Vortices and wall shear stresses in asymmetric and symmetric channels with sinusoidal wavy walls for pulsatile flow at low Reynolds numbers

Numerical simulation and flow visualization were performed to study the dynamical behavior of vortices generated in channels with two different geometries, i.e., a periodically converging–diverging channel and serpentine channel, both having sinusoidal wavy walls. This system for pulsatile flow is used to enhance heat and mass transfer in very viscous liquids. The numerical results predict well the dynamical behavior of vortices and agree with the flow visualizations. For both channels, the vortex expands in each furrow of the channel walls during the deceleration phase and shrinks during the acceleration phase, which leads to fluid exchange between the vortex and the mainstream. The time-averaged vortex strength and wall shear stresses increase, as the frequency of fluid oscillation increases under a fixed oscillatory fraction of the flow rate. However, above a certain value of the frequency, they reversely decrease due to viscous effects. This frequency for the serpentine channel is smaller than that for the converging–diverging channel. The channel geometries are found to have an important effect of the flow characteristics.     

The asymmetric Ekman decay of cyclonic and anticyclonic vortices

Recent studies have shown differences in the behaviour of cyclonic and anticyclonic quasi-two-dimensional vortices in laboratory experiments in a rotating fluid. In this paper, the role of dissipative effects due to bottom topography is investigated as a possible cause for the asymmetry in the spin-down of both types of vortices. The basic mechanism of Ekman friction in 2D mathematical models is the presence of a linear damping term in the vorticity equation, which produces the flow decay. Here, an extended 2D formulation including nonlinear Ekman corrections is considered. The aim is to show that nonlinear Ekman effects are responsible for the different decay of cyclonic and anticyclonic vortices, while the conventional formulation (only containing the linear friction term) predicts a symmetric decay for both cases.In order to illustrate the role of nonlinear Ekman effects, axisymmetric vortices are simulated numerically. The relatively simple structure of such vortices allows a better understanding of their evolution. The main difference in the spin-down process of cyclones and anticyclones is the decay rate, which is faster for cyclonic motion. Furthermore, it is shown that the basic mechanism for such a difference is the outward advection of fluid in cyclones and inward in anticyclones, both effects due to Ekman pumping and suction, respectively. The results derived here intend to provide a physical interpretation which could be applied for more general, non-axisymmetric structures.     

Order in chaotic pseudoplastic flow between coaxial cylinders

Order is found within the chaotic nonlinear flow between rotating coaxial cylinders. The flow stability analysis is carried out for a pseudoplastic fluid through bifurcation diagram and Lyapunov exponent histogram. The fluid is assumed to follow the Carreau–Bird model, and mixed boundary conditions are imposed. The low-order dynamical system, resulted from Galerkin projection of the conservation of mass and momentum equations, includes additional nonlinear terms in the velocity components originated from the shear-dependent viscosity. It is observed that the base flow loses its radial flow stability to the vortex structure at a lower critical Taylor number, as the shear-thinning effects increase. The emergence of the vortices corresponds to the onset of a supercritical bifurcation, which is also seen in the flow of a linear fluid. However, unlike the Newtonian case, shear-thinning Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Complete flow field together with viscosity maps are given for different scenarios in the bifurcation diagram.     

旋涡、湍流与自由表面的相互作用

旋涡及自由表面湍流与自由表面的非定常、非线性相互作用是当前流体力学中一个十分活跃的前沿领域的研究课题,它具有深刻的理论意义和重要的实用背景．旋涡、湍流与自由表面的相互作用是一个非常复杂的非线性、非定常过程,涉及到涡－涡、波－涡相互作用,旋涡在自由表面处的断裂、重联、合并及自由表面湍流中的准拟序结构的形成、发展等复杂动力学过程．关于这一领域的研究已经取得了一些重要成果．对旋涡与自由表面的相互作用的基本过程有了较为清楚的认识;但对湍流与自由表面的相互作用中的许多基本物理过程还知之甚少．本文综述此领域的实验、理论和数值模拟研究的最新进展和主要结果,讨论若干有待解决的问题,并指出进一步的研究方向      

Vortex structures in geophysical convection

An intriguing variety of vortex structures arise during buoyant convection, especially in the presence of background stratification and rotation. These vortices play an important role in environmental fluid motions, bearing upon small-scale turbulence to planetary-scale circulation. A brief review of vortex motions associated with buoyant convection is presented in this paper, emphasizing the sources of vorticity, evolution of vortex structures and their role in oceanic and atmospheric dynamics. The genesis of a variety of vortices, for example, mushroom vortices, geostrophic and ageostrophic vortices, dipolar structures and hetons in buoyant convection flows is described, and parameterizations to represent their properties are discussed. New laboratory and numerical simulation results on vortex-related phenomena in stratified and rotating fluids and their implications in geophysical convective flows are also presented.     

Flow pattern and stability of pseudoplastic axial Taylor–Couette flow

The effect of an axial flow on the stability of the Taylor–Couette flow is explored for pseudoplastic fluids. The fluid is assumed to follow the Carreau–Bird model and mixed boundary conditions are imposed while the axial flow can be independent of rotational flow. The four-dimensional low-order dynamical system, resulted from Galerkin projection of the conservation of mass and momentum equations, includes additional non-linear terms in the velocity components originated from the shear-dependent viscosity. In absence of axial flow the base flow loses its radial flow stability to the vortex structure at a lower critical Taylor number, as the pseudoplasticity effects increases. The emergence of the vortices corresponds to the onset of a supercritical bifurcation which is also seen in the flow of a linear fluid. However, unlike the Newtonian case, pseudoplastic Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Existence of an axial flow, induced by a pressure gradient appears to further advance each critical point on the bifurcation diagram. Complete flow field together with viscosity maps are given for stability regions in the bifurcation diagram.     

New insights into astrophysical jets with the atacama large millimeter array and the Karl G. Jansky very large array

Observations using the Atacama Large Millimeter Array (ALMA) and the Karl G. Jansky Very Large Array (VLA) will address gaps in our understanding of astrophysical disks, jets and outflows from young stellar objects, evolved stars and black holes. ALMA & the VLA will achieve high resolution to map small-scale structure in jets and accretion disks allowing us to explore how material is lifted off the disk and collimated into ionized jets. ALMA will also recover even the most extended emission in large-scale out-flowing molecular material, allowing a detailed study of hydrodynamic mixing and dust formation. This paper highlights those features of the ALMA & VLA telescopes that will contribute to our understanding of astrophysical jets and disks and presents new observations that demonstrate the power of these instruments.     

Irradiated interfaces in the Ara OB1, Carina,Eagle Nebula,and Cyg OB2 massive star formation regions

Regions of massive star formation offer some of the best and most easily-observed examples of radiation hydrodynamics. Boundaries where fully-ionized H II regions transition to neutral/molecular photodissociation regions (PDRs) are of particular interest because marked temperature and density contrasts across the boundaries lead to evaporative flows and fluid dynamical instabilities that can evolve into spectacular pillar-like structures. When detached from their parent clouds, pillars become ionized globules that often harbor one or more young stars. H₂ molecules at the interface between a PDR and an H II region absorb ultraviolet light from massive stars, and the resulting fluoresced infrared emission lines are an ideal way to trace this boundary independent of obscuring dust. This paper presents H₂ images of four regions of massive star formation that illustrate different types of PDR boundaries. The Ara OB1 star formation region contains a striking long wall that has several wavy structures which are present in H₂, but the emission is not particularly bright because the ambient UV fluxes are relatively low. In contrast, the Carina star formation region shows strong H₂ fluorescence both along curved walls and at the edges of spectacular pillars that in some cases have become detached from their parent clouds. The less-spectacular but more well-known Eagle Nebula has two regions that have strong fluorescence in addition to its pillars. While somewhat older than the other regions, Cyg OB2 has the highest number of massive stars of the regions surveyed and contains many isolated, fluoresced globules that have head–tail morphologies which point towards the sources of ionizing radiation. These images provide a collection of potential astrophysical analogs that may relate to ablated interfaces observed in laser experiments of radiation hydrodynamics.     

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.     

The N-vortex problem on a sphere: geophysical mechanisms that break integrability

We describe the dynamical system governing the evolution of a system of point vortices on a rotating spherical shell, highlighting features which break what would otherwise be an integrable problem. The importance of the misalignment of the center-of-vorticity vector associated with a cluster of point vortices with the axis of rotation is emphasized as a crucial factor in the interpretation of dynamical features for many flow configurations. We then describe two important physical mechanisms which break what would otherwise be an integrable problem—the interactions between the local center-of-vorticity vectors of more than one region of concentrated vorticity, and the coupling between the center-of-vorticity vector and the background vorticity field which supports Rossby waves. Focusing on the Polar vortex splitting event of September 2002, we describe simple (i.e., low dimensional) mechanisms that can trigger instabilities whose subsequent development cause the onset of chaotic advection and global particle transport. At the linear level, eigenvalues that oscillate between elliptic and hyperbolic configurations initiate the pinch-off process of a passive patch representing the Polar vortex. At the nonlinear level, the evolution and topological bifurcations of the streamline patterns are responsible for its further splitting, stretching, and subsequent transport over the sphere. We finish by briefly describing how to incorporate conservation of potential vorticity and the development of a model governing the probability density function associated with the point vortex system.     

Optical vortices in the Ginzburg–Landau equation with cubic–quintic nonlinearity

In a dissipative system with cubic–quintic nonlinearity, the curious evolution of optical vortex beams characterized by different topological charges (TCs) is simulated numerically and presented their evolution profiles. We find that new vortices will be induced during propagation, and the behavior of vortices, as affected by the TC and the number of beads of the incident beam, as well as its size, is also discussed. Common rules associated with the initial conditions coming from various incident beams are developed to determine the number of induced vortices and the corresponding rotation direction. Attributed to the nonlinearity, during propagation we see the beams slowly expand to induce new vortices, which commonly appear in oppositely charged pairs, while the net topological charge of the vortex is conserved. Our results not only deepen the understanding of optical vortices, but also widen their potential applications.     

On plasma radiative properties in stellar conditions

The knowledge of stellar evolution is evolving quickly thanks to an increased number of opportunities to scrutinize the stellar internal plasma properties by stellar seismology and by 1D and 3D simulations. These new tools help us to introduce the internal dynamical phenomena in stellar modeling. A proper inclusion of these processes supposes a real confidence in the microscopic physics used, partly checked by solar or stellar acoustic modes. In the present paper we first recall which fundamental physics has been recently verified by helioseismology. Then we recall that opacity is an important ingredient of the secular evolution of stars and we point out why it is necessary to measure absorption coefficients and degrees of ionization in the laboratory for some well identified astrophysical conditions. We examine two specific experimental conditions which are accessible to large laser facilities and are suitable to solve some interesting questions of the stellar community: are the solar internal radiative interactions properly estimated and what is the proper role of the opacity in the excitation of the non-radial modes in the envelop of the β Cepheids and the Be stars? At the end of the paper we point out the difficulties of the experimental approach that we need to overcome.     

Transient squeeze flow of viscoplastic materials

The transient, axisymmetric squeezing of viscoplastic materials under creeping flow conditions is examined. The flow of the material even outside the disks is followed. Both cases of the disks moving with constant velocity or under constant force are studied. This time-dependent simulation of squeeze flow is performed for such materials in order to determine very accurately the evolution of the force or the velocity, respectively, and the distinct differences between these two experiments, the highly deforming shape and position of all the interfaces, the effect of possible slip on the disk surface, especially when the slip coefficient is not constant, and the effect of gravity. All these are impossible under the quasi-steady state condition used up to now. The exponential constitutive model, suggested by Papanastasiou, is employed. The governing equations are solved numerically by coupling the mixed finite element method with a quasi-elliptic mesh generation scheme in order to follow the large deformations of the free surface of the fluid. As the Bingham number increases, large departures from the corresponding Newtonian solution are found. When the disks are moving with constant velocity, unyielded material arises only around the two centers of the disks verifying previous works in which quasi-steady state conditions were assumed. The size of the unyielded region increases with the Bingham number, but decreases as time passes and the two disks approach each other. Their size also decreases as the slip velocity or the slip length along the disk wall increase. The force that must be applied on the disks in order to maintain their constant velocity increases significantly with the Bingham number and time and provides a first method to calculate the yield stress. On the other hand, when a constant force is applied on the disks, they slow down until they finally stop, because all the material between them becomes unyielded. The final location of the disk and the time when it stops provide another, probably easier, method to deduce the yield stress of the fluid.     

Interactions of three-dimensional vicous axisymmetric vortex rings with a free surface

The unsteady nonlinear interaction of three-dimensional vortices with a free surface is a great challenge in fluid mechanics, which has deep theoretical significance and important practical background. Applying the three-dimensional VOF method, the interactions of three-dimensional axisymmetric vortex rings with a free surface in an incompressible viscous fluid are numerically simulated. The influence of the Froude number and the surface tension are studied and the evolution of the vorticity, the trajectories of the vortex rings and the baroclinic vorticity on the surface are obtained. The results agreed well with the experiments reported in the literature. The project supported by the National Natural Science Foundation of China     

A particle‐in‐cell method for the solution of two‐layer shallow‐water equations

A particle‐in‐cell (PIC) numerical method developed for the study of shallow‐water dynamics, when the moving fluid layer is laterally confined by the intersection of its top and bottom surfaces, is described. The effect of ambient rotation is included for application to geophysical fluids, particularly open‐ocean buoyant vortices in which the underlying density interface outcrops to the surface around the rim of the vortex. Extensions to include the dynamical effect of a second moving layer (baroclinicity) and the presence of a lateral rigid boundary (sidewall) are also described. Although the method was developed for oceanographic investigations, applications to other fluid mechanics problems would be straightforward. Copyright © 2000 John Wiley & Sons, Ltd.     

Removing of vortices in incompressible flows by distributed controls

We consider an optimal control problem of fluids flow. The fluid motion is governed by the incompressible time-dependent Navier-Stokes equations. A new optimal control formulation for the reduction and possibly extinction of vortices is proposed. A cost functional based on a local dynamical systems characterization of vortices is investigated. The resulting functional is a non-convex function of the velocity gradient tensor. The optimality system describing first order necessary optimality conditions is derived. The gradient and the second derivative of the cost functional with respect to the distributed control are established.     

Evolution of vortices in the wake of an ARJ21 airplane: Application of the lift-drag model

Wake separation is crucial to aircraft landing safety and is an important factor in airport operational efficiency. The near-ground evolution characteristics of wake vortices form the foundation of the wake separation system design. In this study, we analysed the near-ground evolution of vortices in the wake of a domestic aircraft ARJ21 initialised by the lift-drag model using large eddy simulations based on an adaptive mesh. Evolution of wake vortices formed by the main wing, flap and horizontal tail was discussed in detail. The horizontal tail vortices are the weakest and dissipate rapidly, whereas the flap vortices are the strongest and induce the tip vortex to merge with them. The horizontal tail and flap of an ARJ21 do not significantly influence the circulation evolution, height change and movement trajectory of the wake vortices. The far-field evolution of wake vortices can therefore be analysed using the conventional wake vortex model.     

Numerical simulations of liquid metal experiments on cosmic magnetic fields

Cosmic magnetic fields, including the fields of planets, stars, and galaxies, are produced by the hydromagnetic dynamo effect in moving electrically conducting fluids. They also play an active role in cosmic structure formation by enabling outward transport of angular momentum in accretion disks via the magnetorotational instability. The last 10 years have seen tremendous efforts in studying both effects in liquid metal experiments. This paper is focused on the numerical attempts that were undertaken to understand, optimize, and analyze those experiments.     

非平整运动海底上n层流动中波浪传播的Hamilton逼近

在海洋水域，界面波对大尺度变化流的作用是一种典型的分层流动现象．考虑一不可压缩、无黏的分层势流运动，建立了一个在非平整运动海底上的n层流体演化系统，并对其进行了Hamilton描述．每层流体具有各自的常密度、均匀流水平速度，其厚度由未扰动和扰动部分构成．相对于顶层流体的自由表面，刚性、运动的海底具有一般地形变化特征．在明确指出n层流体运动的控制方程和各层交界面上的运动学、动力学边界条件(包含各层交界面上张力效应)后，对该分层流动力系统进行了Hamilton构造，即给出其正则方程和其下述的正则变量：各交界面位移和各交界面上的动量势密度差。     

Nonuniform convective Couette flow

An exact solution describing the convective flow of a vortical viscous incompressible fluid is derived. The solution of the Oberbeck–Boussinesq equation possesses a characteristic feature in describing a fluid in motion, namely, it holds true when not only viscous but also inertia forces are taken into account. Taking the inertia forces into account leads to the appearance of stagnation points in a fluid layer and counterflows, as well as the existence of layer thicknesses at which the tangent stresses vanish on the lower boundary. It is shown that the vortices in the fluid are generated due to the nonlinear effects leading to the occurrence of counterflows and flow velocity amplification, compared with those given by the boundary conditions. The solution of the spectral problem for the polynomials describing the tangent stress distribution makes it possible to explain the absence of the skin friction on the solid surface and in an arbitrary section of an infinite layer.