A model for universal spatial variations of temperature fluctuations in turbulent Rayleigh-Bénard convection

We propose a theoretical model for spatial variations of the temperature variance σ~2( z, r)( z is the distance from the sample bottom and r the radial coordinate) in turbulent Rayleigh-Bénard convection(RBC).Adapting the "attached-eddy" model of shear flow to the plumes of RBC, we derived an equation for σ~2 which is based on the universal scaling of the normalized RBC temperature spectra. This equation includes both logarithmic and power-law dependences on z/λ_(th), where λ_(th) is the thermal boundary layer thickness. The equation parameters depend on r and the Prandtl number Pr, but have only an extremely weak dependence on the Rayleigh number Ra Thus our model provides a near-universal equation for the temperature variance profile in turbulent RBC.     

Effects of variable viscosity and temperature modulation on linear Rayleigh-Bénard convection in Newtonian dielectric liquid

The linear Rayleigh-Bénard electro-convective stability of the Newtonian dielectric liquid is determined theoretically subject to the temperature modulation with time. A perturbation method is used to compute the critical Rayleigh number and the wave number. The critical Rayleigh number is calculated as a function of the frequency of modulation, the temperature-dependent variable viscosity, the electric field dependent variable viscosity, the Prandtl number, and the electric Rayleigh number. The effects of all three cases of modulations are established to delay or advance the onset of the convection process. In addition, how the effect of variable viscosity controls the onset of convection is studied.     

Onset of Rayleigh-Bénard convection in gases - classical and extended thermodynamics

This paper deals with the determination of the critical parameters that induce instability in the Rayleigh-Bénard arrangement, viz. a gas confined between two rigid plates and heated from below. In order to compute the critical values of the parameters, classical thermodynamics with the Navier-Stokes and Fourier constitutive relations and extended thermodynamics with thirteen moments are used. Linear stability analysis is performed. The results of both theories are illustrated and compared.Received: 26 August 2003, Accepted: 1 September 2003, Published online: 5 December 2003     

Küppers-Lortz instability in rotating Rayleigh-Bénard convection in a porous medium

The Darcy-Lapwood-Brinkman model with the Boussinesq approximation is used to study Küppers-Lortz (KL) instability in the nonlinear regime of rotating Rayleigh-Bénard convection in a sparsely packed porous medium near the onset of stationary convection. The threshold Taylor numbers and critical angles for the onset of KL instability are obtained for different values of Λ, M for finite Prandtl numbers (1.5≤Pr≤100). Heat transfer is studied from Nusselt number at the onset of stationary convection.     

Low-Prandtl-number Bénard–Marangoni convection in a vertical magnetic field

The effect of a homogeneous magnetic field on surface-tension-driven Bénard convection is studied by means of direct numerical simulations. The flow is computed in a rectangular domain with periodic horizontal boundary conditions and the free-slip condition on the bottom wall using a pseudospectral Fourier–Chebyshev discretization. Deformations of the free surface are neglected. Two- and three-dimensional flows are computed for either vanishing or small Prandtl number, which are typical of liquid metals. The main focus of the paper is on a qualitative comparison of the flow states with the non-magnetic case, and on the effects associated with the possible near-cancellation of the nonlinear and pressure terms in the momentum equations for two-dimensional rolls. In the three-dimensional case, the transition from a stationary hexagonal pattern at the onset of convection to three-dimensional time-dependent convection is explored by a series of simulations at zero Prandtl number.     

Measurement of gas transfer across wind-forced wavy air–water interfaces using laser-induced fluorescence

Optical distortions have previously prevented non-intrusive measurements of dissolved oxygen concentration profiles by Laser induced fluorescence (LIF) to within 200 μm of the air–water interface. It is shown that by careful experimental design, reliable measurements can be obtained within 28 μm of moving air–water interfaces. Consideration of previously unidentified optical distortions in LIF imagery due to non-linear effects is presented that is critical for robust LIF data processing and experimental design. Phase resolved gas flux measurements have now been accomplished along wind forced microscale waves and indicate that the highest mean gas fluxes are located in the wave troughs. The local mean oxygen fluxes as determined by LIF techniques can be reconciled to within 40% of those obtained by bulk measurement in the water. These data provide a new perspective on wind-wave enhancement of low solubility gas transfer across the air–water interface.     

Tomographic particle-image velocimetry and thermography in Rayleigh-Bénard convection using suspended thermochromic liquid crystals and digital image processing

Steady-state flow and temperature fields in shallow rectangular enclosures heated from below were visualized and quantitatively characterized by using glycerol as the working fluid and suspended thermochromic liquid crystals as tracers. Couples of photographs taken on 120 transparency film for two orthogonal sets of vertical plane sections were digitized by a 1,200-dpi flatbed scanner and split into HSL (hue-saturation-lightness) components by using commercial general-purpose image processing software. Two-dimensional velocity fields were obtained from the lightness component by a two-frame cross-correlation technique using a commercial particle-image velocimetry (PIV) package. Temperature fields were obtained from the hue component on the basis of an in situ calibration procedure, conducted under conditions of stable thermal stratification. Finally, 2D flow and temperature distributions were interpolated by a purpose-written Fortran program to give 3D flow and thermal fields in the enclosure. Results are presented here for the case of a 1:2:4 aspect ratio cavity at a Rayleigh number of ∼ 14,500, for which a complex 3D flow and temperature distribution was observed. Published online: 7 January 2003     

Rayleigh-Bénard湍流对流实验研究进展

近十年来,人们的注意力集中到关于Ｒｎｙｌｅｉｇｈ－Ｂｅｎａｒｄ硬湍流对流的研究,得到了硬湍流状态下温度场和速度场的主要特征,证实了大尺度环流在热对流中起主导作用等,但对大尺度环流与周围流体及热卷流的相互作用机理还不很清楚,硬湍流是否为Ｒｎｙｌｅｉｇｈ－Ｂｅｎａｒｄ对流的极限状态仍有不同看法,本文将对有关这方面的研究进展作一简要的回顾,并就今后的研究工作发表一些看法．     

Rayleigh-Bénard湍流对流实验研究进展

近十年来,人们的注意力集中到关于Ｒａｙｌｅｉｇｈ－Ｂｅｎａｒｄ硬湍流对流的研究,得到了硬湍流状态下温度场和速度场的主要特征,证实了大惊工充在热对流中起主导作用等,但对大尺度环流与周围流及热郑注的相互作用机理还不很清楚,硬湍流是否为Ｒａｙｌｅｉｇｈ－Ｂｅｎａｒｄ对流的极限状态仍有不同看法,本文将对有关这方面的研究进展作一简要的回顾,并就今后的研究表一些看法。     

Rayleigh–Bénard convection driven by a long wavelength heating

Natural convection in a two-dimensional horizontal layer has been investigated. The layer is confined between two parallel horizontal plates. The upper plate is kept isothermal, while the lower plate has an externally imposed, long wavelength, spatially sinusoidal heating with the amplitude expressed in terms of the Rayleigh number Ra and the wavelength characterized by the wave number α. Only steady-state flow structures and their bifurcations have been considered. The detailed analysis has been carried out for two Prandtl numbers, i.e. Pr = 0.7 and Pr = 7, and only small differences in the bifurcation diagrams have been observed. When Ra < Ra _cr = 427, convection has a simple topology consisting of one pair of counter-rotating rolls per heating period. Secondary motion in the form of rolls aligned in the direction of the primary rolls and concentrated around the hot spots occurs for Ra > 427. When 427 < Ra < ～470 and α < ～0.14, the secondary motion is described by the supercritical pitchfork bifurcation. One of the branches of this bifurcation is associated with an odd number of secondary rolls per half wavelength, with rolls above the hot spots rotating in the direction opposite to the primary rolls. The other branch is associated with an even number of secondary rolls per half wavelength, with the rolls above the hot spots co-rotating with the primary rolls. The new rolls are pinched off in pairs when α decreases. When Ra > ～470 and α > ~0.14, bifurcation assumes the form of “bifurcation from infinity”. The main branch is associated with one pair of rolls per heating period for α > 0.25. Decrease in α along this branch results in the formation of secondary rolls, with the rolls at the hot spot co-rotating with the primary rolls. The lower part of the other branch is associated with one pair of rolls per heating period in the limit α → 0. Increase in α results in pinching off a single roll which counter-rotates with respect to the primary roll at the hot spot.     

Remarks on the Rayleigh-Bénard Convection on Spherical Shells

The main objective of this article is to study the effect of spherical geometry on dynamic transitions and pattern formation for the Rayleigh-Bénard convection. The study is mainly motivated by the importance of spherical geometry and convection in geophysical flows. It is shown in particular that the system always undergoes a continuous (Type-I) transition to a 2l _c -dimensional sphere ${S^{2l_c}}$ , where l _c is the critical wave number corresponding to the critical Rayleigh number. Furthermore, it has shown in Ma and Wang (Physica D 239:3–4, 167–189, 2010) that it is critical to add nonisotropic turbulent friction terms in the momentum equation to capture the large-scale atmospheric and oceanic circulation patterns. We show in particular that the system with turbulent friction terms added undergoes the same type of dynamic transition, and obtain an explicit formula linking the critical wave number (pattern selection), the aspect ratio, and the ratio between the horizontal and vertical turbulent friction coefficients.     

Henri Bénard: Thermal convection and vortex shedding

We present in this article the work of Henri Bénard (1874–1939), a French physicist who began the systematic experimental study of two hydrodynamic systems: the thermal convection of fluids heated from below (the Rayleigh–Bénard convection and the Bénard–Marangoni convection) and the periodical vortex shedding behind a bluff body in a flow (the Bénard–Kármán vortex street). Across his scientific biography, we review the interplay between experiments and theory in these two major subjects of fluid mechanics.     

Rayleigh-Bénard湍流热对流研究的进展、现状及展望

对流现象广泛存在于恒星和行星里.在地球上,对流现象在诸如大气、海洋、地核和地幔等众多动力学系统中起着重要作用.Rayleigh-Bénard(RB)湍流热对流系统是从这些复杂的自然现象中抽象出来的研究对流问题的经典流体力学模型.本文主要从湍流传热、羽流、大尺度流动结构、速度和温度脉动的小尺度统计和非传统RB对流等几个方面着重评述近年来RB对流的若干研究新进展,并对今后的研究做出展望.     

二维Rayleigh-Bénard对流问题稳定性的数值追踪

用分解算子法和延续算法对二维Ｒａｙｌｅｉｇｈ－Ｂｅｎａｒｄ对流问题的稳定性进行了数值追踪研究．画出了 Ｐｒ＝ １０时不同 Ｒａ所对应的流线，等涡线和等温线图；并求出了对于不同Ｐｒ数所对应的临界Ｒａ数，其值大约为２７４０，计算结果与物理分析相一致，与三维实验结果比较也合理．     

Eventually vanished solutions of a forced Liénard system

In this paper, we aim to find eventually vanished solutions, a special class of bounded solutions which tend to 0 as t → ±∞）, to a Lienard system with a time-dependent force. Since it is not a Hamiltonian system with small perturbations, the well-known Melnikov method is not applicable to the determination of the existence of eventually vanished solutions. We use a sequence of periodically forced systems to approximate the considered system, and find their periodic solutions. Difficulties caused by the non- Hamiltonian form are overcome by applying the Schauder＇s fixed point theorem. We show that the sequence of the periodic solutions has an accumulation giving an eventually vanished solution of the forced Lienard system.     

Nonlinear stability analysis of the Bénard problem for fluids with a convex nonincreasing temperature depending viscosity

A nonlinear energy stability analysis of the onset of convection for fluids with viscosity convex nonincreasing function of temperature, is performed. It is shown that condition assuring linear stability, assures nonlinear (conditional) asymptotic stability too.     

Simultaneous velocity and concentration measurements in the near field of a turbulent low-pressure jet by digital particle image velocimetry–planar laser-induced fluorescence

The main purpose of this work is to develop a method for simultaneous measurement of velocity and passive scalar concentration by means of digital particle image velocimetry and planar laser-induced fluorescence. Details of the implementation of the method are given, and the technique is applied to measurements of concentration and velocity in the centre-plane of a liquid jet with a Reynolds number of 6,000. The measurements are compared with large eddy simulations. Mean velocities and concentrations, fluctuating velocities and concentrations, and correlation between fluctuating velocities and concentrations are analysed for the first six diameters downstream of the jet exit. The general agreement between measured and simulated results was found to be good, in particular for mean quantities. Mean profiles are also found to be in good agreement with other experimental work on jets reported in the literature. The “whole-plane” measurement method was found to be very useful for detailed comparisons of turbulent statistics with simulated data. The inadequacy of models for turbulent mass transport based on the standard gradient diffusion concept is demonstrated through the experimental data. Received: 4 October 2000/Accepted: 27 November 2000     

具有水平流动的Rayleigh-Bénard对流进口段特性分析

采用SIMPLE算法对二维流体力学基本方程组进行了数值模拟,对普朗特数Pr=0.0272的具有水平流动的Rayleigh-Bénard对流进口段特性进行了研究。结果表明,在某些流体参数下具有水平流动的Rayleigh-Bénard对流由进口段和行波对流段组成,进口段长度取决于雷诺数和相对瑞利数。对于雷诺数Re=150的情况,当相对瑞利数r≤4时腔体内是水平流动;当r≥12时腔体内是行波对流;在40随着雷诺数变化的表达式。进口段长度随相对瑞利数的增大而减小,随着雷诺数的增大而增大。行波对流区的对流波数随着雷诺数的增大而减小。     

水平流动对周期加热的Rayleigh-Bénard对流的影响

采用二维流体力学基本方程组对普朗特数Pr=0.0272的具有水平流动周期性加热的Rayleigh-Bénard对流特性进行数值模拟.结果说明,当相对瑞利数给定时,对流斑图的形成取决于水平流动强度.由对流斑图随着时间的变化确定了对流周期.随着相对瑞利数的减小,对流周期适应的水平流动强度减小,并且水平流动强度的存在范围减小.随着相对瑞利数的增加,对流周期变小.随着水平流动强度的增加,对流周期变小,并且对流周期变化的梯度变小.随着水平流动强度的增加,两个局部行波对流区的范围减小,水平流动区间增加.然后,随着水平流动强度的进一步增加,第一对流区先消失.当水平流动强度足够大时第二对流区也消失.腔体内形成水平流动.随着相对瑞利数的增大,第一对流区和第二对流区消失的临界水平流动强度也增大.