by Lui Siu Lung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 132-136). / by Lui Siu Lung. / Abstract --- p.i / Acknowledgements --- p.ii / Table of Contents --- p.iii / List of Figures --- p.v / Chapter / Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- The Parameters --- p.1 / Chapter 1.2 --- The Stories of Turbulent Convection --- p.2 / Chapter 1.3 --- The Models: Plumes with no Flow or a Flow with no Plumes? --- p.3 / Chapter 1.4 --- Building up the Picture --- p.5 / Chapter 1.5 --- Starting Point of the Experiment --- p.6 / Chapter 2. --- Setup of the Experimental Environment --- p.8 / Chapter 2.1 --- The Convection Cell --- p.8 / Chapter 2.2 --- The Temperature Probe --- p.12 / Chapter 2.3 --- The Thermistors --- p.15 / Chapter 2.4 --- The Large Scale Circulation and the Plumes --- p.19 / Chapter 2.5 --- Building up the Convection --- p.22 / Chapter 3. --- Hard Turbulence Properties and Scalings in the Normal Cell --- p.27 / Chapter 3.1 --- Heat Transfer Efficiency --- p.27 / Chapter 3.2 --- Thermal Boundary Layer --- p.32 / Chapter 3.3 --- The RMS Temperature Fluctuation --- p.39 / Chapter 3.4 --- Temperature Time Series --- p.42 / Chapter 3.5 --- Histograms --- p.48 / Chapter 3.6 --- Power Spectrum --- p.53 / Chapter 3.7 --- Summary on the Normal Cell --- p.56 / Chapter 4. --- Horizontal-Position-Dependent Thermal Boundary Layer --- p.58 / Chapter 4.1 --- Orientation --- p.59 / Chapter 4.2 --- Along the Large Scale Circulation --- p.60 / Chapter 4.3 --- Perpendicular to the Large Scale Circulation --- p.70 / Chapter 4.4 --- Horizontal Measurement for the A = 2 Cell --- p.78 / Chapter 4.5 --- Summary on the Horizontal Measurement --- p.81 / Chapter 5. --- Sphere in the Cell --- p.84 / Chapter 5.1 --- Heat Transfer Efficiency --- p.84 / Chapter 5.2 --- Thermal Boundary Layer --- p.86 / Chapter 5.3 --- The RMS Temperature Fluctuation --- p.87 / Chapter 5.4 --- Temperature Time Series --- p.88 / Chapter 5.5 --- Histograms --- p.92 / Chapter 5.6 --- Summary on the Sphere Cell --- p.94 / Chapter 6. --- Fingers in the Cell --- p.96 / Chapter 6.1 --- The Gear Cell --- p.96 / Chapter 6.1.1 --- Heat Transfer Efficiency --- p.96 / Chapter 6.1.2 --- Thermal Boundary Layer --- p.98 / Chapter 6.1.3 --- Flow Pattern in the Gear Cell --- p.100 / Chapter 6.1.4 --- Temperature Time Series --- p.104 / Chapter 6.1.5 --- Histograms --- p.109 / Chapter 6.1.6 --- Power Spectrum --- p.110 / Chapter 6.2 --- The Finger Cell --- p.117 / Chapter 6.2.1 --- Heat Transfer Efficiency --- p.117 / Chapter 6.2.2 --- Temperature Time Series --- p.120 / Chapter 6.2.3 --- Histograms --- p.122 / Chapter 6.2.4 --- Power Spectrum --- p.125 / Chapter 6.3 --- Summary on the Finger Cells --- p.127 / Chapter 7. --- Conclusions --- p.129 / References --- p.132 / Appendix --- p.137

Rayleigh-Bénard convection has been extensively studied in literature owing to its ubiquitous nature. However, most of the studies have been confined to geometries where the aspect ratio of the cylinder was less than 1. Here we study the motion of fluid in geometries with aspect ratio greater than 1, with particular application to use of such motion to actuate biochemical reactions, such as the polymerase chain reaction. We show that it is possible to accelerate the rate of reaction by using a geometry that promotes chaotic motion versus a geometry that promotes quasi- periodic motion. We also simulate chemical kinetics using the fluid motion as a starting point and we prove that chaotic motion indeed enhances the rate of the reaction. We also provide qualitative and quantitative measures for chaotic motion in a fluid flow, which helps to distinguish between different types of fluid motion. We highlight the transitions between different types of flow that are possible with Rayleigh-Bénard convection. Finally, we compare our simulations against experimental data obtained from particle image velocimetry, laser induced fluorescence and optical microscopic visualization.

Numerical simulations of combined buoyant and surface tension driven flow, also known as Rayleigh-Bénard-Marangoni (RBM) convection are conducted for heated fluid layers of small aspect ratio (defined as the ratio of the horizontal extent of the domain divided by the depth of the fluid) in square cross-section containers. A particular non-dimensionalization of the governing equations is developed in which the aspect ratio of the domain appears as a continuous parameter. The simulations extend and enhance existing experimental studies of the RBM convection phenomenon by mapping continuous solution branches in aspect ratio and Marangoni number parameter space. Key implementation aspects of the development of the adaptive mesh refinement (AMR) library libMesh are discussed, and a series of simulations of the RBM problem with a stick-slip boundary condition demonstrate the suitability of AMR for computing these flows. / text

The transport of a species in complex flow fields is an important phenomenon related to many areas in science and engineering. There has been significant progress theoretically and experimentally in understanding active transport in steady, periodic flows such as a chain of vortices but many open questions remain for transport in complex and chaotic flows. This thesis investigates the active transport in a three-dimensional, time-dependent flow field characterized by a spatiotemporally chaotic state of Rayleigh-Be?nard convection. A nonlinear Fischer-Kolmogorov-Petrovskii-Piskunov reaction is selected to study the transport within these flows. A highly efficient, parallel spectral element approach is employed to solve the Boussinesq and the reaction-advection-diffusion equations in a spatially-extended cylindrical domain with experimentally relevant boundary conditions. The transport is quantified using statistics of spreading and in terms of active transport characteristics like front speed and geometry and are compared with those results for transport in steady flows found in the literature. The results of the simulations indicate an anomalous diffusion process with a power law 2 < ? < 5/2 a result that deviates from other superdiffusive processes in simpler flows, and reveals that the presence of spiral defect chaos induces strongly anomalous transport. Additionally, transport was found to most likely occur in a direction perpendicular to a convection roll in the flow field. The presence of the spiral defect chaos state of the fluid convection is found to enhance the front perimeter by t^3/2 and by a perimeter enhancement ratio r(p) = 2.3. / Master of Science

Une caractéristique remarquable de la convection de Rayleigh-Bénard qui concerne une couche de fluide horizontale chauffée par le bas et refroidie par le haut, est l’établissement spontané de l’ordre spatial et la formation d’une circulation cohérente à grande échelle. Comment les différents facteurs, tels que la géométrie du domaine et les conditions limites, influencent l’écoulement à grande échelle, restent une question ouverte. Malgré sa simplicité apparente, la convection de Rayleigh-Bénard présente une dynamique à grande échelle incroyablement riche et complexe, tels que des modes de torsion et du battement, la rotation du plan et des cessations de la circulation, qui coexistent souvent et se concourent. Une approche couramment utilisée dans l’étude des cessations, consiste à contraindre la circulation à grande échelle à un plan en limitant le domaine fluide à une cellule carrée (2D) ou à une cellule rectangulaire mince (quasi-2D). Cependant, il n’est pas tout à fait clair si les retournements 2-D et (quasi-)2-D correspondent au même phénomène. Le présent document est consacré à l’étude des modes d’écoulement à grande échelle dans la convection turbulente de Rayleigh-Bénard et de l’influence exercée par différents facteurs sur les structures d’écoulement et sur leur évolution temporelle. La caractérisation proposée combine une analyse statistique avec une approche physique s’appuyant sur le moment angulaire ainsi que sur les énergies cinétiques et potentielles pour mettre en évidence les mécanismes physiques sous-jacents. Nous essayons ensuite de relier ces mécanismes à chacun des modes d’écoulement distinctifs observés et à leur évolution. / One outstanding feature of the Rayleigh-Bénard problem which concerns a horizontal fluid layer heated from below and cooled from above, is the spontaneous establishment of spatial ordering and the formation of a coherent large-scale circulation. How different factors, such as the domain geometry and boundary conditions, influence the sizes and shapes of the large-scale flow remains an open question. Despite its apparent simplicity, Rayleigh-Bénard convection exhibits some incredibly rich and complex large-scale dynamics such as torsional modes, rotation, sloshing, and cessations, which often coexist and compete to each other. One approach, commonly used in the study of cessations is to constrain the large scale circulation to a plane by restricting the fluid domain to a (2-D) square cell or to a slim rectangular cell of small aspect ratio in the transversal direction. However, it is not entirely clear whether the 2-D and (quasi-)2-D reversals correspond to the same phenomenon. The present document is dedicated to the study of the large-scale flow patterns in turbulent Rayleigh-Bénard convection, and of the influence exerted by different factors on the flow structures and on their temporal evolution. The proposed characterization combines a statistical analysis with a physical approach relying on the angular momentum as well as the kinetic and potential energies to highlight the underlying physical mechanisms. We subsequently attempt to tie these mechanisms together to each of the distinctive flow patterns observed and to their evolution.

Dans la configuration de Rayleigh-Bénard, on considère une fine couche de fluide placée entre deux parois horizontales, chauffée par le bas et refroidie par le haut. Cette couche peut être le siège d'une instabilité si le gradient thermique est suffisamment important : on passe alors de l'état conductif à l'état convectif et on parle de bifurcation primaire pour qualifier cette première transition. Cette mise en mouvement du fluide se fait de manière ordonnée : on constate ainsi l'émergence de différents motifs de convection comme des rouleaux, des carrés ou encore des hexagones. Ces structures vont à leur tour subir des instabilités qualifiées de secondaires qui vont limiter la gamme de nombres d'onde stables. On étudie ici théoriquement ces instabilités d'une part à proximité du seuil de la convection grâce à une approche faiblement non linéaire, d'autre part loin des conditions critiques grâce à une approche fortement non linéaire. Le fluide est rhéofluidifiant, ce qui correspond au comportement rhéologique le plus fréquemment rencontré, et est décrit par le modèle de Carreau. À proximité du seuil, on considère deux situations : la première correspond au cas où les plaques ont une conductivité finie, la seconde à celui d'un fluide thermodépendant. Dans chaque cas, l'influence du caractère rhéofluidifiant sur la nature du motif émergeant à la bifurcation primaire et sur les instabilités secondaires est mise en évidence. Pour étudier les motifs de convection loin des conditions critiques, on a recours à une procédure de continuation permettant de déterminer de proche en proche les caractéristiques de l'écoulement comme les champs de vitesse ou de température ainsi que le nombre de Nusselt. / In the Rayleigh-Bénard configuration, we consider a thin layer of fluid confined between two horizontal slabs which is heated from below and cooled from above. This layer undergoes an instability if the thermal gradient is strong enough: a transition from the conductive state to the convective state and called _ primary bifurcation _occurs. Moreover, it happens in an ordered way: we can notice the emergence of various convection patterns such as rolls, squares or hexagons. In their turn, these patterns undergo _ secondary instabilities _ that limit the range of stable wavenumbers. These instabilities are studied theoretically _firstly near the threshold thanks to a weakly nonlinear approach, and secondly far from critical conditions thanks to a strongly nonlinear approach. We consider a shear thinning fluid, the most common rheological behavior, which is described by the Carreau model. Near the threshold, two situations are considered: the first corresponds to finite conductivity plates, the second corresponds to a thermodependent fluid. In each case, the influence of the shear thinning effect on the nature of the pattern emerging at the primary bifurcation and on secondary instabilities is highlighted. To study the convection patterns far from the critical conditions, a continuation procedure is used to determine, step-by-step, the characteristics of the flow, such as the velocity or temperature fields and the Nusselt number.

Kwok Chun-yin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves [121]-122). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Experimental data --- p.7 / Chapter 2.1 --- Turbulent Convection using Helium --- p.7 / Chapter 2.2 --- Turbulent Convection using water --- p.8 / Chapter 3 --- Probability Distribution and Scaling behavior --- p.9 / Chapter 3.1 --- PDF of YT --- p.9 / Chapter 3.1.1 --- Helium Convection --- p.10 / Chapter 3.1.2 --- Water Convection --- p.26 / Chapter 3.1.3 --- Comparison between helium data and Water data --- p.34 / Chapter 3.2 --- T -dependence of the moments of XT --- p.39 / Chapter 3.2.1 --- Helium Convection --- p.39 / Chapter 3.2.2 --- Water Convection --- p.47 / Chapter 4 --- Hierarchical Moment Relation --- p.50 / Chapter 4.1 --- Method of Analysis --- p.50 / Chapter 4.2 --- Results and Discussion --- p.53 / Chapter 4.2.1 --- Helium Convection --- p.53 / Chapter 4.2.2 --- Water Convection --- p.81 / Chapter 5 --- Discussion and Conclusion --- p.95 / Chapter 5.1 --- Passive Scalar --- p.96 / Chapter 5.2 --- Comparison between Turbulent Convection and Passive Scalar --- p.99 / Chapter 5.3 --- Scaling behavior for length scale above and below the Bolgiano scale for turbulent convection using Helium gas --- p.100 / Chapter 5.4 --- Conclusions --- p.107 / Chapter A --- The lognormal model --- p.108 / Chapter B --- Definition of XT --- p.110 / Chapter C --- Reasons for analysis of (xTp) for p≤ 12 --- p.112 / Chapter D --- Functional form of μp implied by the hierarchical relation --- p.119 / Bibliography --- p.122

Zhou Sheng-qi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 66-70). / Text in English; abstracts in English and Chinese. / Zhou Sheng-qi. / Abstract (in Chinese) --- p.i / Abstract (in English) --- p.ii / Acknowledgement --- p.iii / Table of Contents --- p.iv / List of Figures --- p.vi / List of Tables --- p.viii / Chapter / Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Turbulence: a Universal Problem --- p.1 / Chapter 1.2 --- Rayleigh-Benard Convection --- p.2 / Chapter 1.2.1 --- The History of Rayleigh-Benard Convection --- p.2 / Chapter 1.2.2 --- The Dimensionless Parameters --- p.4 / Chapter 1.2.3 --- The Physical Picture of Turbulent Convection --- p.5 / Chapter 1.3 --- Motivation of This Study --- p.8 / Chapter 2. --- Theoretical Base and Experimental Setup --- p.11 / Chapter 2.1 --- The Rayleigh-Benard problem --- p.11 / Chapter 2.1.1 --- The Boussinesq approximation --- p.11 / Chapter 2.1.2 --- The Convection Equation --- p.13 / Chapter 2.2 --- Experimental Setup and Measurement --- p.14 / Chapter 2.2.1 --- The Convection Cell --- p.14 / Chapter 2.2.2 --- The Power Supply and the Refrigerated Recirculator --- p.19 / Chapter 2.2.3 --- The Temperature Probes --- p.19 / Chapter 2.2.4 --- The Temperature Measurement System --- p.20 / Chapter 2.2.5 --- Building up the Convection State --- p.25 / Chapter 3. --- Temperature Power Spectra and the Viscous Boundary Layer in the Thermal Turbulence --- p.27 / Chapter 3.1 --- The Power Spectra Method --- p.27 / Chapter 3.2 --- The Suspicions of the Power Spectra Method --- p.30 / Chapter 3.3 --- Discussion of the Experimental Results --- p.32 / Chapter 3.4 --- Summary --- p.39 / Chapter 4. --- The Correlation Function of Temperature --- p.40 / Chapter 4.1 --- Preparation of Experiment --- p.41 / Chapter 4.1.1 --- Apparatus --- p.41 / Chapter 4.1.2 --- Definition of correlation function --- p.41 / Chapter 4.2 --- Results and Discussion --- p.44 / Chapter 4.2.1 --- The Delay Time (¡’0) --- p.47 / Chapter 4.2.2 --- The Maximum Correlation Coefficient (R) --- p.52 / Chapter 4.2.3 --- The Half Width (¡’h) --- p.58 / Chapter 4.3 --- Summary --- p.61 / Chapter 5. --- Conclusions --- p.63 / References --- p.66

Xi Hengdong = 關於熱羽流和Rayleigh-Bénard對流中大尺度環流形成的實驗研究 / 郗恒東. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 71-75). / Text in English; abstracts in English and Chinese. / Xi Hengdong = Guan yu re yu liu he Rayleigh-Bénard dui liu zhong da chi du huan liu xing cheng de shi yan yan jiu / Xi Hengdong. / Table of Contents --- p.v / List of Figures --- p.xi / List of Tables --- p.xii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Rayleigh-Benard System --- p.1 / Chapter 1.1.1 --- Physical Picture --- p.1 / Chapter 1.1.2 --- Characteristic Parameters --- p.2 / Chapter 1.2 --- Plume and Large Scale Circulation --- p.4 / Chapter 2 --- Experimental Setup and Techniques --- p.8 / Chapter 2.1 --- Apparatus --- p.8 / Chapter 2.1.1 --- Convection Cell --- p.8 / Chapter 2.1.2 --- Other Apparatus --- p.12 / Chapter 2.2 --- Visualization --- p.14 / Chapter 2.3 --- PIV technique --- p.17 / Chapter 2.3.1 --- Image Capture System --- p.20 / Chapter 2.3.2 --- Image Analysis system --- p.26 / Chapter 3 --- Properties of Laminar Plume --- p.30 / Chapter 3.1 --- Shadowgraph and Temperature measurement --- p.30 / Chapter 3.2 --- Velocity Measurement --- p.35 / Chapter 4 --- Onset of Large-scale circulation in turbulent thermal convec- tion --- p.48 / Chapter 5 --- Convection in Rectangular cell --- p.60 / Chapter 6 --- Conclusion --- p.69 / Chapter 6.1 --- Conclusion --- p.69 / Chapter 6.2 --- Perspective for further investigation --- p.71 / Bibliography --- p.72

Cheung Yin Har = 瑞利-柏納德湍流對流中Nusselt與縱橫比的關係以及邊界層性質的研究 / 張燕霞. / Thesis submitted in: October 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 115-119). / Text in English; abstracts in English and Chinese. / Cheung Yin Har = Ruili-Bonade tuan liu dui liu zhong Nusselt yu zong heng bi de guan xi yi ji bian jie ceng xing zhi de yan jiu / Zhang Yanxia. / Abstract --- p.i / 摘要 --- p.iii / Acknowledgments --- p.iv / Contents --- p.v / List of Figures --- p.vii / List of Tables --- p.x / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background of turbulence --- p.1 / Chapter 1.2 --- Rayleigh-Benard convection --- p.3 / Chapter 1.3 --- Theoretical background --- p.4 / Chapter 1.3.1 --- The convection equations --- p.4 / Chapter 1.3.2 --- Characteristic parameters --- p.6 / Chapter 1.3.3 --- Reynolds equations --- p.8 / Chapter 1.4 --- Recent developments --- p.10 / Chapter 1.4.1 --- Heat transport --- p.10 / Chapter 1.4.2 --- Large scale flow and thermal plumes --- p.11 / Chapter 1.4.3 --- Boundary layers --- p.12 / Chapter 1.5 --- Motivation --- p.14 / Chapter 1.5.1 --- Nusselt measurements --- p.14 / Chapter 1.5.2 --- Boundary layer properties measurements --- p.14 / Chapter 1.6 --- Synopsis of this thesis --- p.15 / Chapter Chapter 2 --- Experimental setup and measurement techniques --- p.17 / Chapter 2.1 --- The turbulent convection system --- p.17 / Chapter 2.1.1 --- The convection cells --- p.18 / Chapter 2.1.2 --- The temperature probe --- p.21 / Chapter 2.1.3 --- The thermistors --- p.23 / Chapter 2.2 --- Particle Image Velocimetry (PIV) --- p.25 / Chapter 2.2.1 --- Image capture system --- p.27 / Chapter 2.2.2 --- Image analysis system --- p.36 / Chapter Chapter 3 --- Aspect ratio dependence of heat transport and the flow field --- p.39 / Chapter 3.1 --- Motivation for this experiment --- p.39 / Chapter 3.2 --- Heat transfer efficiency measurements --- p.40 / Chapter 3.3 --- Heat correction --- p.44 / Chapter 3.3.1 --- Temperature correction --- p.44 / Chapter 3.3.2 --- Heat current density J correction --- p.45 / Chapter 3.3.3 --- Finite conductivity of plate --- p.50 / Chapter 3.4 --- Aspect ratio dependence --- p.51 / Chapter 3.4.1 --- Without correction of finite conductivity --- p.51 / Chapter 3.4.2 --- With correction of finite conductivity --- p.59 / Chapter 3.5 --- Time-averaged velocity field --- p.65 / Chapter 3.6 --- Summary --- p.70 / Chapter Chapter 4 --- Local temperature and velocity measurements near the boundary layers --- p.71 / Chapter 4.1 --- Motivation for this experiment --- p.71 / Chapter 4.2 --- Temperature profile measurement --- p.72 / Chapter 4.2.1 --- Temperature and fluctuation profiles --- p.73 / Chapter 4.2.2 --- Thermal boundary thickness --- p.77 / Chapter 4.2.3 --- Temperature time series --- p.79 / Chapter 4.2.4 --- PDF --- p.83 / Chapter 4.3 --- Velocity profile measurement --- p.86 / Chapter 4.3.1 --- 2D velocity and fluctuation profiles --- p.86 / Chapter 4.3.2 --- Scaling properties --- p.93 / Chapter 4.4 --- Shear stress --- p.98 / Chapter 4.4.1 --- Viscous and Reynolds stresses --- p.99 / Chapter 4.4.2 --- Laminar or Turbulent? --- p.101 / Chapter 4.5 --- Summary --- p.104 / Chapter Chapter 5 --- Conclusion --- p.106 / Chapter 5.1 --- Heat flux measurement --- p.106 / Chapter 5.2 --- Boundary layers --- p.107 / Chapter 5.3 --- Perspective for further investigation --- p.108 / Appendix A Heat flux measurement for high Prandtl number --- p.109 / Chapter I. --- Experimental conditions --- p.110 / Chapter II. --- Result and discussion --- p.112 / Chapter III. --- Summary and perspective for further investigation --- p.114 / Bibliography --- p.115