Magnetic stabilization,transition and energy analysis in the Marangoni driven Full-Zone at low Prandtl numbers

The linear stability of the Marangoni-driven Full-Zone is investigated for low Prandtl number fluids. A constant and uniform magnetic field is applied along the axial axis of the liquid bridge to stabilize the axisymmetric base state. Dramatic contraction of the flow circulation in both radial and azimuthal directions is observed with moderate magnetic fields. The numerical solution utilizes a vorticity transport formulation and high resolution spectral collocation scheme with Chebyshev polynomial basis functions. Critical transitions to three-dimensional, stationary flows are observed up to Ha = 300 for Pr = 0.02 and Ha = 500 for Pr = 0.001. A hydrodynamically driven instability is suggested by the perturbation flows and confirmed through an energy analysis.     

Generation of a sheared plasma rotation by emission, propagation, and absorption of drift wave packets

Collisional electron drift wave turbulence generates drift wave packet structures with density and vorticity fluctuations in the central plasma pressure gradient region of a linear plasma device. Tracking these packets reveals that they follow an outward directed spiral-shaped trajectory in the (r,θ) plane, are azimuthally stretched, and develop anisotropy as they approach an axisymmetric, radially sheared azimuthal flow located at the plasma boundary. Nonlinear energy transfer measurements and time-delay analysis confirm that structure absorption amplifies the sheared flow. Similar mechanisms likely operate at the edge of confined toroidal plasmas and should lead to the amplification of sheared flows at the boundary of these devices as well.     

Longwave Marangoni convection in an inhomogeneously heated liquid

The supercritical Marangoni convection has been studied in a plane-parallel liquid layer, bounded by a free deformable gas-liquid interface from above and by a low-heat-conductivity wall from below, occurring under conditions of inhomogeneous heating in the horizontal plane. In a longwave approximation with a small inhomogeneity of heat flux, the process is described by a system of two-dimensional nonlinear equations for the temperature perturbations, vorticity, and free surface deformation. The concept of quasiequilibrium, implying stability of long-range flows, is introduced, which allows the inhomogeneous heat flux to be modeled by a step function. The linear stability is analyzed in the cases of planar and axisymmetric heat fluxes. The boundaries of stability of the convection regimes are determined on the plane of parameters characterizing the degree of supercriticity inside a heated spot and the depth of damping outside the spot. For an axisymmetric spot, the domains of stability with respect to perturbations for various azimuthal numbers are established.     

Axisymmetry Breaking to Travelling Waves in the Cylinder with Partially Heated Sidewall

The transition from an axisymmetric stationary flow to three-dimensional time-dependent flows is carefully studied in a vertical cylinder partially heated from the side, with the aspect ratio A = 2 and Prandtl number Pτ=0.021. The flow develops from the steady toroidal pattern beyond the first instability threshold, breaks the axisymmetric state at a Rayleigh number near 2000, and transits to standing or travelling azimuthal waves. A new result is observed that a slightly unstable flow pattern of standing waves exists and will transit to stable travelling waves after a long time evolution. The onset of oscillations is associated with a supercritical Hopf bifurcation in a system with O（2） symmetry.     

基流对热对流涡旋结构影响的实验结果初步分析

用实验室模拟方法研究了径向温度梯度对热对流涡旋的影响,结果表明,径向温度梯度所引起的基流使热对流涡旋的对称性结构被破坏,使涡旋变成非对称结构,并使涡旋向基流下游偏移,其强度随基流的加强而减弱,直至消失.热对流涡旋越强其对称性结构越稳定,基流对它的影响越小 关键词： 转盘实验 基流 热对流涡旋     

对气象常用坐标系中位涡形式的探讨

气象常用垂直坐标系中的位涡方程及位涡形式是位涡理论及位涡诊断技术的基础.本文依据坐标转换的观点,分别用两种不同的方法推导出等压坐标和等熵坐标中的位涡方程及相应的位涡表达式.一是从三维矢量运动方程出发,由三维涡度方程、连续方程和热力学方程推导位涡方程;二是直接从等压坐标和等熵坐标中的标量运动方程组出发推导位涡方程.结果表明,用两种方法所得到的等压坐标中的位涡方程和位涡表达式形式有所不同,而等熵坐标中用两种方法所得到的位涡方程和位涡形式相同.对垂直坐标系的物理本质分析表明,采用第一种方法时尽管矢量运动方程中的 关键词： 位涡 坐标转换 等压坐标 等熵坐标     

A Particle-Mesh Method for the Shallow Water Equations Near Geostrophic Balance

In this paper we outline a new particle-mesh method for rapidly rotating shallow water flows based on a set of regularized equations of motion. The time-stepping method uses an operator splitting of the equations into an Eulerian gravity wave part and a Lagrangian advection part. An essential ingredient is the advection of absolute vorticity by means of translated radial basis functions. We show that this implies exact conservation of enstrophy. The method is tested on two model problems based on the qualitative features of the solutions obtained (i.e., dispersion or smoothness of potential vorticity contours) as well as on the increase in mean divergence level.     

Unstable Surface Waves in Running Water

We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for a general class of shear flows with inflection points and the maximal unstable wave number is found. Comparison to the rigid-wall setting testifies that the free surface has a destabilizing effect. For a class of unstable shear flows, the bifurcation of nontrivial periodic traveling waves is demonstrated at all wave numbers. We show the linear instability of small nontrivial waves that appear after bifurcation at an unstable wave number of the background shear flow. The proof uses a new formulation of the linearized water-wave problem and a perturbation argument. An example of the background shear flow of unstable small-amplitude periodic traveling waves is constructed for an arbitrary vorticity strength and for an arbitrary depth, illustrating that vorticity has a subtle influence on the stability of free-surface water waves.     

The influence of solid bodies on low Mach number vortex sound

The mechanisms of sound generation by unsteady, subsonic flows in the presence of solid boundaries are investigated. For this purpose an alternative integral representation for the radiated pressure field is applied which is different from the generally used integral representation introduced by Lighthill and Curle. The main advantage of the method is that there is a linear dependence of the integrand on the time derivative of the vorticity fluctuations in the hydrodynamic near field; instead of the ordinary Green function a “vector Green function” is used. This vector Green function can be chosen for a given flow field in such a way that surface integrals do not appear. Finally, the theory is illustrated by two- and three-dimensional model flows. Analytical solutions are determined by applying the method of matched asymptotic expansions.     

Aerothermodynamic Analysis of a Reentry Brazilian Satellite

This work deals with a computational investigation on the small ballistic reentry Brazilian vehicle SAtélite de Reentrada Atmosférica (SARA). Hypersonic flows over the vehicle SARA at zero-degree angle of attack in chemical equilibrium and thermal nonequilibrium are modeled by the direct simulation Monte Carlo method, which has become the main technique for studying complex multidimensional rarefied flows, and which properly accounts for the nonequilibrium aspects of the flows. The emphasis of this paper is to examine the behavior of the primary properties during the high-altitude portion of SARA reentry. In this way, velocity, density, pressure, and temperature field are investigated for altitudes of 100, 95, 90, 85, and 80?km. In addition, comparisons based on geometry are made between axisymmetric and planar two-dimensional configurations. Some significant differences between these configurations were noted on the flowfield structure in the reentry trajectory. The analysis showed that the flow disturbances have different influence on velocity, density, pressure, and temperature along the stagnation streamline ahead of the capsule nose. It was found that the stagnation region is a thermally stressed zone. It was also found that the stagnation region is a zone of strong compression, high wall pressure. Wall pressure distributions are compared with those of available experimental data, and good agreement is found along the spherical nose for the altitude range investigated.     

MC-Smooth: A mass-conserving,smooth vorticity–velocity formulation for multi-dimensional flows

A novel vorticity–velocity formulation of the Navier–Stokes equations – the Mass-Conserving, Smooth (MC-Smooth) vorticity–velocity formulation – is developed in this work. The governing equations of the MC-Smooth formulation include a new second-order Poisson-like elliptic velocity equation, along with the vorticity transport equation, the energy conservation equation, and N_spec species mass balance equations. In this study, the MC-Smooth formulation is compared to two pre-existing vorticity–velocity formulations by applying each formulation to confined and unconfined axisymmetric laminar diffusion flame problems. For both applications, very good to excellent agreement for the simulation results of the three formulations has been obtained. The MC-Smooth formulation requires the least CPU time and can overcome the limitations of the other two pre-existing vorticity–velocity formulations by ensuring mass conservation and solution smoothness over a broader range of flow conditions. In addition to these benefits, other important features of the MC-Smooth formulation include: (1) it does not require the use of a staggered grid, and (2) it does not require excessive grid refinement to ensure mass conservation. The MC-Smooth formulation is a computationally attractive approach that can effectively extend the applicability of the vorticity–velocity formulation.     

Velocity vorticity vector behavior in supersonic flows behind discontinuity surfaces

The behavior of the velocity vorticity vector on a discontinuity surface arising in the supersonic non-uniform flow of combustible gas around a body with the formation of a shock or detonation wave is studied. The free stream is generally vortical and has a given distribution of parameters. The formulas are obtained for the vorticity vector components in a special coordinate system related to the wave. It is shown that in this case the vorticity vector normal to the wave remains continuous across the discontinuity surface, and in the case of axisymmetric flows, also the quantity remains continuous, which is equal to the ratio of the tangent vorticity component to density, although the quantities themselves taken separately undergo a discontinuity. The work was financially supported by the Russian Foundation for Basic Research (Project 05-01-00004) and by the Far-Eastern Branch of RAS (Project 2-C0-009).     

Handling of temperature dependence of viscosity in problems of incompressible medium flow around a cylinder

The viscous incompressible medium (water, air) flow past a circular cylinder is considered with regard for the temperature T dependent viscosity v. The influence of different boundary conditions for temperature on flow structure, the drag coefficient and its components due to the pressure and viscosity is investigated in the problem of the flow past a cylinder at rest for the (diameter-based) Reynolds number Re_D = 40. A relation between the viscosity gradient along a normal to the body surface and the integral vorticity flux from the body surface into the boundary layer is discussed. Unlike the constant viscosity case the vorticity flux may be different from zero, which must lead because of the integral conservation law for the vorticity to an alteration of the far-field boundary conditions for the velocity. In the same connection, the problem is analysed on the heat spot entry into the computational region under consideration for the flow past a circular cylinder. The examples of the symmetrization of separated flow past a cylinder performing rotation oscillations in a uniform free stream (the Taneda problem) are considered. A comparison with flow computations for low Mach numbers M « 1 for the flow of a medium past a cylinder at rest is carried out. At the computation of the equation for heat transfer under the assumption of incompressibility of such media as air, it is proposed to retain the pressure derivative, which is typical of gases. In this case, a better agreement with the computations of compressible flows (for M « 1) is achieved, for example, at the determination of the sizes of a symmetric zone of flow separation past a circular cylinder. An unsteady flow in the neighborhood of the point of joining the zero streamline bounding a closed region of separated flow (the cavity) in a wake of the cylinder at rest is obtained by a numerical simulation at the Reynolds number equal to 40.     

Nonlinear instability of elementary stratified flows at large Richardson number

Elementary stably stratified flows with linear instability at all large Richardson numbers have been introduced recently by the authors [J. Fluid Mech. 376, 319-350 (1998)]. These elementary stratified flows have spatially constant but time varying gradients for velocity and density. Here the nonlinear stability of such flows in two space dimensions is studied through a combination of numerical simulations and theory. The elementary flows that are linearly unstable at large Richardson numbers are purely vortical flows; here it is established that from random initial data, linearized instability spontaneously generates local shears on buoyancy time scales near a specific angle of inclination that nonlinearly saturates into localized regions of strong mixing with density overturning resembling Kelvin-Helmholtz instability. It is also established here that the phase of these unstable waves does not satisfy the dispersion relation of linear gravity waves. The vortical flows are one family of stably stratified flows with uniform shear layers at the other extreme and elementary stably stratified flows with a mixture of vorticity and strain exhibiting behavior between these two extremes. The concept of effective shear is introduced for these general elementary flows; for each large Richardson number there is a critical effective shear with strong nonlinear instability, density overturning, and mixing for elementary flows with effective shear below this critical value. The analysis is facilitated by rewriting the equations for nonlinear perturbations in vorticity-stream form in a mean Lagrangian reference frame. (c) 2000 American Institute of Physics.     

On the use of a uniformly valid analytical cascade response function for fan broadband noise predictions

The present paper extends an existing analytical model of the aeroacoustic response of a rectilinear cascade of flat-plate blades to three-dimensional incident vortical gusts, to the prediction of the noise generated by a three-dimensional annular blade-row. The extended formulation is meant to be implemented in a fan broadband noise prediction tool. The intended applications include the modern turbofan engines, for which analytical modelling is believed to be a good alternative to more expensive numerical techniques. The prediction noise model resorts to a strip theory approach based on a three-dimensional rectilinear cascade model. The latter is based on the Wiener-Hopf technique, and yields the pressure field in the blade passage and the unsteady blade loading. The analytical pressure solution is derived by making an extensive use of the residue theorem. The obtained unsteady blade loading distribution over the blades is then used as a dipole source distribution in an acoustic analogy applied in the annular rigid duct with uniform mean flow. The new achievements are then tested on three-dimensional annular-benchmark configurations and compared with three-dimensional lifting-surface models and three-dimensional Euler linearized codes available in the literature. The accuracy of the model is shown for high hub-to-tip ratio cases. When used as such in a true rectilinear-cascade configuration, it also reproduces the exact radiated field that can be derived directly. For low hub-to-tip ratio configurations, the model departs from three-dimensional computations, both regarding the blade loading and the acoustic radiation. A correction is proposed to account for the actual annular dispersion relation in the rectilinear-cascade response function. The results suggest that the proposed correction is necessary to get closer to the underlying physics of the annular-space wave equation, but that it is yet not sufficient to fully reproduce three-dimensional results.     

Influence of charge relaxation on the capillary disintegration of a jet of a viscous dielectric liquid placed in an electrostatic field collinear with the axis of the jet

A dispersion relation is derived for capillary waves with an arbitrary symmetry on the surface of a charged jet of a finite-conductivity viscous liquid placed in an electric field collinear with the axis of the jet. Analytical calculations are carried out in an approximation that is linear in dimensionless wave amplitude. In the case of axisymmetric waves, the instability of which causes disintegration of the jet into drops, the finiteness of the potential equalization rate has a noticeable effect only for jets of poorly conducting liquids. The charge relaxation shows up in that “purely relaxation” periodic and aperiodic liquid flows arise. When the conductivity of the liquid declines, the instability growth rates for unstable waves increase and their spectrum extends toward short waves. A charge present on the surface of the jet enhances its instability. An increase in the charge surface diffusion coefficient variously influences the capillary and relaxation branches of the solution: the damping ratio increases in the former case and decreases in the latter. As the diffusion coefficient rises, relaxation flows may become unstable.     

Large eddy simulation of orientation and rotation of ellipsoidal particles in isotropic turbulent flows

The rotational motion and orientational distribution of ellipsoidal particles in turbulent flows are of significance in environmental and engineering applications. Whereas the translational motion of an ellipsoidal particle is controlled by the turbulent motions at large scales, its rotational motion is determined by the fluid velocity gradient tensor at small scales, which raises a challenge when predicting the rotational dispersion of ellipsoidal particles using large eddy simulation (LES) method due to the lack of subgrid scale (SGS) fluid motions. We report the effects of the SGS fluid motions on the orientational and rotational statistics, such as the alignment between the long axis of ellipsoidal particles and the vorticity, the mean rotational energy at various aspect ratios against those obtained with direct numerical simulation (DNS) and filtered DNS. The performances of a stochastic differential equation (SDE) model for the SGS velocity gradient seen by the particles and the approximate deconvolution method (ADM) for LES are investigated. It is found that the missing SGS fluid motions in LES flow fields have significant effects on the rotational statistics of ellipsoidal particles. Alignment between the particles and the vorticity is weakened; and the rotational energy of the particles is reduced in LES. The SGS-SDE model leads to a large error in predicting the alignment between the particles and the vorticity and over-predicts the rotational energy of rod-like particles. The ADM significantly improves the rotational energy prediction of particles in LES.     

Relativistic vortex dynamics in axisymmetric stationary perfect fluid configuration

Relativistic formulation of Helmholtz’s vorticity transport equation is presented on the basis of Maxwell-like version of Euler’s equation of motion. Entangled characteristics associated with vorticity flux conservation in a vortex tube and in a stream tube are displayed on basis of Greenberg’s theory of spacelike congruence of vortex lines and \(1+1+(2)\) decomposition of the gradient of fluid’s 4-velocity. Vorticity flux surfaces are surfaces of revolution about the rotation axis and are rotating with fluid’s angular velocity due to gravitational isorotation in a stationary axisymmetric perfect fluid configuration. Fluid’s angular velocity, angular momentum per baryon, injection energy, and invariant rotational potential are constant on such vorticity flux surfaces. Gravitation causes distortion of coaxial cylindrical vorticity flux surfaces in the limit of post-Newtonian approximation. The rotation of the fluid with angular velocity relative to vorticity flux surfaces generates swirl which causes the stretching of material vortex lines being wrapped on vorticity flux surfaces. Fluid helicity which is conserved in the fluid’s rest frame does not remain conserved in a locally nonrotating frame because of the existence of swirl. Vortex lines are twist free in the absence of meridional circulations, but the twisting of spacetime due to dragging effect leads to the increase in vorticity flux in a vortex tube.     

肋条湍流减阻机理的研究

本文采用热线实验和大涡模拟数值计算方法,对三角形肋条的局部摩擦阻力和表面流场进行了测量和模拟,并对肋条的减阻机理进行了分析。结果发现,在整体减阻情况下,肋条表面局部摩擦阻力在展向位置分布不均匀,在肋尖附近区域为局部增阻区,在肋底附近为局部减阻区。在此基础上,通过涡动力学分析建立了局部摩擦力和流场涡运动之间的理论关系式,定量得出法向涡量和展向涡量的扩散流率是决定壁面摩擦阻力的两个因素。进一步研究发现,法向涡量和展向涡量的扩散流率主要集中在肋尖及其两侧,使得该区域能量输运和耗散强烈,形成局部增阻区。而在肋底附近,法向涡量和展向涡量的扩散流率较小,涡运动微弱,形成局部减阻区。