高瑞利数下水平自然热对流的幂律关系

采用数值模拟方法，研究了高度和宽度比为1∶10的狭长矩形腔内的水平自然热对流. 根据对瑞利数(Rayleigh数)Ra在10⁴ <Ra<10¹¹内情形的计算结果，将流动分为三个不同的区间：线性区、连续过渡区、1/5次幂律区. 虽然流量和努塞尔数(Nusselt数)Nu随瑞利数的变化都包括了三个参数演化区间，但从一个区间到另外一个参数区间的转变时并不是同步的，其中努塞尔数的转变总是超前流量的转变. 对比前人的研究发现，流量1/3次幂律的结果是由于瑞利数不够高所致. 此外，模拟结果也表明Siggers等的理论分析过高估计了热通量强度，实际的温度边界层内努塞尔数和瑞利数为1/5次幂律关系.     

Chaos from turbulence: stochastic-chaotic equilibrium in turbulent convection at high Rayleigh numbers

It is shown that the correlation function of the mean wind velocity generated by a turbulent thermal convection (Rayleigh number Ra ～ 10(11)) exhibits exponential decay with a very long correlation time, while the corresponding largest Lyapunov exponent is certainly positive. These results together with the reconstructed phase portrait indicate the possible presence of chaotic component in the examined mean wind. Telegraph approximation is also used to study the relative contribution of the chaotic and stochastic components to the mean wind fluctuations and an equilibrium between these components has been studied in detail.     

Onset of oscillatory binary fluid convection in finite containers

The onset of oscillatory convection in binary fluid mixtures in a two-dimensional domain with realistic boundary conditions on all boundaries is determined as a function of the fluid parameters and the aspect ratio Gamma of the container. The first unstable mode has either odd or even parity under left-right reflection. Depending on Gamma and the separation ratio S, this mode has the form of a standing wave, or a "chevron," consisting of a pair of waves propagating outwards from the cell center (or, in some cases, inwards towards it). Codimension--two points at which odd and even parity modes are simultaneously marginally stable are determined, as are various Takens-Bogdanov points. For fixed Sinfinity, and to the gap (in Rayleigh number and oscillation frequency) between successively unstable modes. The results quantify the parameter regime in which the weakly nonlinear dynamics of the system can be described in terms of the interaction of the first odd and even parity oscillatory modes.     

Simulation of leaky Rayleigh wave at air-solid cylindrical interfaces by finite element method

The finite element method is used to simulate the laser-excited leaky Rayleigh wave at air-solid cylindrical interfaces. A whole arithmetic of fluid-solid interaction is presented, which includes a coupling matrix that describing the process of the interaction between fluid and solid, the Arbitrary Lagrangian-Eulerian (ALE) formulation for treating the variation of fluid domain, which results from the Rayleigh wave propagating on the cylindrical interface, etc. Typical calculation is executed and the results show that the polarity of leaky Rayleigh waveform gradually changes as it propagates on the air-solid cylindrical interface.     

Simulation of COPO II Lo experiments on natural convection of heat generating liquid at high Rayleigh numbers

The methodology is described and the results are presented concerning numerical modeling of COPO II Lo experiments on heat transfer in liquid with internal heat generation at very high internal Rayleigh numbers typical for natural convection in a core melt that can appear during progress of severe accident at a nuclear power plant (NPP). The work is keeping in the course of development of CFD-based tool for quantitative analysis of heat transfer in a stratified molten pool of different configurations possible in severe accident scenarios with melt retention in the reactor vessel or in the VVER core catcher. Such CFD methodology would be used for testing of simplified correlation models for simulation of the core melt interaction with NPP structures in system code SOCRAT. During verification the available experimental data on the core melt thermohydraulics were analyzed, and it was concluded that they are insufficient to measures of CFD quality. The data uncertainties, along with the complexities of convective flow, uncertainties of the reactor core melt conditions, limitations of experimental possibilities and of turbulence modeling, actually constrain the multivariate CFD simulations of natural convection at very high Rayleigh numbers. RANS turbulence models only can be efficiently applied here, and they are to be checked for such purposes. In a series of numerical modeling of COPO II Lo experiments and some others, availability of a k-? realizable model with included buoyancy effects was estimated, and the optimal set of CFD options was formed for minimizing numerical artifacts. It was demonstrated that in the investigated range of Rayleigh numbers the k-? model works qualitatively correctly, but is inclined to systematical deformation of the melt boundary heat transfer distribution. This allows one to use this model for qualitative multivariate CFD estimations but requires improvement of the model or finding of its efficient and more exact equivalent.     

Time-dependent radiation transfer with Rayleigh scattering in finite slab media

The time-dependent radiation transfer equation in a finite plane geometry with Rayleigh scattering is studied. The traveling wave transformation is used to obtain the corresponding stationary-like equation. Pomraning-Eddington approximation is then used to find the solution. Numerical results for reflectivity at the left boundary and transmissivity from the right boundary are presented at different times. The medium is assumed to have specular-reflecting boundaries with angular-dependent externally incident flux. Two different weight functions are introduced to force the boundary conditions to fulfill.     

Stability of highly shifted equilibria in a large-aspect-ratio tokamak

High beta poloidal tokamaks can confine plasma pressures an order of magnitude higher than their low beta poloidal counterparts. The theoretical stability of these high beta poloidal magnetohydrodynamics equilibria was left unresolved for many years. Using modern computational tools, such configurations are now found stable to Mercier, resistive and high-n (ideal and resistive) ballooning criteria as well as fixed and free-boundary modes for a wide range of current density profiles in the framework of a low field large-aspect-ratio machine.     

A bubble-stabilized least-squares finite element method for steady MHD duct flow problems at high Hartmann numbers

In this paper we devise a stabilized least-squares finite element method using the residual-free bubbles for solving the governing equations of steady magnetohydrodynamic duct flow. We convert the original system of second-order partial differential equations into a first-order system formulation by introducing two additional variables. Then the least-squares finite element method using C⁰$C^0$ linear elements enriched with the residual-free bubble functions for all unknowns is applied to obtain approximations to the first-order system. The most advantageous features of this approach are that the resulting linear system is symmetric and positive definite, and it is capable of resolving high gradients near the layer regions without refining the mesh. Thus, this approach is possible to obtain approximations consistent with the physical configuration of the problem even for high values of the Hartmann number. Before incoorperating the bubble functions into the global problem, we apply the Galerkin least-squares method to approximate the bubble functions that are exact solutions of the corresponding local problems on elements. Therefore, we indeed introduce a two-level finite element method consisting of a mesh for discretization and a submesh for approximating the computations of the residual-free bubble functions. Numerical results confirming theoretical findings are presented for several examples including the Shercliff problem.     

Representation of optical fields using finite numbers of bits

We consider the problem of representation of a finite-energy optical field, with a finite number of bits. The optical field is represented with a finite number of uniformly spaced finite-accuracy samples (there is a finite number of amplitude levels that can be reliably distinguished for each sample). The total number of bits required to encode all samples constitutes the cost of the representation. We investigate the optimal number and spacing of these samples under a total cost budget. Our framework reveals the trade-off between the number, spacing, and accuracy of the samples. When we vary the cost budget, we obtain trade-off curves between the representation error and the cost budget. We also discuss the effect of degree of coherence of the field.     

Subsonic leaky Rayleigh waves at liquid-solid interfaces

The paper is devoted to the study of leaky Rayleigh waves at liquid-solid interfaces close to the border of the existence domain of these modes. The real and complex roots of the secular equation are computed for interface waves at the boundary between water and a binary isotropic alloy of gold and silver with continuously variable composition. The change of composition of the alloy allows one to cross a critical velocity for the existence of leaky waves. It is shown that, contrary to popular opinion, the critical velocity does not coincide with the phase velocity of bulk waves in liquid. The true threshold velocity is found to be smaller, the correction being of about 1.45%. Attention is also drawn to the fact that using the real part of the complex phase velocity as a velocity of leaky waves gives only approximate value. The most interesting feature of the waves under consideration is the presence of energy leakage in the subsonic range of the phase velocities where, at first glance, any radiation by harmonic waves is not permitted. A simple physical explanation of this radiation with due regard for inhomogeneity of radiated and radiating waves is given. The controversial question of the existence of leaky Rayleigh waves at a water/ice interface is reexamined. It is shown that the solution considered previously as a leaky wave is in fact the solution of the bulk-wave-reflection problem for inhomogeneous waves.     

Rayleigh Scattering at Atoms with Dynamical Nuclei

Scattering of photons at an atom with a dynamical nucleus is studied on the subspace of states of the system with a total energy below the threshold for ionization of the atom (Rayleigh scattering). The kinematics of the electron and the nucleus is chosen to be non-relativistic, and their spins are neglected. In a simplified model of a hydrogen atom or a one-electron ion interacting with the quantized radiation field in which the helicity of photons is neglected and the interactions between photons and the electron and nucleus are turned off at very high photon energies and at photon energies below an arbitrarily small, but fixed energy (infrared cutoff), asymptotic completeness of Rayleigh scattering is established rigorously. On the way towards proving this result, it is shown that, after coupling the electron and the nucleus to the photons, the atom still has a stable ground state, provided its center of mass velocity is smaller than the velocity of light; but its excited states are turned into resonances. The proof of asymptotic completeness then follows from extensions of a positive commutator method and of propagation estimates for the atom and the photons developed in previous papers. The methods developed in this paper can be extended to more realistic models. It is, however, not known, at present, how to remove the infrared cutoff. Activities supported, in part, by a grant from the Swiss National Foundation. Work partially supported by U.S. National Science Foundation grant DMS 01-00160. Supported by a NSF postdoctoral fellowship.     

Rayleigh and Lamb waves at liquid-solid boundaries

The equations governing Rayleigh and Lamb mode propagation are examined for free and for liquid-loaded solids. Examples are given to show under what conditions the free-solid approach yields acceptable solutions for the velocities and under what conditions the more involved liquid-loaded solid formulism must be used.     

Polarisation dependent loss calculation in echelle gratings using finite element method and Rayleigh expansion

We describe a numerical method to compute the reflectivity of a metallised integrated echelle grating. The modelling is based on a combination of a finite element method in the region inside the grating teeth and the Rayleigh field expansion outside. Results show a net dependence of the efficiency on the polarisation state (directly related to PDL), as a function of the wavelength, due to two factors: a lower reflectivity for the TM light in the operating order and a shift in the maximum of the response curve.     

格子Boltzmann方法分析加热尺寸和瑞利数对可变形开口腔内自然对流的影响

采用格子Boltzmann方法对可变形腔体内自然对流问题进行数值研究，给出平均努赛尔数的经验关系式.腔体左壁加热长度分为左壁面的整个区域（H）和左壁面的中间区域（0.5H）两种情况，右壁向外界环境开放，上下边界绝热且可以上下移动，以此调节右出口尺寸.主要研究瑞利数（10⁴ ≤ Ra ≤ 10⁶），右出口尺寸（1.0H ≤ L ≤ 2.0H），左壁加热尺寸（L_h=0.5H或L_h=H）对腔体内等温线、流线、局部努塞尔数和平均努赛尔数的影响.结果表明：腔体内换热随着瑞利数的增大越来越强烈，表现为椭圆形准静止区域更加靠近上绝热壁，且热分层厚度逐渐变小，平均努赛尔数增加.而右出口尺寸的增加，对于两种加热尺寸下腔内的换热效果有不同程度影响，其中与加热尺寸为左壁面的全部区域L_h=H相比，加热尺寸为左壁面的中间情况L_h=0.5H时，右侧开口尺寸的增加对换热效果的影响不显著.此外，左壁加热尺寸为0.5H时显示出比加热尺寸为H时更高的平均传热效率.最后，针对不同的加热尺寸，提出加热面平均努赛尔数与Ra数及右壁面开口尺寸L^*之间函数关系的经验预测，拟合效果满足工程实践与设计需要.     

Pulsed Rayleigh wave scattered at a surface crack

This paper investigates Rayleigh wave interaction with machined slots on flat aluminium blocks to simulate surface breaking cracks. Using a finite element method, Rayleigh wave scattering by narrow slots of varied depth ranging from 0.5 mm to 20 mm is calculated. Pulsed wideband Rayleigh waves with a centre frequency of 590 kHz and -6 dB bandwidth of 520 kHz is considered. Reflection and transmission coefficients are calculated and compare well with the published literature. We and other workers have reported enhancement of the measured amplitude or particle velocity of an apparent Rayleigh wave close to a surface defect. In this paper, it is found that the predicted enhancement of in-plane components of particle velocities close to a crack is significantly higher than that of the out-of-plane components of particle velocities which appears to be mainly due to the mode-converted surface skimming longitudinal wave from the crack that has mainly in-plane components near the sample surface. The enhancement of the in-plane particle velocity will be observed regardless of the type of in-plane sensitive ultrasonic detector used. The explanation of the discrepancy of the reflection and transmission coefficients obtained by pulsed and narrow band or pseudo continuous Rayleigh waves is discussed. The later-arriving Rayleigh waves from reverberation along the inside of the crack surface are observed, as has been previously reported by other workers, and this may also be used to gauge slot depth.     

New look at the large numbers

A new interpretation for the large number hypothesis is given, referring to the close connection between the Bekenstein-Hawking entropy and Weizsäckers ur theory.     

激光激发黏弹表面波有限元数值模拟

研究黏弹性材料中激光激发的Rayleigh波的传播特征. 考虑到黏弹性材料的黏性特征,在频域内建立黏弹性材料中激光激发Rayleigh波的有限元数值模型. 在验证有限元频域数值模型正确性的基础上,模拟脉冲激光作用在黏弹性材料上激发出Rayleigh波,进而讨论激光激发的黏弹Rayleigh波的传播特征,并比较黏弹性材料与弹性材料中激光激发的Rayleigh波差异,同时分析了材料的黏性劲度参量变化对Rayleigh波特征的影响. 关键词： 表面波 激光超声 有限元方法 黏弹性