Fluctuations in a fluid under a stationary heat flux II. Slow part of the correlation matrix

The general formulas, derived in a previous paper, are used to calculate the correlation functions of the hydrodynamic variables in the Rayleigh-Bénard system. The behavior of the correlation functions on a time scale slow compared to that of sound propagation is determined, using systematically nonequilibrium hydrodynamic eigenmodes. These (slow) eigenmodes of the linearized Boussinesq equations in the presence of gravity and a temperature gradient are the viscous and the visco-heat modes. They are determined for ideal heat-conducting plates with stick boundary conditions. The visco-heat modes are found to behave qualitatively different from those obtained with slip boundary conditions. Using these eigenmodes, the slow part of the correlation functions can be determined explicitly. On a small length scale, as probed by light scattering, we recover the same expression for the Rayleigh line as quoted in the literature. On larger length scales, as probed by microwaves, the coupling of gravity to the temperature gradient gives rise to a convective instability (heating form below) or to propagating visco-heat modes (heating from above). The corresponding correlation functions and the Rayleigh line are calculated and discussed.     

Study of the effects of three types of time-periodic vertical oscillations on the linear and nonlinear realms of Rayleigh-Bénard convection in hybrid nanoliquids

In the paper, the effect of time-periodic gravity modulation with trigonometric sine, triangular, and square waves-forms on Rayleigh Bénard convection in water-alumina nanoliquids and water-alumina-copper hybrid nanoliqiuds is studied by using a single-phase model. Using a perturbation method, linear stability analysis is performed for all the three wave-forms. A generalized Lorenz model that has the influence of nanoliquids and modulation incorporated in it is derived using a truncated Fourier series representation. The Lorenz model is then transformed into a Ginzburg-Landau model using the method of multiscales, and the solution is used to study heat transport. For trigonometric sine, triangular and square wave-forms of modulations comparison are made on their effect on the onset of convection and the heat transport. The linear stability analysis reveals that the critical Rayleigh number obtained in the case of a triangular wave-form is less compared to the value obtained in the cases of trigonometric sine and square wave-forms. This leads to an enhanced heat transfer situation in the case of triangular wave-form compared to that in the other two wave-forms. It is also found that such an enhancement in heat transport increases with amplitude and decreases with the modulation frequency. Thus, the modulation is found to be a regulating mechanism on heat transport. Further, it is observed that water-alumina-copper facilitates maximum heat transport compared to that by water-alumina and water, leading to the conclusion that hybrid nanoliquids facilitate enhanced heat transport compared to that by mono nanoliquids.     

瑞利激光雷达探测南京上空平流层大气温度

为了解平流层大气温度变化规律,利用瑞利-拉曼-米散射激光雷达对南京上空平流层温度进行长期观测,对观测数据的分析表明:夜晚平流层温度受到重力波的影响,重力波破碎会导致局部温度升高,温度相对变化可以达到12%;在季节变化的过渡月份(4月和10月),平流层中低层温度会有所升高,对应的平流层高层温度降低;平流层温度月变化方面,除局部由于行星星际波的影响外,各月份平流层温度整体上相对比较稳定,激光雷达所测大气温度与大气模式温度具有一定的差别。最后,利用平流层温度廓线提取了重力波信息。     

黑腔冷冻靶传热与自然对流的数值模拟研究

惯性约束聚变的设计要求在靶丸内形成均匀光滑的氘氚冰层, 靶丸周围的热环境对冰层的质量特别是低阶粗糙度有很大的影响. 本文对自主研发的黑腔冷冻靶实验装置中的热物理问题展开了数值模拟, 重点考察了黑腔冷冻靶的传热和流体力学特性. 通过参数分析得到了自然对流对靶丸温度均匀性产生影响的临界条件. 比较了黑腔不同布置朝向时的流场和温度分布, 结果显示黑腔水平布置时自然对流更加强烈, 造成的靶丸温度不均匀性也更大. 在此基础上, 讨论了消除自然对流影响的可能性, 结果发现仅当黑腔垂直布置时利用黑腔分区方法能够消除对流效应对靶丸温度不均匀性的影响而黑腔水平布置时不能消除. 研究结论对于实验中冷冻靶结构的设计、改进和实验的开展等具有指导意义.     

Pinning and long-time-scale behavior in traveling-wave convection

We study nonlinear traveling-wave (TW) and stationary states of convection in experiments in ethanol-water mixtures. While the TW phase velocity as a function of Rayleigh number has been recently shown to be in agreement with the predictions of theory and numerical calculations, we find that this velocity is temporally modulated at frequencies corresponding to the travel time of a single convection roll and of a roll pair past a point stationary in the convection cell. This modulation could be due to the pinning of the convection pattern by experimental inhomogeneities. For large Rayleigh numbers where stationary overturning convection is expected, we sometimes observe extremely slow unidirectional TW states. For larger Rayleigh numbers, this slow TW state starts and stops intermittently on a characteristic time scale of several days. The possible origin of these phenomena and their potential utility are discussed.     

Importance of direction of vibration on the onset of Soret-driven convection under gravity or weightlessness

This paper considers the influence of the direction of vibration on the stability threshold of two-dimensional Soret-driven convection. The configuration is an infinite layer filled with a binary mixture, which can be heated from below or from above. The limiting case of high-frequency and small-amplitude vibration is considered for which the time-averaged formulation has been adopted. The linear stability analysis of the quasi-mechanical equilibrium shows that the problem depends on five non-dimensional parameters. These include the thermal Rayleigh number ( Ra_T), the vibrational parameter (R), the Prandtl number ( Pr), the Lewis number (Le), the separation ratio (S) and the orientation of vibration with respect to the horizontal heated plate (). For different sets of parameters, the bifurcation diagrams are plotted Ra_c = f (S) and k_c = g(S), which are the critical thermal Rayleigh and the critical wave numbers, respectively. Our results indicate that, relative to the classical case of static gravity, vibration may affect all regions in Ra_c-S stability diagram. In the case of mono-cellular convection, by using a regular perturbation method, a closed-form relation for the critical Rayleigh number is found. Several physical situations in the presence or in the absence of gravity (micro-gravity) are discussed.     

On the low-frequency sound scattering in a moving microinhomogeneous medium

The Rayleigh law that governs low-frequency sound attenuation due to the scattering by inhomogeneities in a microinhomogeneous medium is generalized to the case of particles moving in a flow or falling under gravity. Corrections to the scattering’s cross section that adjust the Rayleigh law to the case of a potential flow around inhomogeneities are calculated. It is shown that, when microinhomogeneities are moving in a viscous medium, the characteristics of discrete scatterers may considerably deviate from the Rayleigh law. Based on the data on the velocity and size distribution of falling drops of water in air, refinements are proposed for the laws of low-frequency sound scattering by rain.     

Overview of channel models for underwater wireless communication networks

Acoustic communication in Underwater Wireless Communication Networks (UWCNs) has several challenges due to the presence of fading, multipath and refractive properties of the sound channel which necessitate the development of precise underwater channel models. Some existing channel models are simplified and do not consider multipath or multipath fading. In this paper, a detailed survey on ray-theory-based multipath Rayleigh underwater channel models for underwater wireless communication is presented and the research challenges for an efficient communication in this environment are outlined. These channel models are valid for shallow or deep water. They are based on acoustic propagation physics which captures different propagation paths of sound in the underwater and consider all the effects of shadow zones, multipath fading, operating frequency, depth and water temperature. The propagation characteristics are shown through mathematical analysis. Transmission losses between transceivers are investigated through simulations. Further simulations are carried out to study the bit error rate effects and the maximum internode distances for different networks and depths considering a 16-QAM modulation scheme with OFDM as the multicarrier transmission technique. The effect of weather season and the variability of ocean environmental factors such as water temperature on the communication performance are also shown. The mathematical analysis and simulations highlight important considerations for the deployment and operation of UWCNs.     

相干瑞利散射海水水下温度测量技术的理论研究

海水水下温度的快速大范围测量是海洋监测的重要内容,在民用和军事领域都有着至关重要的意义,本文提出了采用相干瑞利散射方法测量海水水下温度的新方法:用宽带高速光电探测器接收本振激光和海水后向瑞利散射光相干产生的差频信号,进行傅里叶变换分析获取海水瑞利散射展宽谱,从而反演海水温度,首先从海水的热力学特性出发,对利用瑞利散射谱测量海水水下温度的基本原理进行了理论研究和软件模拟;然后对采用相干探测测量海水瑞利散射谱的测量方法进行了理论分析和软件模拟;在此基础上对瑞利散射海水水下温度测量精度进行了分析,得出当水体瑞利散射频谱半宽度测量精度为1 MHz时,测温精度约为0.35 K。     

A numerical study of laminar natural convective heat transfer inside a closed cavity with different aspect ratio

Two-dimensional steady-state laminar natural convection was studied numerically for differentially heated air-filled closed cavity with adiabatic top and bottom walls. The temperature of the left heated wall and cooled right wall was assumed to be constant. The governing equations were iteratively solved using the control volume approach. In this paper, the effects of the Rayleigh number and the aspect ratio were examined. Flow and thermal fields were exhibited by means of streamlines and isotherms, respectively.Variations of the maximum stream function and the average heat transfer coefficient were also shown. The average Nusselt number and was correlated to the Rayleigh number based on curve fitting for each aspect ratio. The investigation covered the range 10⁴ ≤ RA ≤ 10⁷ and is done at Prandtl number equal to 0.693. The result shows the average Nusselt number is the increasing function of Rayleigh number. As the aspect ratio increases, Nusselt number decreases along the hot wall of the cavity. As Rayleigh number increases, Nusselt number increases. Result indicates that at constant aspect ratio, with increase in Rayleigh number the heat transfer rate increases.     

Optical measurement of acoustic pressure amplitudes-at the sensitivity limits of Rayleigh scattering

Rayleigh scattering is a measurement technique applicable for the determination of density distributions in various technical or natural flows. The current sensitivity limits of the Rayleigh scattering technique were investigated experimentally. It is shown that it is possible to measure density oscillations caused by acoustic pressure oscillations noninvasively and directly. Acoustical standing waves in a rectangular duct were investigated using Rayleigh scattering and compared to microphone measurements. The comparison showed a sensitivity of the Rayleigh scattering technique of 75 Pa (7·10(-4) kg/m(3)) and a precision of 14 Pa (1·10(-4) kg/m(3)). Therefore, it was also shown that Rayleigh scattering is applicable for acoustic measurements.     

瑞利布里渊光时域分析系统中电光调制器的理论模型与实验研究

瑞利布里渊光时域分析系统能够以非破坏性方式实现单光源、单端工作,利用强度型电光调制器同时调制脉冲基底和脉冲信号是获得该系统所需连续光和脉冲光的关键技术.本文理论分析、仿真和实验研究了一种将脉冲信号输入到电光调制器偏置端、微波信号输入到电光调制器射频端同时调制脉冲基底和脉冲信号的新调制方法,探讨了电光调制器用于瑞利布里渊光时域分析系统时的最佳工作点问题.结果表明,当调制脉冲基底和脉冲时分别将电光调制器偏置在传输曲线的谷点和峰点,并根据实际系统的组成和性能指标要求选择合适的微波调制信号幅度,可获得满足瑞利布里渊光时域分析系统要求的连续光和脉冲光.本文的研究结果为瑞利布里渊光时域分析系统的最佳化设计提供了理论依据.     

瑞利布里渊光时域分析系统中电光调制器的理论模型与实验研究

瑞利布里渊光时域分析系统能够以非破坏性方式实现单光源、单端工作,利用强度型电光调制器同时调制脉冲基底和脉冲信号是获得该系统所需连续光和脉冲光的关键技术.本文理论分析、仿真和实验研究了一种将脉冲信号输入到电光调制器偏置端、微波信号输入到电光调制器射频端同时调制脉冲基底和脉冲信号的新调制方法,探讨了电光调制器用于瑞利布里渊光时域分析系统时的最佳工作点问题.结果表明,当调制脉冲基底和脉冲时分别将电光调制器偏置在传输曲线的谷点和峰点,并根据实际系统的组成和性能指标要求选择合适的微波调制信号幅度,可获得满足瑞利布里渊光时域分析系统要求的连续光和脉冲光.本文的研究结果为瑞利布里渊光时域分析系统的最佳化设计提供了理论依据.     

Logarithmic corrections to scaling in turbulent thermal convection

We use a simplified model of turbulent convection to compute analytically heat transport in a horizontal layer heated from below, as a function of the Rayleigh and the Prandtl number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we recover power classical scaling regimes of the Nusselt versus Rayleigh number, with exponent 1/3 or 1/4. At larger Reynolds number, velocity and temperature fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the Nusselt versus Rayleigh or Prandtl. Instead, we obtain logarithmic corrections to the classical soft (exponent 1/3) or ultra-hard (exponent 1/2) regimes, in a way consistent with the most accurate experimental measurements available nowadays. This sets a need for the search of new measurable quantities that are less prone to dimensional theories.     

Large scale structures in Rayleigh-Bénard convection at high Rayleigh numbers

Direct numerical simulations of Rayleigh-Bénard convection in a plane layer with periodic boundary conditions at Rayleigh numbers up to 10(7) show that flow structures can be objectively classified as large or small scale structures because of a gap in spatial spectra. The typical size of the large scale structures does not always vary monotonically as a function of the Rayleigh number but broadly increases with increasing Rayleigh number. A mean flow (whose average over horizontal planes differs from zero) is also excited but is weak in comparison with the large scale structures. The large scale circulation observed in experiments should therefore be a manifestation of the large scale structures identified here.     

Plume dynamics in quasi-2D turbulent convection

We have studied turbulent convection in a vertical thin (Hele-Shaw) cell at very high Rayleigh numbers (up to 7x10(4) times the value for convective onset) through experiment, simulation, and analysis. Experimentally, convection is driven by an imposed concentration gradient in an isothermal cell. Model equations treat the fields in two dimensions, with the reduced dimension exerting its influence through a linear wall friction. Linear stability analysis of these equations demonstrates that as the thickness of the cell tends to zero, the critical Rayleigh number and wave number for convective onset do not depend on the velocity conditions at the top and bottom boundaries (i.e., no-slip or stress-free). At finite cell thickness delta, however, solutions with different boundary conditions behave differently. We simulate the model equations numerically for both types of boundary conditions. Time sequences of the full concentration fields from experiment and simulation display a large number of solutal plumes that are born in thin concentration boundary layers, merge to form vertical channels, and sometimes split at their tips via a Rayleigh-Taylor instability. Power spectra of the concentration field reveal scaling regions with slopes that depend on the Rayleigh number. We examine the scaling of nondimensional heat flux (the Nusselt number, Nu) and rms vertical velocity (the Peclet number, Pe) with the Rayleigh number (Ra(*)) for the simulations. Both no-slip and stress-free solutions exhibit the scaling NuRa(*) approximately Pe(2) that we develop from simple arguments involving dynamics in the interior, away from cell boundaries. In addition, for stress-free solutions a second relation, Nu approximately nPe, is dictated by stagnation-point flows occurring at the horizontal boundaries; n is the number of plumes per unit length. No-slip solutions exhibit no such organization of the boundary flow and the results appear to agree with Priestley's prediction of Nu approximately Ra(1/3). (c) 1997 American Institute of Physics.     

Physical model of the dependence of the Nusselt number on the Rayleigh number

The dependence of the Nusselt number on the Rayleigh number at the stage preceding the turbulent regime of convection is substantiated and obtained in analytic form. At this stage, the Nusselt number can be described by the power dependence on the Rayleigh number, which contains five constants. One of these constants is the same for all liquids and is the critical Rayleigh number Ra_cr = 1700 ± 51. The remaining four constants are strictly individual for each type of liquid. For liquid helium, the critical Rayleigh number Ra_cr = 35000 ± 4000 has the threshold value (Ra₁^mix)th = 37 085.75. This value is determined by the small ratio of the diameter of the vessel to its height, as well as the formation of a cylindrical convection cell at the bottom of the vessel with a mode number of 2 and a radial number determined by the fourth root of the firstorder Bessel function of the first kind.     

Thermal and inertial modes of convection in a rapidly rotating annulus

The nature of the primary instabilities that arise in a fluid contained in a fast rotating cylindrical annulus with slightly inclined plane top and bottom boundaries, radial gravity, and internal heating is numerically analyzed. It is shown that for moderate and high Prandtl numbers, the onset of convection is described by a competition of azimuthal thermal modes with different radial structure, which dominate in different regions of the parameter space. By the combined effect of the inclined ends and rotation, there are modes that are attached to the heated wall and slanted to the prograde direction of rotation, and others which are straight and fill the convective layer. Nevertheless, for very small Prandtl numbers the velocity field of the dominant modes corresponds essentially to the inertial solution of the Poincare equation, and the temperature perturbation is forced by this velocity field. In addition, a detailed exploration of the critical Rayleigh numbers and precession frequencies of the convective modes versus the radius ratio and the Coriolis parameter, for different Prandtl numbers, is presented.     

Influence of the Interface Kinetics of Crystallization and Dissolution on the Scaling Laws in Solution System for Crystal Growth

The influence of interface kinetics on scaling laws in a solution system for crystal growth is studied. Because the variation of the solution density caused by the solute concentration change can be omitted and only that caused by the temperature change is taken into account, the interface kirtcrics does not affect the scaling laws of the fluid velocity and the temperature distribution index S_θ. By taking the interface kinetics into account, the curves of the concerltration distriluriun index S_Φ versus the Rayleigh number Ra, the Prandtl number Pr or the Schmidt number Sc are changed. When Ra and Sc are small, S_Φ approaches a constant S_Φ⁰: independent of Ra, Sc and λ. When Ra and Sc are large, the influence of the interface kinetics on the curves of S_Φ is negligible. The interface kinetics affects the curves of the average dimensionley crystal growth rate V_cg versus Ra, Sc or Pr only when Ra and Sc are large. In this case, V_cg is still a power function of Ra, Pr or Sc in certain regions of the parameter (Ra, Pr and Sc) space, but the esponents and coefficients of porver functions are varied.     

Full investigation of the backscattering in resonator fiber optic gyro

Resonator Fiber optic gyro (RFOG) is a high accuracy inertial rotation sensor based on the Sagnac effect. The optical fiber ring resonator (OFRR) is the key rotation sensing element. The backscattering characteristics of the OFRR are fully investigated. The Rayleigh backscattering dominates the backscattering spectrum with the input power below the threshold. High carrier suppression is crucial to reduce this Rayleigh backscattering error. Being different from the intrinsic Rayleigh scattering of the fiber, the stimulated Brillouin scattering (SBS) in the OFRR should be avoided. This is because the finesse and the resonance notch depth of the OFRR decrease for the pump depletion through the SBS process. The shot noise limited sensitivity (SLS) of the RFOG is improved by increasing the input power. Through analysis, it is found that the threshold input power is improved after phase modulation. The SLS of the RFOG is analyzed at different modulation parameters and its relevant SBS threshold. Accordingly, the optimized modulation frequency and the corresponding maximum input power are all obtained. A simple method of testing the frequency shift in the SBS is also proposed. In this method, the central frequency of the laser source is locked to the resonance frequency of the OFRR in one direction. A steady SBS light is observed and its frequency shift is measured together.