Total Number Of Vortices Research Articles

РАСПРОСТРАНЕНИЕ ПРОБНЫХ ИМПУЛЬСОВ ВТОРОГО ЗВУКА В СРЕДЕ С КВАНТОВОЙ ТУРБУЛЕНТНОСТЬЮ В СВЕРХТЕКУЧЕМ ГЕЛИИ

Experimental investigation of the propagation of single probe pulses of a second sound in superfluid helium in a long capillary with a developed vortex system formed by a constant thermal flow was done. The processes of formation and decay of the vortex system and the effect of the capillary length (the total number of vortices in the volume) on the attenuation of probe pulses were studied.

The global vortex analysis of Jupiter and Saturn based on Cassini Imaging Science Subsystem

Presented in this manuscript are observations exploring vortices with diameters larger than 1000km on Jupiter and Saturn. These images are taken from the Imaging Science Subsystem onboard the Cassini Spacecraft. The analyses of Saturn’s vortices show that there are significantly more vortices in the Southern Hemisphere (SH) than in the Northern Hemisphere (NH) during the time from 2004 to 2010. In particular, the concentration of vortices are completely different between the two hemispheres, especially in the latitude band around 40°N where the 2010 giant storm occurred. In the SH, the latitude band around 40°S has the highest concentration of vortices on Saturn. Contrasting results show that vortices are lacking in the latitudinal band around 40°N in the NH before the eruption of the 2010 giant storm, although zonal wind characteristics are similar at both locations. Global maps of Saturn at different times suggest that the total numbers of large vortices dramatically decreased from 29±1 to 11±2 in the SH and from 11±2 to 7±1 in the NH during this time period (2004–2010), just before the eruption of the giant storm at the end of 2010. The goal here is to present observational trends and evaluate if the temporal variation in the total number of vortices is related to the eruption of the 2010 giant storm. The comparison of jovian and saturnian vortices shows that the contrast of the two hemispheres is different between the two giant planets, likely due to the different obliquities, hence different seasonal cycles on the two planets. Jovian vortices tend to display a near equal distribution of vortices across hemispheres, while saturnian vortices are distributed unevenly. The comparison also reveals that on both planets, there is a correlation between the highest number of vortices and the westward jet peaks. This suggests that atmospheric instabilities play a critical role in generating vortices on both planets.

Taylor vortices in the flow between two coaxial cylinders one of which has a step change in radius

A numerical study of the flow between two coaxial cylinders, where one of the cylinders has a step change in radius, is carried out. The inner cylinder rotates and the outer cylinder is stationary. Computation is restricted to axisymmetric motion since instability in flow between coaxial cylinders is found to first occur in the form of axisymmetric Taylor vortices. In the presence of a step, Taylor vortices are found to appear first in the region where the gap between the cylinders is larger and approximately when the local Taylor number in this region reaches the critical Taylor number for onset of instability. Subsequently, Taylor vortices appear in the region where the gap is narrower, and when the local Taylor number in that region exceeds the critical Taylor number. The Taylor vortices have inward flow at a stationary end plate, and outward flow at an end plate which rotates with the same angular velocity as the inner cylinder. Similar results were obtained by Sprague et al (2008 Phys. Fluids 20 014102) for a step on inner cylinder configuration. The step functions as another end plate, if the step size is large. Whereas, it has no effect, if the step size is small. In most situations, these determine whether the number of Taylor vortices in the wide and narrow gap regions is even or odd. When the end plates rotate synchronously, but at a different speed from the inner cylinder, a change from even to odd or odd to even number of vortices in each region occurs at certain rotation rates of the end plates by sudden appearance or disappearance of a vortex at the end of the column. For a certain range of rotation rates of the end plates, the total number of vortices in the entire fluid column is odd, although the end conditions are symmetrical.

Influence of the least-squares phase on optical vortices in strongly scintillated beams

The optical vortices that exist in strongly scintillated beams make it difficult for conventional adaptive optics systems to remove the phase distortions. When the least-squares reconstructed phase is removed, the vortices still remain. However, we found that the removal of the least-squares phase induces a portion of the vortices to be annihilated during subsequent propagation, causing a reduction in the total number of vortices. This can be understood in terms of the restoration of equilibrium between explicit vortices, which are visible in the phase function, and vortex bound states, which are somehow encoded in the continuous phase fluctuations. Numerical simulations are provided to show that the total number of optical vortices in a strongly scintillated beam can be reduced significantly after a few steps of least-squares phase corrections.

Experimental and Theoretical Study on Rolling Effectiveness of Multiple Control Surfaces

It is well known that the effectiveness of a trailing-edge control surface can be substantially diminished due to the elastic twist of an airfoil or rolling wing. This aeroelastic phenomenon is known as control surface reversal when the lift or rolling rate vanishes at a sufe ciently large ratio of e ow dynamic pressure to airfoil or wing stiffness. However, a leading-edge control surface can be used to counteract control surface reversal, and, indeed, in principle, a leading-edge control surface can entirely cancel the tendency of the trailing-edge control surface to undergo reversal. Moreover, analysis shows that by using a simple adaptive control strategy, one can use a combination positive and negative control surface rotations to maximize lift and rolling effectiveness or minimize control surface rotations. In the present work, a theoretical ‐experimental study of the effectiveness of trailingand leading-edge control surfaces has been made for a rolling wing ‐fuselage model. An experimental model and wind-tunnel test are used to assess the theoretical results. The theoretical model includes the inherently nonlinear dry friction damping moment between the spindle support and the experimental aeroelastic wing model for the rollingdegreeoffreedom.Athree-dimensionalvortexlatticeaerodynamictheoryisemployed.Newinsightsintothe behavior and design of an adaptiveaeroelastic wing using trailing- and leading-edge control surfacesare provided. Nomenclature c = wing chord length K® = torsional stiffness km, kn = numbers of vortex elements on the wing in x and y directions, respectively kmm = total number of vortices on both the wing and wake in the x direction L = total lift on the wing Llocal = local lift along the span

Homogenization of harmonic maps with large number of vortices and applications in superconductivity and superfluidity

We study a nonlinear homogenization problem of harmonic maps which describes an ideal superconducting or an ideal superfluid medium with a large number of vortices and the degree conditions prescribed at the external insulating boundary. We derive the homogenized problem which describes the limiting behavior of the fluxes when the total number of vortices tends to infinity. The homogenized problem is described in terms of the effective vorticity and the effective anisotropy tensor. The calculation of this tensor amounts to solving a linear cell problem, which is well studied in the homogenization literature and can be solved by using existing numerical packages. The convergence of the fluxes is rigorously proved. We also discuss unusual features of the homogenized limit for the wave functions. The proofs are based on a variational approach which does not require periodicity and can be used in more general situations.

On vortex phase of systems with pairing of spatially separated electrons and holes

The possibility of the emergence of a macroscopic amount of planar vortices with identical circulation in systems with pairing of spatially separated electrons and holes was predicted by us recently [S. I. Shevchenko, Phys. Rev. B56, 10355 (1997); ibid. B57, 14809 (1998)]. In the present work, we consider a structure formed by planar vortices in a disk-shaped sample in a magnetic field whose two-dimensional divergence differs from zero. The total number of vortices and the energy of a system of vortices are determined as functions of the external magnetic field and the sample size. It is found that the energy of the vortex structure is proportional to the volume of the system, and hence a vortex state is a new thermodynamic phase of the investigated system (analogous to the Shubnikov phase in conventional superconductors).

Kinetic equation for point vortices in a shear flow

The kinetic equation for a set of Stewart point vortices moving on the background of a shear flow with uniform vorticity is derived. Besides the total number of vortices with certain amplitude values, this equation provides conservation of the total vorticity of vortex gas on each shear flow stream line. Such conservation laws prevent, in the general case, relaxation of the system to the Maxwell equilibrium distribution of vortices. In fact, the system is shown to tend to an equilibrium state, in which vortex gas vorticity on each stream line of shear flow is formed by vortices with equal amplitude signs, only the most intense vortices being concentrated in more exited regions, while less intensive vortices are concentrated at the periphery of perturbed domains. Applicability of the kinetic equation obtained for the description of Helmholtz vortices sets is discussed.

Zonal vortex method and impulsively started flow around a circular cylinder

IN this paper, a zonal vortex method and its application to simulating the impulsively started flow of a circular cylinder are presented. This method treats the attached viscous flow region and the separated flow region separately. The attached flow region is computed through solving boundarylayer equations by the finite-difference method. Only the separated flow is computed through solving Navier-Stokes equations by the vortex method. Since the separated flow region has a length scale of 0(1), in the vortex method used for this region, the number of new vortices introduced at the surface of the body per time step is relatively insensitive to the Reynolds number of the flow. For simulation of highReynolds-number flows with massive separation, the total number of vortices in the flowfield, hence the computer storage and computer time, is greatly reduced. Contents The impulsively started flow around a circular cylinder is complex and all of the phenomena of fluid mechanics are presented. Because of its fundamental importance, this flow has become a typical problem in the study of separated flows. Bouard and Coutanceau1 have done careful experimental studies on this problem and provided valuable data for comparison with numerical solutions. Smith and Stansby2 have recently calculated this flow using a vortex method. In this method, the vorticity equation is solved using random walk for diffusion and the vortex-in-cell method for convection in a time-stepping procedure. Vortices are introduced at the surface at each time step to satisfy the no-slip condition. Their calculations revealed detailed flow features of the wake and were in good agreement with experimental observations in Ref. 1. Their numerical experiment showed that accurate simulation requires the introduction of a sufficiently large number of vortices at the surface per time step. This number increases as the Reynolds number increases. Therefore, for simulation of a high-Reynolds-number flow by the vortex method, the total number of vortices in the flow may become very large as time increases, requiring large computer storage and computer time. In this paper, the vortex method is improved by a zonal approach. For a high-Reynolds- number flow with massive separation, the vorticity in the upstream of the separation point is confined in a layer near the surface of the body. The length scale of the thickness of this layer is 0(Re~l/2). The length scale of the separated flow region is 0(1). It is difficult to accommodate these two scales when solving the NavierStokes equations in the whole flow region. The approach of

Computation of wind tunnel wall effects in ducted rotor experiments

Ducted propellers and turbines operating in a square closed wind tunnel test section are analyzed. A multiple image method is used to account for tunnel wall interference effects and a detailed method of singularities model is used for the ducted rotor. The size of the rotor wake is computed, taking into account the tunnel walls. Several ducted rotor model/wind tunnel dimension ratios are examined, ranging between 0.02 and 0.50. In addition, ducted rotor disk loading coefficients, CT , between - 30 and 0.89 are considered (the negative values correspond to the rotor acting as a propeller; the positive values indicate that the rotor is a turbine). Values of ideal propeller thrust are reduced by over 30% at the highest value of propeller disk loading (CT = — 30). The tunnel wall effect for a ducted turbine is less than for a ducted propeller and is opposite in direction. For the nearoptimum condition CT. =0.89, the ideal turbine power is increased by about 8% for the largest model/tunnel ratio considered. Nomenclature CP. = ideal thrust power coefficient for DAP (diffuseraugmented propeller) or ideal power coefficient for DAWT (diffuser-augmented wind turbine) CT() = disk loading coefficient based on freestream dynamic head D = dimension of wind tunnel test section E = complete elliptic integral, Eq. (5) K = complete elliptic integral, Eq. (4) kn = function of ring vortex coordinates and field point coordinates, Eq. (3) TV = the number of images along the side of a square image array q = velocity in r direction r = radial coordinate rp = ideal power augmentation ratio R = diffuser radius at a particular value of z S = the number of vortex rings used to represent the diffuser surface T = total number of vortices used to represent both the diffuser and the wake u = velocity in x direction U0 = freestream velocity, dimensional v = velocity in y direction w = velocity in z direction (axial direction) x = lateral coordinate in plane perpendicular to mean flow y = vertical coordinate in plane perpendicular to mean