PIV)at low Reynolds number(Rec=2.41×10^(4)and 4.61×10^(4)).The effects of angle of attack(α=8°,12°,and 16°)on the mean flow characteristics and vortex dynamics are discussed.The size of the recirculation within the slat cove and the intensity of the shed vortices originating from the slat cusp shear layer are found to generally decrease as the angle of attack increases.The joint time-frequency analyses show that disturbances of different frequencies exist in the slat cusp shear layer and they trigger the different vortex shedding patterns of the slat cusp shear layer.The self-sustained oscillation within the slat cove,normally observed at high Reynolds number(Re_(c)~10^(6)),is proved to be responsible for the disturbances of different frequencies and the related vortex dynamics in the current study.

Propagation dynamics of deformed 2D vortex Airy beams

Due to their intriguing properties including self-accelera- tion, non-diffraction, and self-healing, Airy beams have attracted a lot of attention and inspired tremendous potential applications in manipulation, biophotonics, and communication fields such as manipulation of particles,

PROPULSIVE PERFORMANCE AND VORTEX SHEDDING OF A FOIL IN FLAPPING MOTION

The propulsive performance and vortex shedding of oscillating foil, whichmimics biological locomotion, were numerically investigated. The objectives of this study were todeal with unsteady force, in particular thrust force, exerted on the foil in pitching and plungingmotions, and to explore the relation of the propulsive performance with vortex structures near thefoil and vortex shedding in the near wake. The two-dimensional incompressible Navier-Stokesequations in the vorticity and stream-function formulation were solved by fourth-order essentiallycompact finite difference schemes for the space derivatives and a fourth-order Runge-Kutta schemefor the time advancement. To reveal the mechanism of the propulsive performance, the unsteady forceand the shedding of the trailing- and leading-edge vortices of the foil were analyzed. The effectsof some typical factors, such as the frequency and amplitude of the oscillation, the phasedifference between the pitching and plunging motions, and the thickness ratio of the foil, on thevortex shedding and unsteady force were discussed.

Liutex-based vortex control with implications for cavitation suppression

Viewed as sinews and muscles of fluid motion,coherent vortical structures with their interactions are key to understanding the flow dynamics.Based upon this observation,we explore the possibility of efficient flow control by directly manipulating vortices numerically inside the flow field based on the vortex definition and identification system of Liutex.The objective is twofold:(1)to study the vortex dynamics,for example,by observing the response of the flow to strengthening or weakening of certain vortices,and(2)to obtain efficient vortex-based control strategies which might lead us to practical applications.In the present numerical study,the manipulating of vortices is achieved by introducing additional source(force)terms to the Navier-Stokes equations,which hereafter will be collectively called Liutex force field model.Methodologies including controlling the rotation strength and centripetal force of particular vortices are detailed in a flow past a cylinder with different control purposes at Reynolds number of 200.Further examples are provided with a cavitating flow around two-dimensional Clark-Y hydrofoil,with particular interests on cavitation suppression.It is illustrated particular vortex with cavitation encircled could be effectively suppressed.

FORCE CHARACTERISTICS AND VORTEX SHEDDING OF A PITCHING FOIL IN SHEAR FLOWS

The objective of this study is to deal with unsteady force acting on a pitching foil in shear flow and to study the relation of the force characteristics with vortex shedding near the foil. The two dimensional incompressible Navier Stokes equations in the vorticity and stream function formulation were solved with the fourth order essentially compact finite difference schemes for the space derivatives and a fourth order Runge Kutta scheme for the time advancement. The force characteristics and vortex shedding of the pitching foil in shear flows were investigated. The effects of some typical factors, including the incoming flow shear, the oscillating frequency and amplitude, on the vortex shedding and force behavior were analyzed and discussed.

Large eddy simulation of tip leakage cavitating flow focusing on cavitation-vortex interaction with Cartesian cut-cell mesh method

In the present paper, flow configurations of cavitating flow around a straight NACA0009 foil with a gap between the foil tip and sidewall are investigated numerically by large eddy simulation（LES） coupled with Zwart-Gerber-Belamri（ZGB） cavitation model. A Cartesian cut-cell method is used for mesh generation, which is of good orthogonality and high quality. A good agreement is obtained between simulation and experiment. Two influencing factors on vorticity distributions, the interaction between different vortices and the occurrence of cavitation, are discussed in detail based on the numerical results. A series of ？-shaped loops are observed during the development of the induced vortex, which is a result of the instability of vortex pair. This finding may provide a new viewpoint to control the evolution of tip-leakage vortex（TLV） cavitation. Moreover, it is found that the dilatation term plays a much more important role in the evolution of TLV cavitation compared with that in sheet cavitation.

On the role of hemodynamics in predicting rupture of the abdominal aortic aneurysm

Hemodynamics plays a crucial role in the growth of an abdominal aortic aneurysm(AAA)and its possible rupture.Due to the serious consequences that arise from the aneurysm rupture,the ability to predict its evolution and the need for surgery are of primary importance in the medical field.Furthermore,the presence of intraluminal thrombus(ILT)strongly affects the evolution of the pathology.In this study,we analyzed the influence of hemodynamics on the growth and possible rupture of AAAs.Numerical investigations of pulsatile non-Newtonian blood flow were performed in six patient-specific AAAs reconstructed from diagnostic images,having different sizes and shapes,and with or without ILT.Wall shear stress and vorticity distribution in the bulge and their evolution during the cardiac cycle were analyzed.The results indicate that blood flow dynamics acts synergistically with atherosclerotic degeneration in the development of the disease.The high surface complexity and tortuosity of the aneurysms significantly affect the blood motion,and the presence of inflection in the aneurysm centerline has a noticeable effect on the vortex dynamics.Links between regions of slow recirculating flows,low values of time-averaged wall shear stress,high values of oscillatory shear index,and zones of ILT deposition were found.In the absence of ILT,possible thrombus accumulation areas and consequent aneurysm growth were identified.The findings of this study highlight the importance of hemodynamics in assessing the vulnerability of the aortic wall and underline the crucial role of patient-specific investigations in predicting the rupture of individual aneurysms.