Vortex Core Region Research Articles

Principal Component Analysis of Doppler Radar Data. Part I: Geometric Connections between Eigenvectors and the Core Region of Atmospheric Vortices

Abstract This is the first in a three-part series of papers that present the first applications of principal component analysis (PCA) to Doppler radar data. Although this novel approach has potential applications to many types of atmospheric phenomena, the specific goal of this series is to describe and verify a methodology that establishes the position and radial extent of the core region of atmospheric vortices. The underlying assumption in the current application is that the streamlines of the nondivergent component of the horizontal wind are predominantly circular, which is a characteristic often observed in intense vortices such as tropical cyclones. The method employs an S2-mode PCA on the Doppler velocity data taken from a single surveillance scan and arranged sequentially in a matrix according to the range and azimuth coordinates. Part I begins the series by examining the eigenvectors obtained from such a PCA applied to a Doppler velocity model for a modified, Rankine-combined vortex, where the ratio of the radius of maximum wind to the range from the radar to the circulation center is varied over a wide range of values typically encountered in the field. Results show that the first two eigenvectors within the eigenspace of range coordinates represent over 99% of the total variance in the data. It is also demonstrated that the coordinates of particular cusps in the curves of the eigenvector coefficients plotted against their indices are geometrically related to both the position of circulation center and the radius of maximum wind.

Particle classification in Taylor vortex flow with an axial flow

Particle classification phenomenon in Taylor vortex flow with an axial flow was investigated experimentally and numerically. The flow-visualization experiment by a laser-induced fluorescence method clearly revealed that there existed two distinct mixing regions at low Reynolds numbers. The tracer near the vortex cell boundary was rapidly transported axially owing to the bypass flow effect. On the other hand, the fluid element was confined to the vortex core region without being exchanged with the outer flow region. In order to observe particle classification phenomenon, polymethyl methacrylate (PMMA) particles suspended in the same aqueous solution of glycerol as the working fluid were fed into the top of the apparatus. Particle size was initially ranging from 10 to 80 µm. The ratio of the particle density to the fluid density was 1.04–1.05, which means the density difference between particle and fluid is very small. The suspended solution was withdrawn using a hypodermic needle every a certain time period at 30 mm above the bottom of apparatus. The fluid was sampled both near the outer wall and in vortex core. The particles sampled at 42 min having the size of 20–50 µm were mainly observed in the vortex core region. On the other hand, a large population of particles having the size of about 50–80 µm could be seen in the outer region of vortex. It was found that large particles located near the outer edge of vortices were quickly transported axially owing to the bypass flow effect. Numerical simulation also revealed that the loci of particles depended on the particle size.

LES of the turbulent coherent structures and particle dispersion in the gas–solid wake flows

To deeply understand the particle dispersion and examine the reliability of large eddy simulation (LES) method in two-dimensional gas–solid free shear flows, a particle-laden plane wake flow was numerically investigated. The gas-phase field was solved by using large eddy simulation method, and the particle trajectories were traced in Lagrangian framework based on one-way coupling. The coherent structures and particle dispersion were simulated and compared with previous experiment results. The typical coherent structures alternately forming from the near-wall region, shedding and moving towards the downstream positions were observed. Due to the effects of the coherent structures, the particles demonstrate a more organized dispersion process in the space and a periodic dispersion characteristic in the time. However, for particles at different Stokes numbers, the dispersion patterns are different. Although the particles at smaller Stokes number congregate mainly in the vortex core regions and the particles at larger Stokes number assemble in the vortex braid regions, the particles at intermediate Stokes numbers concentrate highly in the boundary regions of the coherent structures. The two-phase flow characteristics obtained by the present large eddy simulation are in quantitative agreement with previous experiment results.

Large eddy simulation of the gas??particle turbulent wake flow

To find out the detailed characteristics of the coherent structures and associated particle dispersion in free shear flow, large eddy simulation method was adopted to investigate a two-dimensional particleladen wake flow. The well-known Sub-grid Scale mode introduced by Smagorinsky was employed to simulate the gas flow field and Lagrangian approach was used to trace the particles. The results showed that the typical large-scale vortex structures exhibit a stable counter rotating arrangement of opposite sign, and alternately form from the near wall region, shed and move towards the downstream positions of the wake with the development of the flow. For particle dispersion, the Stokes number of particles is a key parameter. At the Stokes numbers of 1.4 and 3.8 the particles concentrate highly in the outer boundary regions. While the particles congregate densely in the vortex core regions at the Stokes number of 0. 15, and the particles at Stokes number of 15 assemble in the vortex braid regions and the rib regions between the adjoining vortex structures.

Antiferromagnetic vortex core in Tl(2)Ba(2)CuO(6+delta) studied by nuclear magnetic resonance.

Spatially resolved NMR is used to probe the magnetism in and around vortex cores of nearly optimally doped Tl(2)Ba(2)CuO(6+delta) (T(c)=85 K). The NMR relaxation rate T(-1)1 at the 205Tl site provides direct evidence that the antiferromagnetic (AF) spin correlation is significantly enhanced in the vortex core region. In the core region Cu spins show a local AF ordering with moments parallel to the layers at T(N)=20 K. Above T(N) the core region is in the paramagnetic state which is a reminiscence of the state above the pseudogap temperature (T(*) approximately 120 K), indicating that the pseudogap disappears within cores.

Antiferromagnetic vortex core in HTSC studied by spatially resolved NMR

Spatially resolved NMR is used to probe the magnetism in the vortex state of Tl2Ba2CuO6+δ (Tc=85 K). We found that (1): T1−1 at 205Tl is extremely enhanced toward to the vortex core, (2): T1 process becomes largely inhomogeneous nearby the vortex core, and (3): the T-dependence of T1−1 at the vortex core region shows a peak at T=20 K. These results indicate a clear evidence of the local AF order inside the vortex core. The suppression of the d-wave superconducting order parameter leads to the nucleation of islands with the local AF order.

Path integral calculation of superfluid [formula omitted] vortex core structure

A structure of a superfluid 4 He vortex core is studied with a path integral Monte Carlo method. The distribution of superfluid and normal fluid densities around the vortex core is obtained. The total particle density decreases in the vortex core region. The radius of the core is nearly equal to the particle diameter. The vortex core is filled with normal fluid in the temperature region T≃ T λ . In the low temperature region, the normal fluid component of a vortex core decreases remarkably. Consequently the number of particle density of a vortex core region becomes extremely small.

Lagrangian estimations of ozone loss in the core and edge region of the Arctic polar vortex 1995/1996: Model results and observations

Ozone evolution and diabatic descent in the Arctic polar vortex in winter 1995/1996 was studied with a newly developed diabatic trajectory–chemistry model (DTCM). To study the chemical and dynamic evolution of the species in the polar vortex, 400 diabatic trajectories were calculated in the vortex core and edge region by using three-dimensional (3-D) wind data provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). The averaged diabatic descending motion and ozone behavior were obtained for particles started from the core and from the edge region of the vortex. The difference in ozone-loss rates as well as the difference in descending rates between the vortex core and the vortex-edge region was not statistically significant. The average cumulative ozone loss of 65 ± 16% in the vortex core obtained from the model calculations was consistent with the estimates obtained with a different method (Match experiment). The model results for the vortex core were compared with those obtained using trajectories with the vertical winds calculated on the basis of radiative cooling rates as used by the SLIMCAT 3-D chemical transport model. Although the trajectories based on cooling rates exhibited lower descending rates than those based on 3-D analyzed wind data, the ozone behavior was similar for both types of trajectory. Ozonesonde data from two stations (Ny-Alesund in the vortex core and Yakutsk in the vortex edge) were compared with the model results. For Lagrangian estimation of the ozone loss at these stations, the descending rates obtained by the diabatic trajectory calculations were used. Good agreements were obtained between the model results and observations for both the vortex core and edge region. These results suggest that strong ozone depletion occurred not only in the core, but also in the edge region of the vortex, and that air masses from the mid-latitudes did not appreciably affect the degree of ozone depletion in this winter–spring period. The sensitivity of the model to different descending rates and to the presence of large nitric acid trihydrate (NAT) particles was also examined.

Spatially-Resolved NMR Study on Antiferromagnetic Vortex Core in HTSC

Magnetism in the vortex core of nearly-optimal doped Tl2Ba2CuO6+δ (Tc=85 K) is investigated by a spatially-resolved NMR. The NMR relaxation rate T−11 at 205Tl site provides a direct evidence of the significant enhancement of the AF spin correlations in the vortex core region and shows clearly a local AF ordering of the core region Cu spins at TN=20 K. Above TN the core region is in the paramagnetic state which is a reminiscence of the state above the pseudogap temperature (T*∼−120 K), indicating that the pseudogap disappears within the vortex core.

Antiferromagnetic vortex core in HTSC studied by spatially resolved NMR

Spatially-resolved NMR is used to probe the magnetism in the vortex state of nearly optimally doped high- T c cuprate Tl 2Ba 2CuO 6+ δ ( T c =85 K ). We found that (1) the nuclear spin–lattice relaxation rate T 1 −1 at 205 Tl is extremely enhanced toward the vortex core and (2) T 1 process become largely inhomogeneous in the vortex state and (3) the temperature dependence of T 1 −1 at the vortex core region shows a peak at T∼20 K . These results indicates a clear evidence of the antiferromagnetic (AF) order inside the vortex core, and that the suppression of the d-wave superconducting order parameter leads to the nucleation of islands with AF order.

The Importance of Three Physical Processes in a Minimal Three-Dimensional Tropical Cyclone Model

Abstract The minimal three-dimensional tropical cyclone model developed by Zhu et al. is used to explore the role of shallow convection, precipitation-cooled downdrafts, and the vertical transport of momentum by deep convection on the dynamics of tropical cyclone intensification. The model is formulated in σ coordinates and has three vertical levels, one characterizing a shallow boundary layer, and the other two representing the upper and lower troposphere, respectively. It has three options for treating cumulus convection on the subgrid scale and a simple scheme for the explicit release of latent heat on the grid scale. In the model, as in reality, shallow convection transports air with low moist static energy from the lower troposphere to the boundary layer, stabilizing the atmosphere not only to itself, but also to deep convection. Also it moistens and cools the lower troposphere. For realistic parameter values, the stabilization in the vortex core region is the primary effect: it reduces the deep conv...

Site selection NMR study on electronic state in and near vortex core of YBa 2Cu 4O 8

We report a site-selective 17O spin–lattice relaxation rate T 1 −1 in the vortex state of YBa 2Cu 4O 8. We found that T 1 −1 at the planar sites exhibits an unusual nonmonotonic NMR frequency dependence. Based on T 1 −1 in the vortex core region, we establish strong evidence that the local density of states within the vortex core is strongly reduced.

Vortexwide denitrification of the Arctic polar stratosphere in winter 1999/2000 determined by remote observations

Denitrification has been studied using measurements of stratospheric HNO3 and N2O by the Airborne Submillimeter Radiometer (ASUR), operated on board the NASA DC‐8 during SOLVE/THESEO 2000. Lidar measurements taken on board the same aircraft have been used to distinguish between temporary uptake of HNO3 in polar stratospheric clouds (PSCs) and denitrification events. To derive an NOy budget, ClNO3 data by balloonborne and ground‐based Fourier transform infrared measurements and a model estimate of NOx + 2N2O5 have been considered. The HNO3 profiles of sporadic ASUR measurements without PSC coverage in January suggest that denitrification had started in the vortex core region by then. Vortexwide denitrification was found in mid‐March 2000. Corrected for diabatic descent using the N2O measurements, a vortex‐averaged NOy deficit between 1.2 ± 0.9 ppb at about 16 km altitude and 5.3 ± 2.7 ppb at about 20.5 km altitude was derived compared to December 1999, based on an observed decrease in HNO3 between 2.2 and 3.5 ppb during this time period. A shift in the NOy partitioning from HNO3 toward ClNO3 of about 0.4 to 0.7 ppb was observed in mid‐March compared to December, indicating that chlorine deactivation was occurring. Comparisons with the SLIMCAT three‐dimensional chemical transport model applying denitrification schemes based on ice and nitric acid trihydrate particles in equilibrium, respectively, reveal agreement within the error bars at higher altitudes (∼19 km) but show discrepancies at lower altitudes (∼16 km). It is suggested that more sophisticated denitrification schemes are needed to generally describe denitrification processes.

Quasiparticle excitation in and around the vortex core of underdopedYBa2Cu4O8studied by site-selective NMR

We report a site-selective ^{17}O spin-lattice relaxation rate T_1^{-1} in the vortex state of underdoped YBa_2Cu_4O_8. We found that T_1^{-1} at the planar sites exhibits an unusual nonmonotonic NMR frequency dependence. In the region well outside the vortex core, T_1^{-1} cannot be simply explained by the density of states of the Doppler-shifted quasiparticles in the d-wave superconductor. Based on T_1^{-1} in the vortex core region, we establish strong evidence that the local density of states within the vortex core is strongly reduced.

Effect of Inhomogeneous Mixing on Chemical Reaction in a Taylor Vortex Flow Reactor.

Effect of inhomogeneous mixing on chemical reactions in a Taylor vortex flow reactor was experimentally investigated by using a second-order reaction system. The flow-visualization experiment by a laser induced fluorescence method was also carried out to observe the cross-sectional view of mixing behavior in the inside of Taylor vortex cells. In the reaction experiment, the reaction among hydrogen peroxide, iodide ions and hydrogen ions, i.e. 2H+ + 2I– + H2O2 → I2 + 2H2O, was used. The temporal evolution of the concentration of iodine was observed from the temporal variation of color of iodine. The flow-visualization experiment clearly revealed the existence of two different mixing zones within a Taylor vortex cell at low Reynolds numbers. Namely, the fluid flowing near the cell boundary was axially well-mixed, while the fluid element confined to the vortex core region was poorly exchanged with the outer well-mixed flow region. This vortex core region, called an isolated mixing region (IMR), decreased as increasing the Reynolds number. It has been found in the reaction experiment that the reaction rate is larger in laminar and singly-periodic wavy Taylor vortex flow regimes than in quasi-periodic and chaotic Taylor vortex flow regimes.

A study on swirling flows in a rectangular channel (LDV measurement, flow visualization and large eddy simulation)

The purpose of this study is to make clear the behavior of swirling pipe flows with non-circular section. We have investigated experimentally and numerically the swirling flows in a rectangular channel with aspect ratio of 1.3, which is one of the typical pipe flow with non-circular section. In this paper, experimental apparatus with water circulation system is produced, and LDV measurement of the swirling flows is performed in order to clarify the mean velocities and turbulent quantity with higher accuracy. In addition, flow visualization for movement of vortex core region in the swirling flows is carried out using tracer method. Moreover, large eddy simulation (LES) of the flow field is made and compared with the experimental results. As results of these investigations, the behavior of the swirling flows in the rectangular channel is totally discussed.

Distribution of suspended particles in a Taylor–Poiseuille vortex flow reactor

Vortex flow reactors (VFRs) are specially suited to work with shear-sensitive particles, due to the gentle and efficient stirring characteristics of Taylor vortices. For heterogeneous VFRs, the distribution of the solid phase must be accounted for in detail. This work presents residence-time distributions (RTDs) of agarose gel particles ( φ av =214 μm ), suspended in different liquid solutions. Reactor porosity was 90%. The mass transfer coefficients of a lumped-parameter model of the reactor are estimated from residence time distributions of a tracer. The VFR has radius ratio η=0.664 and aspect ratio Γ=14.9. Axial flow rates were selected to provide a mean residence time of 1850 s, adequate for many applications. Minimum rotation rates of the inner cylinder were imposed by suspended particles’ homogeneity criteria. The VFR operational region was: 0.0645< Re ax<0.592 and 98< Re θ <3820, corresponding to very high values of the ratio Re θ / Re ax (between 5293 and 6236). Under these conditions, the vortices were stationary, and circumvented by a by-pass stream. Our results indicate that the gel particles are unevenly distributed in the vortex core and by-pass regions. Mean residence times for the particles are substantially greater than for the liquid. The mathematical model presented here can accommodate this behavior, using a partition coefficient for the solid phase.

Vortex interaction and mixing in a driven gaseous axisymmetric jet

Vortex formation and merging are investigated in the near field of a driven axisymmetric jet. Acoustic forcing is used to obtain repeatable vortex pairing events, and simultaneous passive scalar and cold-chemistry planar laser-induced flourescence are used to obtain instantaneous images of molecularly mixed jet fluid fraction. The time-varying scalar dissipation field and area-averaged stirredness of the vortex core region are measured at various stages of vortex interaction. These mixing properties are analyzed in conjunction with the observed vortex dynamics, such as the time-dependent vortex convection velocity. The results indicate that there are several phases of the pairing event with distinct mixing characteristics, including vortex roll-up, interaction, coalescence, and reentrainment. Vortex roll-up is nearly laminar with molecular diffusion between the layers of jet and co-flow fluid. The most dramatic change in the mixing state of the leading vortex, which includes the appearance of a uniformly mixed core region, occurs as the trailing vortex approaches and interferes with co-flow fluid entrainment. Vortex coalescence is marked by gross deformation and stretching of the trailing vortex, and rapid homogenization of the diffusion layers. Finally, re-entrainment of pure fluid after the pairing event results in an elongated, nonrotating structure. These stages of vortex pairing correspond to the temporal evolution of vorticity observed in previous studies.

Resonant absorption at the vortex-core states ind-wave superconductors

We predict a resonant microwave absorption on collective vortex modes in a superclean $d$-wave superconductor at low temperatures. Energies of the collective modes are multiples of the distance between the exact quantum levels of bound states in the vortex core at lower temperatures and involve delocalized states for higher temperatures. The characteristic resonant frequency is larger than the cyclotron frequency ${\ensuremath{\omega}}_{c}$ but lower than the Caroli-de Gennes-Matricon minigap ${\ensuremath{\Delta}}^{2}{/E}_{F};$ it has a $\sqrt{H}$ dependence on the magnetic field and decreases down to ${\ensuremath{\omega}}_{c}$ with increasing temperature. We calculate the vortex mass as a response to a slow acceleration. This mass is equal to the mass of electrons inside the vortex core region with the area of the order of ${\ensuremath{\xi}}^{2}\sqrt{{H}_{c2}/H}$; it increases with temperature and diverges for $\stackrel{\ensuremath{\rightarrow}}{H}0$. We discuss the universal flux-flow regime predicted by Kopnin and Volovik [Phys. Rev. Lett. 79, 1377 (1997)] and show that it exists in a broader temperature range than has been originally found.

Prediction of Viscous Trailing Vortex Structure from Basic Loading Parameters

An analytical method has been developed to predict the structure of a fully developed trailing vortex with a viscous core. Vortex structure is calculated from the load distribution on the generating wing and fundamental conservation laws are satisfied. The present rollup model implicitly addresses viscous effects in the vortex core region by assuming a turbulent mixing process in the core during formation. Mixing theory suggests the appropriate functional form of the solution velocity profiles within this region, with constants that are determined uniquely by the method for arbitrary wing loading distributions. Important structural properties such as vortex strength, core size, and peak swirl velocity are calculated directly from these solution constants. The viscous core model was validated against two recent experimental studies, which provided new insight into vortex growth