激波在异种气体中传播及诱导的剪切混合研究

利用二阶迎风TVD格式求解多组分,层流全N－S方程,针对直通道和突扩直通道,研究了马赫数为2和4的激波在H2和空气界面上的传播及诱导的燃料剪切混合,计算结果表明：（1）直通道中,剪切层中的激波阵面要发生畸变,存在对混合起主要作用的卷吸涡,激波马赫数不同,卷吸涡结构和横向混合的尺寸也不同,激波马赫数低,剪切混合效果好,（2）在突扩直通道中,马赫数为2和4的激波在H2中产生不同强度激波,在剪切层中都能产生顺时针,尺度较大的卷吸涡,后台阶增强了剪切层的混合。     

On the position of a vortex in a two-dimensional model of atmosphere

As a continuation of our work, Rozanova et al. (2010) [1] we study possible trajectories of a long time existing vortex in a model of the atmosphere dynamics, where the vortex can be interpreted as a tropical cyclone. The model can be obtained from the system of primitive equations governing the motion of air over the Earth’s surface after averaging over the height. We consider approximations of l-plane and β-plane used in geophysics for modeling of middle scale processes and equations on the whole sphere as well. We associate with a cyclone a special class of smooth solutions having a form of a localized steady non-singular vortex moving with a bearing field. We show that the solutions satisfy the equations of the model either exactly or with a discrepancy which is small in a neighborhood of the trajectory of the center of vortex. We show both analytically and numerically that the trajectory of a localized vortex keeps the features of trajectory of vortex with a linear profile of velocity, where the exact solution can be obtained.     

Aerodynamic Sound due to a Point Source near a Half-plane

In this paper we extend Jones's analysis of the diffractionof sound in three dimensions by a semi-infinite plane with aplane vortex sheet attached in the two cases when the wave equationis in the form for still air and when convection is present.It is found that in so far as the moving medium is concernedthe imposition or otherwise of the Kutta-Joukowski conditiondoes not have much influence on the scattered field away fromthe diffracting plane; when the source is near the edge thefield has the same directionality and order of magnitude. Onthe other hand, near the wake the Kutta-Joukowski conditionproduces a much stronger field than elsewhere even when thesource is not near the edge. We also conclude that the samephenomenon occurs for arbitrary sources and not just for theline source discussed by Jones.     

The Motion of a Vortex Pair in a Stratified Atmosphere

The movement of a horizontal vortex pair through an inhomogeneous fluid is considered. The problem is formulated first for the case when the ambient fluid is uniform, the fluid moving with the vortex pair has a different density, and the motion is supposed laminar and inviscid. An approximate solution is obtained, which predicts that the distance between the vortices stays constant and the vortices accelerate at a constant rate. This solution is then applied to motion in a stratified atmosphere and it is found that the vortices oscillate vertically with a frequency and amplitude depending on the initial conditions and the stratification. Finally, approximate equations are constructed to describe the effects of turbulent entrainment into the fluid moving with the vortex pair, and an estimate of the damping is obtained.     

Reflection and Refraction of Solitons by the KdV–Burgers Equation in Nonhomogeneous Dissipative Media

We study the behavior of the soliton that encounters a barrier with dissipation while moving in a nondissipative medium. We use the Korteweg–de Vries–Burgers equation to model this situation. The modeling includes the case of a finite dissipative layer similar to a wave passing through air–glass–air and also a wave passing from a nondissipative layer into a dissipative layer (similar to light passing from air to water). The dissipation predictably reduces the soliton amplitude/velocity. Other effects also occur in the case of a finite barrier in the soliton path: after the wave leaves the dissipative barrier, it retains the soliton form, but a reflection wave arises as small and quasiharmonic oscillations (a breather). The breather propagates faster than the soliton passing through the barrier.     

The limiting vortex in the similarity solution for a swirling flow

It is known that the similarity solution for a viscous swirling flow over a stationary disk does not exist if the driving vortex far away from the disk is a potential vortex, while the solution exists for a rigid body vortex. Previously, the breakdown has been determined to occur if the azimuthal velocity of the driving vortex decreases faster than a certain power of the radial distance from the axis of symmetry. The decay parameter at which the similarity solution ceases to exist is computed here by a more direct method, and the reason for the breakdown becomes apparent. The analysis confirms (and slightly improves) the known value of the parameter. The case where the fluid, now assumed to be conducting, is subject to an axial magnetic field and the asymptotic behavior of the solution far away from the axis are also briefly discussed.     

Asymptotic and numerical solutions of three‐dimensional boundary‐layer flow past a moving wedge

We consider a laminar boundary‐layer flow of a viscous and incompressible fluid past a moving wedge in which the wedge is moving either in the direction of the mainstream flow or opposite to it. The mainstream flows outside the boundary layer are approximated by a power of the distance from the leading boundary layer. The variable pressure gradient is imposed on the boundary layer so that the system admits similarity solutions. The model is described using 3‐dimensional boundary‐layer equations that contains 2 physical parameters: pressure gradient (β) and shear‐to‐strain‐rate ratio parameter (α). Two methods are used: a linear asymptotic analysis in the neighborhood of the edge of the boundary layer and the Keller‐box numerical method for the full nonlinear system. The results show that the flow field is divided into near‐field region (mainly dominated by viscous forces) and far‐field region (mainstream flows); the velocity profiles form through an interaction between 2 regions. Also, all simulations show that the subsequent dynamics involving overshoot and undershoot of the solutions for varying parameter characterizing 3‐dimensional flows. The pressure gradient (favorable) has a tendency of decreasing the boundary‐layer thickness in which the velocity profiles are benign. The wall shear stresses increase unboundedly for increasing α when the wedge is moving in the x‐direction, while the case is different when it is moving in the y‐direction. Further, both analysis show that 3‐dimensional boundary‐layer solutions exist in the range −1<α<∞. These are some interesting results linked to an important class of boundary‐layer flows.     

The Doppler Effect in a Warm Uniaxial Plasma

In this paper we consider the character of the radiation emittedby a radiator moving with uniform velocity through a warm, uniaxialplasma. It is shown that the dispersive and anisotropic natureof the plasma plays an important role in determining both theDoppler shift in frequency and the power spectrum of the radiation.The power spectrum and the Doppler relation between the frequencyand the direction of the emitted radiation are calculated when(a) the motion is parallel to the magnetic field, and (b) themotion is perpendicular to the magnetic field. It is shown thatthe Doppler shift and the power spectrum are substantially differentin these two cases. The formulae for the {caron}erenkov radiationemitted by a moving charged particle may be obtained from thosefor Doppler radiation. In the last section we show that a particlemoving parallel to the axis of symmetry excites a power spectrumwhich is linear with frequency, whereas a particle moving perpendicularto that axis excites a power spectrum that is sharply peakednear the plasma frequency.     

The motion of a cylindrical body in a stratified fluid under the action of a radiation force

The free motion of a thin cylindrical body is investigated based on a previously derived expression for the radiation force acting on moving point sources in a stratified fluid. The fundamental equations of motion are derived, the limits of applicability of the approximation used are indicated and the results of calculations of typical trajectories of a body which begins to move with a specified velocity from a position of neutral buoyancy at an angle to the horizon are presented. Calculations of the trajectory of motion of a thin cylindrical body in a stratified fluid when the total radiation force is taken into account show that the effect of the lateral component of this force is considerable and leads not only to quantitative corrections but also to qualitative effects (for example, to an increase in the oscillations of the body and a change in its direction of motion). The results obtained pertain both to the motion of solids in fluids and to the translational motion of vortex dipoles in weakly stratified media.     

Travelling Waves with a Singularity in Magnetic Nanowires

We model the evolution of the magnetization in an infinite cylinder by harmonic map heat flow with an additional external field. Using variational methods, we prove the existence of corotationally symmetric travelling wave solutions with a moving vortex. We moreover show that for weak and strong fields the travelling waves connect the original state anti-parallel to the external magnetic field with the totally reversed state in direction of the external field. Our results match numeric simulations. For thicker wires several groups have found a reversal mode where a domain wall with a corotational symmetry and a vortex is propagating through the wire.     

Regularising discretizations of the Birkhoff-Rott equation

A thin shear layer moving from the trailing edge of a two-dimensional aerofoil section downstream can be interpreted as a curve of discontinuity for the tangential velocity and may be approximated by a vortex sheet in inviscid, incompressible fluid flow. It is well known that vortex sheets are subject to instabilities of Kelvin-Helmholtz type which lead to roll-up phenomena in the wake. The motion of such sheets is governed by the Birkhoff-Rott equation. In the case of Kelvin-Helmholtz instability it seems clear that a curvature singularity occurs at a certain critical time and that consistent discretizations of the Birkhoff-Rott equation may fail to yield reliable results even before the time of occurrence of a singularity. We discuss the modification of the Biot-Savart kernel in the sense of Krasny who regularized the kernel by means of a global parameter. Using discrete Fourier transform we show the damping influence of this regularization technique. We modify the kernel carefully by introducing a regularization found in ordinary vortex methods and show that reliable results may be obtained up to and slightly after the singularity formation without increasing the accuracy of the computation.     

The Sound Field of a Source That Executes in a Liquid Layer a Motion Represented as the Sum of a Subsonic Uniform Rectilinear Motion and a Periodic Motion. Exact (Explicit) Solutions

The problem on the sound field generated in a liquid layer by a moving point source that was turned on at a moment infinitely distant in the past is considered. Properties of the layer and the source under consideration are chosen in such a way that the solution of the problem can be constructed in the form of a triple series, separating variables in a moving coordinate system. The expressions obtained for the terms of this series (for normal waves) are not only exact but also explicit outside a neighborhood of the source in the sense that they are products of elementary and known functions of coordinates and time. Bibliography: 10 titles.     

The influence of turbulence on a columnar vortex with axial flow

The interaction between a columnar vortex and external turbulence is investigated numerically. A q -vortex is immersed in an initially isotropic homogeneous turbulence field, which itself is produced numerically by a direct numerical simulation of decaying turbulence. The formation of turbulent eddies around the columnar vortex and the vortex-core deformations are studied in detail by visualizing the flow field. In the less-stable case with q = –1.5, small thin spiral structures are formed inside the vortex core. In the unstable case with q = –0.45, the linear unstable modes grow until the columnar vortex make one turn. Its growth rate agrees with that of the linear analysis of Mayer and Powell[1]. After two turns of the vortex, the secondary instability is excited, which causes collapse of the columnar q -vortex and the sudden appearance of many fine scale vortices. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermal analysis of moving induction heating of a hollow cylinder with subsequent spray cooling: Effect of velocity,initial position of coil,and geometry

In this paper, temperature analysis of the complete process of moving induction heat treatment is performed using numerical methods. A non-linear and transient magneto-thermal coupled problem with a moving coil which is considered as moving heat source, is investigated by an efficient finite-element procedure. A vertical hollow circular cylinder is heated by the moving coil at a given velocity along it, and the heated parts then quenched by a moving water–air spray. The effects of natural convection with air on the both inner and outer surfaces of cylinder, and also radiation of outer surface of cylinder with ambient are taken into account. For quenching of work-piece, a specific kind of atomized spray cooling which utilizes a mixture of water and air with different mass fractions is used. This procedure includes moving boundary conditions, temperature-dependent properties, and change in magnetic permeability of specified alloy at the Curie temperature. Obtained numerical results have been verified by comparison with analytical solutions using Green’s function methods. Also, the effect of velocity, initial position of inductor and inner to outer radius ratio on temperature distribution are investigated.     

The Small Vorticity Nonlinear Critical Layer for Kelvin Modes on a Vortex

We consider in this paper the propagation of neutral modes along a vortex with velocity profile being the radial coordinate. In the linear stability theory governing such flows, the boundary in parameter space separating stable and unstable regions is usually comprised of modes that are singular at some value of r denoted r_c , the critical point. The singularity can be dealt with by adding viscous and/or nonlinear effects within a thin critical layer centered on the critical point. At high Reynolds numbers, the case of most interest in applications, nonlinearity is essential, but it develops that viscosity, treated here as a small perturbation, still plays a subtle role. After first presenting the scaling for the general case, we formulate a nonlinear critical layer theory valid when the critical point occurs far enough from the center of the vortex so that the vorticity there is small. Solutions are found having no phase change across the critical layer thus permitting the existence of modes not possible in a linear theory. It is found that both the axial and azimuthal mean vorticity are different on either side of the critical layer as a result of the wave–mean flow interaction. A long wave analysis with O (1) vorticity leads to similar conclusions.     

Self-similar point vortices and confinement of vorticity

This papers deals with the large time behavior of solutions of the incompressible Euler equations in dimension 2. We consider a self-similar configuration of point vortices which grows like the square root of the time. We study the confinement properties of a blob of vorticity initially located around the first point vortex and moving in the velocity field produced by itself and by the other point vortices. We find a su?cient condition on the point vortices such that the vorticity stays confined around the first point vortex at a rate better than the square root of the time. The relevance to the large time behavior of the Euler equations is discussed.     

浅水横流中异重冲击射流的大尺度涡结构

采用RNG湍流模型对浅水横流中异重冲击射流的大尺度涡结构进行了详细的数值研究．分析了冲击区滞止点上游壁面涡结构和近区Scarf涡结构的尺度、形成机理和演化特征．计算得到了上游壁面涡的特征尺度,结果表明上游壁面涡具有高度的三维性,其特征尺度依赖于流速比和环境水深．近区Sarf涡结构对横流冲击射流的横向浓度分布具有重要的影响．当流速比相对较小时,在底层壁射流与环境横流的横向边界附近出现明显的高浓度聚集现象,计算结果表明Scarf涡结构对这一高浓度聚集区的形成起主导作用．     

Nonlinear high-wavenumber Bnard convection

Weakly nonlinear two-dimensional roll cells in Bnard convectionare examined in the limit as the wavenumber a of the roll cellsbecomes large. In this limit the second harmonic contributionsto the solution become negligible, and a flow develops wherethe fundamental vortex terms and the correction to the meanare determined simultaneously, rather than sequentially as inthe weakly nonlinear case. Extension of this structure to Rayleighnumbers O(a³) above the neutral curve is shown to be possible,with the resulting flow field having a form very similar tothat for strongly nonlinear vortices in a centripetally unstableflow. The flow in this strongly nonlinear regime consists ofa core region, and boundary layers of thickness O(a^–1)at the walls. The core region occupies most of the thicknessof the fluid layer and only mean terms and cos az terms playa role in determining the flow; in the boundary layer all harmonicsof the vortex motion are present. Numerical solutions of thewall layer equations are presented and it is also shown thatthe heat transfer across the layer is significantly greaterthan in the conduction state.     

热源强迫的边界层低涡解及其应用

考虑边界层低涡为受非绝热加热和摩擦强迫并满足热成风平衡的轴对称涡旋系统,采用Boussinesq近似,通过求解柱坐标系中涡旋模式的初值问题,分析了热源强迫对低涡流场结构的影响．结果表明:热源强迫对低涡的流场结构有重要影响,并且这种影响的具体表现形式与加热的径向分布有密切关系．对边界层涡旋解讨论的结果可以解释青藏高原低涡系统的某些重要结构特征．     

The diffusion of a discontinuity of the shear stress at the boundary of a viscoplastic half-plane

For the problem of the diffusion of a discontinuity of the shear stress at the boundary of a half-plane, which is a special case of the general problem of the diffusion of a vortex layer, the classes of media and types of assignment of boundary conditions for which self-similar solutions exist are discussed. For a viscoplastic medium in a half-plane the problem reduces to the problem in a layer of time-variable thickness, the solution of which does not possess the property of analyticity. The long-term asymptotic of this problem are investigated. In the case where, at an accessible boundary, it is possible simultaneously to measure both the shear stress and the horizontal velocity, an algorithm is proposed for finding a quantity that is difficult to measure, A namely, the thickness of the zone of viscoplastic flow.