Bessel vortices in spin-1 Bose-Einstein condensates with Zeeman splitting and spin-orbit coupling

We investigate the ground states of spin-orbit coupled spin-1 Bose-Einstein condensates in the presence of Zeeman splitting.By introducing the generalized momentum operator,the linear version of the system is solved exactly,yielding a set of Bessel vortices.Additionally,based on linear solution and using variational approximation,the solutions for the full nonlinear system and their ground state phase diagrams are derived,including the vortex states with quantum numbers m=0,1,as well as mixed states.In this work,mixed states in spin-1 spin-orbit coupling(SOC)BEC are interpreted for the first time as weighted superpositions of three vortex states.Furthermore,the results also indicate that under strong Zeeman splitting,the system cannot form localized states.The variational solutions align well with numerical simulations,showing stable evolution and meeting the criteria for long-term observation in experiments.

Large-scale particle trapping by acoustic vortices with a continuously variable topological charge

Strengthened directivity with higher-order side lobes can be generated by the transducer with a larger radius at a higher frequency. The multi-annular pressure distributions are displayed in the cross-section of the acoustic vortices(AVs)which are formed by side lobes. In the near field, particles can be trapped in the valley region between the two annuli of the pressure peak, and cannot be moved to the vortex center. In this paper, a trapping method based on a sector transducer array is proposed, which is characterized by the continuously variable topological charge(CVTC). This acoustic field can not only enlarge the range of particle trapping but also improve the aggregation degree of the trapped particles. In the experiments, polyethylene particles with a diameter of 0.2 mm are trapped into the multi-annular valleys by the AV with a fixed topological charge. Nevertheless, by applying the CVTC, particles outside the radius of the AV can cross the pressure peak successfully and move to the vortex center. Theoretical studies are also verified by the experimental particles trapping using the AV with the continuous variation of three topological charges, and suggest the potential application of large-scale particle trapping in biomedical engineering.

Helical particle manipulation based on power-exponent-phase acoustic vortices generated by a sector transducer array

The characteristics of traditional acoustic vortices(AVs) were verified by the cross-sectional axisymmetric pressure distributions with perfect phase spirals around the center pressure null. In order to generate a non-axisymmetric pressure distribution, the concept of power-exponent-phase was first introduced into the formation of AV beams, named “powerexponent-phase acoustic vortices(PAVs)” in this paper. Based on a ring-array of sector transducers, the helical distribution of the low-pressure valley in cross-sections of PAVs, which enables particles to move from a distant position to the center low-potential well along a certain spiral passageway, was proved theoretically. The particle manipulation behavior for PAVs with a power order of 2 is numerically modeled and experimentally confirmed. The results show that PAVs with a nonaxisymmetric spiral pressure distribution can be used to realize the directional transport of particles in an enlarged scope,suggesting prospective application potential in biomedical engineering.

Effect of an Inclined Slots on the Power Consumption and Vortices Size in a Rushton Turbine Agitated Tank

Mechanical agitation in baffled vessels with turbines plays a vital role in achieving homogeneous fluid mixing and promoting various transfer operations.Therefore,designing vessels with optimal energy efficiency and flow dynamics is essential to enhance operational performance and eliminate flow perturbations.Hence,the present research focuses on a numerical investigation of the impact of inclined slots with different angles installed at the side-wall of a cylindrical vessel equipped with a Rushton turbine.This study explores power consumption and vortex size while considering various rotation directions of the impeller with different rotation speeds.The numerical simulations are conducted for Reynolds numbers ranging from 104 to 105,using the RANS k-εturbulence model to govern the flow inside the stirred vessel,accounting for mass and momentum balances.The results have shown that the installation of slots reduces power consumption and vortex size compared to conventional vessel configu-rations.Moreover,increasing the slot angle from 0 to 32.5°further reduces energy consumption and vortex size,especially with negative rotation speeds.On the other hand,increasing the Reynolds numbers leads to a decrease in power consumption and an increase in vortex size.The present research therefore proposes a design for con-structing Rushton-turbine stirred vessels offering optimal operation,characterized by reduced energy consumption and minimized vortex size.

The Early Mesozoic NE-SW Extensional Model and Exhumation Processes at the Southeastern Margin of the Central Asian Orogenic Belt:Insights from the Strain and Kinematic Vorticity Analysis of the Sonid Zuoqi Ductile Detachment Zone

The Sonid Zuoqi ductile detachment zone is located at the southeastern margin of the Central Asian orogenic belt(CAOB),striking EW and dipping to the S.The major rock type of the Sonid Zuoqi ductile detachment zone is mylonite derived from granite.The sequence of mylonite features is:(1)S and C foliations of mylonite,and(2)extensional crenulation cleavage(ecc)or C′and the kinematic vorticity(Wk)value changed from 0.70 to 0.95 and from 0.37 to 0.69,respectively;the strain type of the mylonites within the Sonid Zuoqi ductile detachment zone is compressional to planar strain.The strong deformation mylonite and Halatu plutons yielded a zircon U-Pb age of 244 Ma and a zircon(U-Th)/He age of 214 Ma,respectively.Based on the strain and kinematic vorticity analysis,together with the zircon U-Pb and zircon(U-Th)/He ages and the regional tectonic background,the study area experienced three stage evolution:tangential simpleshear(244 Ma),simple-shear-dominated general shear represented by upper crustal extension(224 Ma)and pure-shear-dominated general shear represented by the Halatu pluton doming(214 Ma),which constrained the early Mesozoic NE-SW crustal extension at the southeastern margin of the CAOB.This NE-SW extension probably originated from the postorogenic extensional collapse of the CAOB,subsequent exhumation being controlled by the far afield effects of the closure of the Mongol-Okhotsk belt.

Boundary Conditions for Momentum and Vorticity at an Interface between Two Fluids

Boundary conditions for momentum and vorticity have been precisely derived, paying attention to the physical meaning of each mathematical expression of terms rigorously obtained from the basic equations: Navier-Stokes equation and the equation of vorticity transport. It has been shown first that a contribution of fluid molecules crossing over a conceptual surface moving with fluid velocity due to their fluctuating motion is essentially important to understanding transport phenomena of momentum and vorticity. A notion of surface layers, which are thin layers at both sides of an interface, has been introduced next to elucidate the transporting mechanism of momentum and vorticity from one phase to the other at an interface through which no fluid molecules are crossing over. A fact that a size of δV, in which reliable values of density, momentum, and velocity of fluid are respectively defined as a volume-averaged mass of fluid molecules, a volume-averaged momentum of fluid molecules and a mass-averaged velocity of fluid molecules, is not infinitesimal but finite has been one of the key factors leading to the boundary conditions for vorticity at an interface between two fluids. The most distinguished characteristics of the boundary conditions derived here are the zero-value conditions for a normal component of momentum flux and tangential components of vorticity flux, at an interface.

A Study of the Effect of Topography on the Merging of Vortices

Eight sets of numerical experiments are performed in 48 hours of integtation by using a barotropic primitive equation model with a topographic term so as to investigate the effect of topography on the merging of vortices. It is pointed out that the introduction of topography may change the track of vortices, and it causes the low vortices and vorticity lumps to be detained on the southeast side of the topography, thus creating a favorable condition for the merging of the low vortex and vorticity lumps. It is also shown that the effect of topography may cause double mergers of vortices in a horizontally shearing basic flow, and it can strengthen the low vortex remarkably.

Effect of the Interaction of Different Scale Vortices on the Structure and Motion of Typhoons

Five numerical experiments have been performed in this paper by using a quasigtostrophic barotropical model to investigate the interaction of different scale vortiCes on the structure and motion of typhoons.Results show that this interaction may arouse the irregular changes of the asymmetric structure of typhoons,thus leading to anomalous Phenomena such as meandering tracks and sudden changes in the motion speed of typhoons;the ￣t Of this interaction on the strucure and motion may be quite different when the smaller vortex is situated in different Posihons of the typhoon circulation.

Comparison of a Manual and an Automated Tracking Method for Tibetan Plateau Vortices

Tibetan Plateau vortices （TPVs） are mesoscale cyclones originating over the Tibetan Plateau （TP） dnring the extended summer season （April-September）. Most TPVs stay on the TP, but a small number can move off the TP to the east. TPVs are known to be one of the main precipitation-bearing systems on the TP and moving-off TPVs have been associated with heavy precipitation and flooding downstream of the TP （e.g., in Sichuan province or over the Yangtze River Valley）. Identifying and tracking TPVs is difficult because of their comparatively small horizontal extent （400-800 kin） and the limited availability of soundings over the TP, which in turn constitutes a challenge for short-term predictions of TPV-related impacts and for the climatological study of TPVs. In this study, （i） manual tracking （MT） results using radiosonde data from a network over and downstream of the TP are compared with （ii） results obtained by an automated tracking （AT） algorithm applied to ERA-Interim data. Ten MT-TPV cases are selected based on method （i） and matched to and compared with the corresponding AT-TPVs identified with method （ii）. Conversely, ten AT-TPVs are selected and compared with the corresponding MT-TPVs. In general, the comparison shows good results in cases where the underlying data are in good agreement, but considerable differences are also seen in some cases and explained in terms of differences in the tracking methods, data availability/coverage and disagreement between sounding and ERA-Interim data. Recommendations are given for future efforts in TPV detection and tracking, including in an operational weather forecasting context.

REGULARIZATION OF PLANAR VORTICES FOR THE INCOMPRESSIBLE FLOW

In this paper, we continue to construct stationary classical solutions for the incompressible planar flows approximating singular stationary solutions of this problem. This procedure is carried out by constructing solutions for the following elliptic equations{-△u=λ∑1Bδ（x0,j）（u-kj）p＋,in Ω,u=0,onΩ is a bounded simply-connected smooth domain, ki （i = 1,… , k） is prescribed positive constant. The result we prove is that for any given non-degenerate critical pointX0=（x0,1,…,x0,k of the Kirchhoff-Routh function defined on Ωk corresponding to （ k1,……kk ）there exists a stationary classical solution approximating stationary k points vortex solution. Moreover, as λ→＋∞ shrinks to {x05}, and the local vorticity strength near each x0,j approaches kj, j = 1,… , k. This result makes the study of the above problem with p _〉 0 complete since the cases p 〉 1, p = 1, p = 0 have already been studied in [11, 12] and [13] respectively.

Active control of turbulence for drag reduction based on the detection of near-wall streamwise vortices by wall information

The spatial relations between the measurable wall quantities （streamwise shear stress τwx, spanwise shear stress τwz, and pressure fluctuations Pw） and the near-wall streamwise vortices （NWSV） are investigated via direct numerical simulation （DNS） databases of fully developed turbulent channel flow at a low Reynolds number. In the stan- dard turbulent channel flow, the results show that all the wall measurable variables are closely associated with the NWSV. But after applying a stochastic interference, the relation based on τwx breaks down while the correlations based on Pw and τwz are still robust. Hence, two wall flow quantities based on Pw and τwz are proposed to detect the NWSV. As an appli- cation, two new control schemes are developed to suppress the near-wall vortical structures using the actuation of wall blowing/suction and obtain 16 % and 11% drag reduction, respectively.

A Preliminary Study of the Dynamics of Eastward Shifting Cyclonic Vortices

The dynamics of eastward shifting cyclonic vortices are investigated in terms of a barotropic primitive equation model, and six experiments are performed. Both the interaction of a cyclonic vortex with vorticity lumps and the interaction of the vortex with the shearing basic flow may induce the strengthening of the vortex in a short period, however, the vortex intensity still shows a general decreasing tendency over the whole integration time period. The interaction among the shearing basic flow, cyclonic vortex, and multiple vorticity lumps can change the tendency. The merging of the cyclonic vortex with vorticity lumps in the shearing basic flow of positive vorticity is directly responsible for the maintenance and development of the cyclonic vortex.

Effects of tip perturbation and wing locations on rolling oscillation induced by forebody vortices

The wing rock motion is frequently suffered by a wing-body configuration with low swept wing at high angle of attack. It is found from our experimental study that the tip perturbation and wing longitudinal locations affect significantly the wing rock motion of a wing-body. The natural tip perturbation would make the wing rock motion of a nondeterministic nature and an artificial mini-tip perturbation would make the wing rock motion deterministic. The artificial tip perturbation would, as its circumferential location is varied, generate three different types of motion patterns： （1） limit cycle oscillation, （2） irregular oscillation, （3） equilibrium state with tiny oscillation. The amplitude of rolling oscillation corresponding to the limit cycle oscillatory motion pattern is decreased with the wing location shifting downstream along the body axis.

Simulations of the Motion of Tropical Cyclone-like Vortices in the Presence of Synoptic and Mesoscale Circulations

Initial mesoscale vortex effects on the tropical cyclone （TC） motion in a system where three components coexist （i.e., an environmental vortex （EV）, a TC, and mesoscale vortices） were examined using a barotropic vorticity equation model with initial fields where mesoscale vortices were generated stochastically. Results of these simulations indicate that the deflection of the TC track derived from the initial mesoscale vortices was clearly smaller than that from the beta effect in 60% of the cases. However, they may have a more significant impact on the TC track under the following circumstances. First, the interaction between an adjacent mesoscale vortex and the TC causes the emergence of a complicated structure with two centers in the TC inner region. This configuration may last for 8 h, and the two centers undergo a cyclonic rotation to make the change in direction of the TC motion. Second, two mesoscale vortices located in the EV circulation may merge, and the merged vortex shifts into the EV inner region, intensifying both the EV and steering flow for the TC, increasing speed of the TC.

Analysis of the Caudal Vortices Evolvement around Flapping Foil

The viscous flow field around two-dimensional flapping （ heaving and pitching） foils was numerically computed. The structural characteristics of caudal vortices were investigated and the contour curves at different phase angles were obtained. The relationships between the structural characteristics of the vortices and the force acting on the foil and between the widths of the caudal vortex street and of the caudal flow field were analyzed. A method to determine the shedding frequency of the vortices was proposed.

Effects of the Blade Shape on the Trailing Vortices in Liquid Flow Generated by Disc Turbines

Particle image velocimetry technique was used to analyze the trailing vortices and elucidate their rela-tionship with turbulence properties in a stirred tank of 0.48 m diameter,agitated by four different disc turbines,in-cluding Rushton turbine,concaved blade disk turbine,half elliptical blade disk turbine,and parabolic blade disk turbine.Phase-averaged and phase-resolved flow fields near the impeller blades were measured and the structure of trailing vortices was studied in detail.The location,size and strength of vortices were determined by the simplified λ2-criterion and the results showed that the blade shape had great effect on the trailing vortex characteristics.The larger curvature resulted in longer residence time of the vortex at the impeller tip,bigger distance between the upper and lower vortices and longer vortex life,also leads to smaller and stronger vortices.In addition,the turbulent ki-netic energy and turbulent energy dissipation in the discharge flow were determined and discussed.High turbulent kinetic energy and turbulent energy dissipation regions were located between the upper and lower vortices and moved along with them.Although restricted to single phase flow,the presented results are essential for reliable de-sign and scale-up of stirred tank with disc turbines.

Experimental investigation on tip vortices and aerodynamics of a wing with ground effect

The tip vortices and aerodynamics of a NACA0012 wing in the vicinity of the ground were studied in a wind tunnel.The wing tip vortex structures and lift/drag forces were measured by a seven-hole probe and a force balance,respectively.The evolution of the flow structures and aerodynamics with a ground height were analyzed.The vorticity of tip vortices was found to reduce with the decreasing of the ground height,and the position of vortex-core moved gradually to the outboard of the wing tip.Therefore,the down-wash flow induced by the tip vortices was weakened. However,vortex breakdown occurred as the wing lowered to the ground.From the experimental results of aerodynamics,the maximum lift-to-drag ratio was observed when the angle of attack was 2.5°and the ground clearance was 0.2.

FORMATION AND EVOLUTION OF THE STREAMWISE VORTICES IN MIXING LAYERS

The evolution of the three-dimensional time-developing mixing layer was simulated numerically using the pseudo-spectral method. The initial perturbations consisted of the two-dimensional fundamental wave and the streamwise-invariant three-dimensional disturbance. A comparison of the formations of the streamwise vortices with different amplitude functions for three-dimensional disturbances was made. In one case the results are similar to that of Rogers and Moser (1992), whereas a different way in which the quadrupole forms and sudden expansion of the rib were observed in another case. The simulation also confirms that stretching by the forming roller rather than Rayleigh centrifugal instability is responsible for the formation of the rib. Finally, numerical flow visualization results were presented. (Edited author abstract) 9 Refs.

Distribution characteristics of intensity and phase vortices of speckle fields produced by N-pinhole random screens

We analyze the distribution properties of phase and phase vortices in a speckle field generated by N-pinhole random screens, and find that the phase vortex distributions show similarity and clustering in local regions. The phase patterns have a lot of sets composed of two phase vortices with opposite signs or four phase vortices which are positive and negative vortices alternately. Cases are also found where two adjacent phase vortices have the same topological charges. The density of phase vortices becomes larger with the increase of the radius of circumference and the number of pinholes on screen.Then, the relative positions of phase vortices can be adjusted by changing the radius of circumference and the number of pinholes.

Random phase screen influence of the inhomogeneous tissue layer on the generation of acoustic vortices

The influence of the inhomogeneous tissue layer on the generation of acoustic vortices （AV） is studied theoretically and experimentally based on the phase screen model. By considering the time-shift of a random phase screen, the formula of acoustic pressure for the AV beam generated by a circular array of eight planar piston sources is derived. With the actual correlation length of the abdominal wall, numerical simulations before and after the insertion of the inhomogeneous tissue layer are conducted, and also demonstrated by experimental measurements. It is proved that, when the thickness variation of the phase screen is less than one wavelength, no significant influence on the generation of AVs can be produced. The variations of vortex nodes and antinodes in terms of the location, shape, and size of AVs are not obvious. Although the circular pressure distribution might be deformed by the phase interference with a larger thickness variation, AVs can still be generated around the center axis with perfect phase spirals in a reduced effective radius. The favorable results provide the feasibility of AV generation inside the human body and suggest the application potential of AVs in object manipulation for biomedical engineering.