Dynamics of vorticity at a sphere

The article discusses the two-dimensional flow of an incompressible liquid between two infinitely close concentric spheres, due to an initial distribution of the vorticity differing from zero. The concept of point singularities (vortices, sources, and sinks) at a sphere is introduced. Equations of motion are obtained for point vortices, as well as invariants of the motion, known for the plane case [1]. The simplest case of the mutual motion of a pair of vortices is considered. Equations are obtained for the motion of point vortices at a rotating sphere. Integral invariants for the continuous distribution of the vorticity are obtained, having the dynamic sense of the total kinetic energy and the momentum of the liquid at the sphere. The effect of the topology of the sphere on the dynamics of the vorticity is noted, and a comparison is made with the plane case.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 57–65, November–December, 1977.     

旋转浅水系统Rossby孤立涡旋的实验研究

我们建立了具有自由表面的旋转抛物面浅水系统，进行空间流体图样演化的实验研究。利用流动显示和激光散射技术获得相干涡旋的信息。实验结果表明，在纬带区内存在强剪切可能导致形成持续存在的相干涡旋链。在旋转随动坐标系中拍摄的照片以及自相关分析证明，确有大尺度的Ｒｏｓｓｂｙ孤立涡旋的发生、漂移和演化。     

PIV analysis of flow around a container ship model with a rotating propeller

The flow characteristics of the propeller wake behind a container ship model with a rotating propeller were investigated using a two-frame PIV (Particle Image Velocimetry) technique. Ensemble-averaged mean velocity fields were measured at four different blade phases and ensemble-averaged to investigate the flow structure in the near-wake region. The mean velocity fields in longitudinal planes show that a velocity deficit is formed in the regions near the blade tips and hub. As the flow develops in the downstream direction, the trailing vortices formed behind the propeller hub move upward slightly due to the presence of the hull wake and free surface. Interaction between the bilge vortices and the incoming flow around the hull causes the flow structure to be asymmetric. Contour plots of the vorticity give information on the radial distribution of the loading on the blades. The radial velocity profiles fluctuate to a greater extent under the heavy (J=0.59) and light loading (J=0.88) conditions than under the design loading condition (J=0.72). The turbulence intensity has large values around the tip and trailing vortices. As the wake develops in the downstream direction, the strength of the vorticity diminishes and the turbulence intensity increases due to turbulent diffusion and active mixing between the tip vortices and the adjacent wake flow.     

Topography effects on vortices in a rotating fluid

This paper reviews some aspects of topography effects on the dynamics of barotropic monopolar, dipolar and tripolar vortices in a rotating fluid. It is shown that the modulated point-vortex model (essentially based on conservation of potential vorticity) is capable of describing the flow evolution correctly, as can be concluded from comparisons with numerical simulations and laboratory observations.

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Sommario In questo articolo sono passati in rassegna alcuni aspetti degli effetti topografici nella dinamica dei vortici barotropici, monopolari, dipolari e tripolari in un fluido rotante. Si osserva che il modello di vortice puntiforme modulato (essenzialmente basato sulla conservazione della vorticità potenziale) è capace di descrivere correttamente l'evoluzione del flusso, come si può concludere dal paragone con simulazioni numeriche ed osservazioni di laboratorio.

     

Magnetic effect on the formation of longitudinal vortices in a rotating laminar boundary layer

This paper presents a numerical study of magnetic effect on the formation of longitudinal vortices in a rotating laminar boundary layer. The criterion for the position marking the onset of longitudinal vortices is defined in this paper. The onset position characterized by the rotational Goertler number G_δ,rot, depends on the local rotation number, Reynolds number, the magnetic field parameter, the Prandtl number and the wave number. The results show that positive rotation destabilizes the flow. The flow is found to become more unstable to the vortex mode of instability as the value of magnetic field parameter M increases. The numerical data shows good agreement with the experimental results. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical analysis of the rotating viscous flow approaching a solid sphere

A numerical simulation is performed to investigate the flow induced by a sphere moving along the axis of a rotating cylindrical container filled with the viscous fluid. Three‐dimensional incompressible Navier–Stokes equations are solved using a finite element method. The objective of this study is to examine the feature of waves generated by the Coriolis force at moderate Rossby numbers and that to what extent the Taylor–Proudman theorem is valid for the viscous rotating flow at small Rossby number and large Reynolds number. Calculations have been undertaken at the Rossby numbers (R_o) of 1 and 0.02 and the Reynolds numbers (R_e) of 200 and 500. When R_o=O(1), inertia waves are exhibited in the rotating flow past a sphere. The effects of the Reynolds number and the ratio of the radius of the sphere and that of the rotating cylinder on the flow structure are examined. When R_o ? 1, as predicted by the Taylor–Proudman theorem for inviscid flow, the so‐called ‘Taylor column’ is also generated in the viscous fluid flow after an evolutionary course of vortical flow structures. The initial evolution and final formation of the ‘Taylor column’ are exhibited. According to the present calculation, it has been verified that major theoretical statement about the rotating flow of the inviscid fluid may still approximately predict the rotating flow structure of the viscous fluid in a certain regime of the Reynolds number. Copyright © 2004 John Wiley & Sons, Ltd.     

Vortex shedding from a circular cylinder with a slit and concave rear surface

Vortex shedding from short circular cylinders with a slit was studied using a flow visualization and amplitude spectrum analysis of a thermoanemometry probe signal. It was found that a circular cylinder with a slit and concave rear surface produces stronger vortices than other bluff cylinders but that these vortices are very vulnerable to the end wall conditions. It was established that two small splitter plates (tails) fixed directly behind the cylinder at the end walls effectively isolate the vortices shed from the cylinder from the end wall boundary layer effects. For this arrangement a perfect regularity of vortex shedding and almost constant Strouhal number were achieved in the Reynolds number test range of about 250 to 43,000.On a leave from Technical University, 60965 Poznan, Piotrowo 3, Poland.     

Vortex-speed selection within the boundary-layer flow over a rotating sphere placed in an enforced axial flow

This paper furthers existing work into the instability mechanisms within the boundary-layer flow over a rotating sphere through the study of amplification rates within the convectively-unstable region. The onset of convective instability is associated with the experimentally observed onset of spiral vortices reported in the literature. Axial flow is found to stabilize the boundary layer by both delaying the onset of convective instability at all latitudes and also by significantly reducing the spatial amplification rates. We find that the type II (streamline curvature) mode becomes increasingly amplified with respect to the type I (crossflow) mode and is therefore likely to be selected in practice for sufficiently high axial flow rates. Furthermore, in experiments where special care is taken to remove all surface roughness, we predict that vortices will rotate at around 75% of the local surface speed. This is consistent with the experimental observations of Kobayashi & Arai who note a speed of around 76% under particular experimental conditions. These predictions are entirely consistent with related work on the rotating-disk and cone boundary layers.     

Vortex stretching and filaments

This paper presents a new technique to produce controlled stretched vortices. Intense elliptical vortices are created by stretching of an initial vorticity sheet. The initial vorticity comes from a laminar boundary layer flow and the stretching is parallel to the vorticity vectors. This low velocity flow enables direct observation of the formation and destabilization of vortices. Visualizations are combined with quasi-instantaneous measurements of a full velocity profile. The velocity profile is obtained with an ultrasonic pulsed Doppler velocimeter. The evolution of the central diameter of the vortices is related to the stretching. It is observed that destabilization occurs by pairing of two vortices, by hairpin deformation, and by breakdown of vortices into a “coil shape”.     

不定原点喷嘴射流中流体物理的实验研究

为了能够更好地了解不定源喷嘴（indeterminate origin nozzle）射流中的物理过程，本文应用平面激光诱导荧光技术对一个大尺度的水射流进行了实验研究。流场显示的实验结果表明不定源喷嘴在射流的剪切层引入了蘑菇形反向旋转的涡对。这些涡的矢量方向与射流方向相同或相反，被称为流向涡（streamwise vortex）。由于射流中存在开尔文一亥姆霍兹不稳定，每当一个横向涡（spanwisevortex，即涡的矢量方向与射流方向垂直）从喷嘴脱流时会产生瞬时的低压，该瞬时低压促使向内发展的流向涡对在喷嘴的凹槽处生成。这些涡对在向下游流动的过程中会重组并在喷嘴的尖峰面生成向外发展的涡对。这些流向涡极大地影响了射流的发展。流向涡与横向涡的相互作用促使射流更早地发展成为湍流。由于流向涡同时也在射流中引入了径向的剪切流动，因此导致了更多的湍流生成从而增强了射流与周围流体的混合。     

不定原点喷嘴射流中流体物理的实验研究(英文)

为了能够更好地了解不定源喷嘴(indeterminate origin nozzle)射流中的物理过程,本文应用平面激光诱导荧光技术对一个大尺度的水射流进行了实验研究。流场显示的实验结果表明不定源喷嘴在射流的剪切层引入了蘑菇形反向旋转的涡对。这些涡的矢量方向与射流方向相同或相反,被称为流向涡(streamwise vortex)。由于射流中存在开尔文-亥姆霍兹不稳定,每当一个横向涡(spanwise vortex,即涡的矢量方向与射流方向垂直)从喷嘴脱流时会产生瞬时的低压,该瞬时低压促使向内发展的流向涡对在喷嘴的凹槽处生成。这些涡对在向下游流动的过程中会重组并在喷嘴的尖峰面生成向外发展的涡对。这些流向涡极大地影响了射流的发展。流向涡与横向涡的相互作用促使射流更早地发展成为湍流。由于流向涡同时也在射流中引入了径向的剪切流动,因此导致了更多的湍流生成从而增强了射流与周围流体的混合。     

Effects of a bent structure on the linear viscoelastic response of diluted carbon nanotube suspensions

Commonly isolated carbon nanotubes in suspension have been modelled as a perfectly straight structure. Nevertheless, single-wall carbon nanotubes (SWNTs) contain naturally side-wall defects and, in consequence, natural bent configurations. Hence, a semi-flexile filament model with a natural bent configuration was proposed to represent physically the SWNT structure. This continuous model was discretized as a non-freely jointed multi-bead–rod system with a natural bent configuration. Using a Brownian dynamics algorithm the dynamical mechanical contribution to the linear viscoelastic response of naturally bent SWNTs in dilute suspension was simulated. The dynamics of such system shows the apparition of new relaxation processes at intermediate frequencies characterized mainly by the activation of a mild elasticity. Storage modulus evolution at those intermediate frequencies strongly depends on the flexibility of the system, given by the rigidity constant of the bending potential and the number of constitutive rods.     

On the beltram I flows

To illustrate the general properties of the Beltrami flows, a new sufficient and necessary condition of the general solution of the Beltrami flows has been given, on whose basis some sufficient and necessary conditions and sufficient conditions in literature are unified. The advantages of the new expressions are that one may get solutions of Beltrami flows with constant proportional factors which satisfy some given asymptotic decaying conditions at infinity. Finally, we find a class of spherical vortices of Beltrami flows, where the motion trajectories of the fluid particles are confined within a sphere or two adjacent concentric spherical shells. We find that the superpositions of the spherical vortices of the same order with different polar axes may produce chaotic trajectories. The project is supported by the National Foundamental Research Programme of State Commission of Sciences and Technology.     

Evolution of Concentrated Vortices in a Viscous Fluid

Evolution of the vortices of monopole and dipole types in a viscous fluid is considered numerically. Theory and numerical results are compared for some particular exact solutions. A good agreement is obtained for the dipole vortices (viscous Chaplygin-Lamb vortices) moving with variable velocities due to viscosity. For the monopole type vortices, the agreement is more or less good only at an initial stage of their evolution; while in the long-lime asymptotics the law of vorticity decay other than the theoretical one is discovered. The reason for such a discrepancy is discussed. The interactions of dipole vortices with each other and with rigid boundaries are studied too. The stability of dipole vortices with complex internal structures is considered briefly.     

Direct numerical simulation of particle transport by hairpin vortices in a laminar boundary layer

The transport of solid particles by coherent wall structures is studied here. This phenomenon is present in numerous environmental and engineering flows. The flow above a wall-mounted hemisphere is used for generating hairpin vortices in a laminar boundary layer in a controlled way. By means of direct numerical simulation (DNS) of the fluid flow and simultaneous Lagrangian tracking of particles, the influence of hairpin vortices on solid particles released in the wake of the obstacle is analyzed.     

旋涡与行进表面水波相互作用的实验研究

采用振动板式造波器在二维水槽中生成近似单色的行进表面水波，采用夹板式涡发生器生成稳定上浮的涡对，在Ｆｒｏｕｄｅ数约为０．５的条件下，得到了水下涡对与不同波长和振幅的行进表面水波相互作用时的干扰图象，以实验方法验证了理论分析和数值计算的结果，并为进一步研究旋涡与行进表面水波的相互作用提供了一种实验研究方法     

DNS OF 2D TURBULENT FLOW AROUND A SQUARE CYLINDER

Two-dimensional ‘turbulent’ flow around a rectangular cylinder has been simulated at Re=10,000 using a sixth- order-accurate finite volume method for the discretization of convection and diffusion. The spatial discretization consists of a combination of a seventh- order upwind-biased method for the convective terms and an eighth-order central method for the diffusive terms, discretized on a stretched and staggered grid. To cope with the stretching of the grid, Lagrange interpolations are used. The method applied to obtain a boundary condition for the velocity in the x-direction at the outflow boundary is shown not to affect the flow in the interior of the computational domain in a way that is visible in various snapshots of the vorticity field. The variation in the velocity in the x-direction with time is itself found to be relatively small near the outflow boundary. Several turbulence statistics have been gathered from a simulation of the flow developed during 77 dimensionless time units. Snapshots of the vorticity field of the developed flow show the presence of a vortex-street- like structure. Typical 2D turbulent behaviour, such as the appearance of monopolar, dipolar and tripolar vortices due to the amalgamation of vorticity in the wake and the x^−1/2 scaling of the velocity defect in the wake, has been obtained. © 1997 John Wiley & Sons, Ltd.     

Shapes of a rotating rheonomic rod

The case of a rotating fluid mass is one of the classical fields of mechanics [1]. In particular, the solution of creep problems for a rotating mass is actual in geophysics in connection with Earth gravity force simulation on rotating samples under laboratory conditions [2]. A special case of a rheonomic rod in a potential field was studied in [3], where it was shown that the main problem about the rod shapes is the problem of determining the relations between the Lagrangian and Euler coordinates in the creep process.In what follows, we show how this problem can be solved for a rotating rod.     

Population,characteristics and kinematics of vortices in a confined rectangular jet with a co-flow

Vortex behavior and characteristics in a confined rectangular jet with a co-flow were examined using vortex swirling strength as a defining characteristic. On the left side of the jet, the positively (counterclockwise) rotating vortices are dominant, while negatively rotating vortices are dominant on the right side of the jet. The characteristics of vortices, such as population density, average size and strength, and deviation velocity, were calculated and analyzed in both the cross-stream direction and the streamwise direction. In the near-field of the jet, the population density, average size and strength of the dominant direction vortices show high values on both sides of the center stream with a small number of counter-rotating vortices produced in the small wake regions close to jet outlet. As the flow develops, the wake regions disappear, these count-rotating vortices also disappear, and the population of the dominant direction vortices increase and spread in the jet. The mean size and strength of the vortices decrease monotonically with streamwise coordinate. The signs of vortex deviation velocity indicate the vortices transfer low momentum to high-velocity region and high momentum to the low velocity region. The developing trends of these characteristics were also identified by tracing vortices using time-resolved particle image velocimetry data. Both the mean tracked vortex strength and size decrease with increasing downstream distance overall. At the locations of the left peak of turbulent kinetic energy, the two-point spatial cross-correlation of swirling strength with velocity fluctuation and concentration fluctuation were calculated. All the correlation fields contain one positively correlated region and one negatively correlated region although the orientations of the correlation fields varied, due to the flow transitioning from wake, to jet, to channel flow. Finally, linear stochastic estimation was used to calculate conditional structures. The large-scale structures in the velocity field revealed by linear stochastic estimation are spindle-shaped with a titling stream-wise major axis.