Jin, Xiaoli = 關於脈衝驅動熱湍流的實驗研究 / 金晓莉. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 83-86). / Text in English; abstracts in English and Chinese. / Jin, Xiaoli = Guan yu mai chong qu dong re tuan liu de shi yan yan jiu / Jin Xiaoli. / Abstract --- p.ii / Acknowledge --- p.iv / Table of Contents --- p.vii / List of Figures --- p.xii / List of Tables --- p.xiii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Rayleigh-Benard convection --- p.1 / Chapter 1.2 --- Turbulence driven by time-dependent forcing --- p.5 / Chapter 1.3 --- Motivation --- p.7 / Chapter 1.4 --- Organization of the thesis --- p.8 / Chapter 2 --- Experimental Setup --- p.10 / Chapter 2.1 --- The Convection cell --- p.10 / Chapter 2.2 --- Heating and Cooling --- p.14 / Chapter 2.3 --- Temperature and voltage measurement --- p.15 / Chapter 2.3.1 --- Temperature probes --- p.16 / Chapter 2.3.2 --- Data acquisition: digital multimeter --- p.17 / Chapter 2.3.3 --- Data acquisition: AC Wheatstone bridge and Lock-in amplifier --- p.18 / Chapter 3 --- Steadily driven thermal turbulence: constant heating --- p.21 / Chapter 3.1 --- Local temperature fluctuations --- p.21 / Chapter 3.2 --- Signatures of plume emissions inside conducting plates --- p.26 / Chapter 3.3 --- Nusselt number --- p.33 / Chapter 3.4 --- Correlation functions and Power spectrums --- p.35 / Chapter 4 --- Kicked turbulence: periodically pulsed heating --- p.38 / Chapter 4.1 --- Periodically pulsed heating power --- p.38 / Chapter 4.2 --- In-plate temperature signals --- p.39 / Chapter 4.3 --- Rayleigh number controlling --- p.42 / Chapter 4.3.1 --- Experimental results --- p.42 / Chapter 4.3.2 --- Theoretical explanation: mean-field theory --- p.47 / Chapter 4.4 --- In-plate temperature fluctuation --- p.55 / Chapter 4.5 --- Correlation functions and power spectra --- p.58 / Chapter 4.6 --- Nusselt number enhancement --- p.62 / Chapter 4.6.1 --- Motivation --- p.62 / Chapter 4.6.2 --- Experiment --- p.64 / Chapter 4.6.3 --- Results --- p.66 / Chapter 4.6.4 --- Discussion --- p.70 / Chapter 5 --- Modulated turbulence: sinusoidal heating --- p.75 / Chapter 5.1 --- Motivation --- p.75 / Chapter 5.2 --- Nusselt number measurement --- p.76 / Chapter 6 --- Conclusion --- p.80 / Chapter 6.1 --- Periodically kicked turbulence --- p.80 / Chapter 6.2 --- Sinusoidally modulated turbulence --- p.81 / Chapter 6.3 --- Future works --- p.82 / Bibliography --- p.82

Lau Chun Keung = 受調諧下溫度湍流的實驗研究 / 劉振強. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 86-88). / Text in English; abstracts in English and Chinese. / Lau Chun Keung = Shou diao xie xia wen du tuan liu de shi yan yan jiu / Liu Zhenqiang. / Chapter 1 --- Acknowledgments --- p.iii / Chapter 2 --- Introduction --- p.1 / Chapter 2.1 --- Pulsating flow --- p.1 / Chapter 2.2 --- Rayleigh Bernard Convection: Equations and Parameters --- p.5 / Chapter 2.3 --- Rayleigh Benard Convection: Physical Picture --- p.7 / Chapter 2.4 --- Previous work on Turbulent Convection --- p.10 / Chapter 2.5 --- Motivation --- p.11 / Chapter 3 --- Experimental Setup --- p.13 / Chapter 3.1 --- The Convection cell --- p.13 / Chapter 3.2 --- Heating and Cooling --- p.18 / Chapter 3.3 --- Temperature and Voltage measurement --- p.20 / Chapter 3.3.1 --- Temperature Probes --- p.20 / Chapter 3.3.2 --- "Data, acquisition: Multimeters and Lock-In" --- p.22 / Chapter 4 --- Experimental Results --- p.27 / Chapter 4.1 --- Steady State Convection --- p.27 / Chapter 4.1.1 --- Experimental parameters and its determination --- p.27 / Chapter 4.1.2 --- Fluctuations at various locat ion of cell --- p.28 / Chapter 4.1.3 --- Nusselt Number --- p.37 / Chapter 4.2 --- Modulated Convection --- p.38 / Chapter 4.2.1 --- Parameters of the system --- p.40 / Chapter 4.2.2 --- Temperature variation at the plates: general picture --- p.41 / Chapter 4.2.3 --- Temperature variation at the plates: modulatiou frequency dependence --- p.42 / Chapter 4.2.4 --- Phase differences between response and modulation --- p.58 / Chapter 4.2.5 --- Temperature Variation at the Plates: Further Exploration of Parameter Space --- p.61 / Chapter 4.2.6 --- Local Signals at Mid-Height under modulation --- p.63 / Chapter 4.2.7 --- Time lag between two probes --- p.76 / Chapter 5 --- Conclusion --- p.83 / Chapter 5.1 --- Conclusion --- p.83 / Chapter 5.2 --- Outlook for further studies --- p.85 / Bibliography --- p.86 / Thermal dissipation rate --- p.89

Zhou Quan = 关於热湍流中标量场混合和自组织结构的实验研究 / 周全. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 89-94). / Text in English; abstracts in English and Chinese. / Zhou Quan = Guan yu re tuan liu zhong biao liang chang hun he he zi zu zhi jie gou de shi yan yan jiu / Zhou Quan. / Abstract --- p.ii / Acknowledge --- p.iii / Table of Contents --- p.v / List of Figures --- p.xii / List of Tables --- p.xiii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Rayleigh-Benard System --- p.2 / Chapter 1.1.1 --- Physics Picture --- p.2 / Chapter 1.1.2 --- Basic Equations and Characteristic Parameters --- p.3 / Chapter 1.2 --- Passive and Active Scalars --- p.6 / Chapter 1.3 --- Large-Scale Circulation (LSC) --- p.7 / Chapter 2 --- Passive and Active Scalars in Convective Thermal Turbulence --- p.9 / Chapter 2.1 --- Experimental Setup and Measurement Techniques --- p.9 / Chapter 2.1.1 --- Rectangular Cell --- p.9 / Chapter 2.1.2 --- Temperature probe: thermistor --- p.12 / Chapter 2.1.3 --- Laser Induced Fluorescence (LIF) --- p.16 / Chapter 2.2 --- Passive Scalar Measurements --- p.24 / Chapter 2.2.1 --- Concentration Time Series --- p.24 / Chapter 2.2.2 --- Statistical Properties --- p.26 / Chapter 2.3 --- Active Scalar Measurements --- p.35 / Chapter 2.4 --- Relationship between passive scalar and active scalar --- p.41 / Chapter 2.4.1 --- Cross-correlation Functions --- p.41 / Chapter 2.4.2 --- Structure Functions --- p.48 / Chapter 2.5 --- Summary --- p.60 / Chapter 3 --- The Azimuthal Motion of the Mean Wind in Turbulent Rayleigh- Benard Convection --- p.63 / Chapter 3.1 --- Experimental Setup and Measurement Techniques --- p.64 / Chapter 3.1.1 --- Cylindrical Cell --- p.64 / Chapter 3.1.2 --- Particle Image Velocimetry (PIV) --- p.65 / Chapter 3.2 --- Azimuthal Motion of the Mean Wind in the Γ = 1.0 Cell --- p.68 / Chapter 3.2.1 --- Time-trace of the LSC orientation Φ --- p.69 / Chapter 3.2.2 --- Statistical properties of azimuthal motion of the mean wind --- p.73 / Chapter 3.3 --- Azimuthal Motion of the Mean Wind in theΓ = 0.5 Cell --- p.77 / Chapter 3.3.1 --- Time-trace of the LSC orientation Φ --- p.78 / Chapter 3.3.2 --- Statistical properties of azimuthal motion of the mean wind --- p.80 / Chapter 3.4 --- Summary --- p.85 / Chapter 4 --- Conclusion --- p.86 / Chapter 4.1 --- Scalar Mixing --- p.86 / Chapter 4.2 --- The Azimuthal Motion of the LSC --- p.87 / Chapter 4.3 --- Perspective for Further Investigation --- p.88 / Bibliography --- p.88

We investigate the role of boundary layer forcing and surface heterogeneities on the intensity and spectral distribution of the convective circulations of an idealized convective system. Our ultimate goal is to further the understanding of atmospheric convection. However, we depart from realistic atmospheric convection and study an idealized convective system known as the Rayleigh-Benard model in two dimensions. We extended the classical Rayleigh-Benard model to include the effects of boundary heterogeneities. These effects are included, inparticular through a sinusoidally variable surface temperature. In this idealized model, the Rayleigh number plays the role of convective available potential energy (CAPE) in atmospheric convection, while the boundary heterogeneities in the temperatureplay the role of boundary layer forcing. In particular, we study the effects of boundary forcing on the intensity and spectral distribution of convective circulations in great detail.We consider the problem in the linear and weakly nonlinear regimes. In the linear regime, we find an analytical solution for Rayleigh-Benard convection with boundary forcing. We show that the inclusion of periodic boundary forcing causes discontinuities in the linear solution when critical conditions are approached. In the nonlinear regime, we find the solution by direct numerical simulation. The nonlinearities not only remove the discontinuities, but also lead to the appearance of non-trivial modes in the solution.The classical modes appear when the Rayleigh number issupercritical and the amplitude of the boundary forcing is small. Modes governed by boundary forcing dominate when its amplitude is large. Non-trivial modes with wavenumbers different from either the classical or the boundary modes appear only for intermediate values of the boundary forcing. The transitions between regions dominated by the classical Rayleigh forcing, mixed forcing, andboundary forcing depend on the Rayleigh number and the wavenumber of the boundary forcing. We conclude that boundary forcing has non-trivial effects on convective circulations. This result might have important implications for atmosphericconvection. Indeed, it suggests that atmospheric convection over the relatively homogeneous oceans would have different spectral distribution compared to that over heterogeneous land surfaces. This result is consistent with observations.

No description available.

In the first part of the thesis, we carried out direct two-dimensional (2D) multipoint measurements of the velocity fields in a turbulent Rayleigh-Benard convection cell to study the properties of small-scale convective turbulence. The local homogeneity and isotropy of the velocity field are tested using a number of criteria and are found to hold to an excellent degree. The properties of velocity circulation Gammar are also studied. The results show that the circulation appears to be more effective to capture the effect of local anisotropy than the velocity field itself. The distribution of Gammar is found to depend on the scale r, reflecting strong intermittency. It is further found that velocity circulation has the same anomalous scaling exponents as the longitudinal and transverse structure functions for low-order moments (p ≲ 5). Whereas, for high-order moments (p ≳ 5), the anomalous scaling exponents for circulation are found to be systematically smaller than the scaling exponents of the longitudinal and transverse structure functions. / In the second part of the thesis, the simultaneous visualization of the temperature and velocity fields was used to study the properties of thermal plumes. Our visualization reveals the process of the morphological evolution between sheetlike and mushroomlike plumes, which were also quantified by the height dependence of plume numbers and of vorticity fluctuations. A direct connection between the heat transport and coherent structures, i.e. thermal plumes, was established, which shows that it is plume number that primarily determines the Nu-Ra scaling relation. Individual plumes were extracted and their statistical and geometric properties were studied. It is found that the log-normal distribution is universal for thermal plumes and the log-normal statistics may be used to model them. In addition, both our quantitative characteristic and direct 3D spatial visualizations indicate that the previously-believed sheetlike plumes should be reconsidered to be only one-dimensional structures. / In the third part of the thesis, the planar laser-induced fluorescence technique was induced to study the 2D passive scalar mixing in high-Schmidt-number buoyancy-driven turbulence. The passive scalar mixing evolution was studied and various geometric properties, such as shape complexity, fractal dimension and local curvature, were used to characterize the isoconcentration contours of the 2D passive scalar fields. It is found that when the flow gets more turbulent the shape of passive scalar packets becomes closer to a circular shape and the passive scalar mixing becomes more isotropic, indicating the increased mixing and stirring of the turbulent flow. / The objective of this thesis is to address the following three key issues in turbulent thermal convection, i.e. turbulent fluctuations in small scales, coherent structures and passive scalar mixing in buoyancy-driven turbulence. / Zhou, Quan = 對流熱湍流中能量級串, 相干結構和標量場混合的实验研究 / 周全. / Adviser: Ke-Qing Xia. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3576. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 103-117). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307. / Zhou, Quan = Dui liu re tuan liu zhong neng liang ji chuan, xiang gan jie gou he biao liang chang hun he de shi yan yan jiu / Zhou Quan.

The thesis develops two characterizations of spatio-temporal complex patterns. While these are developed for the patterns of fluid flow in experiments on Rayleigh-Benard Convection(RBC), they are adaptable to a wide range of spatially extended systems. The characterizations may be especially useful in cases where one does not have good models describing the dynamics, making numerical and analytic studies difficult. In Spiral Defect Chaos(SDC), a weakly turbulent regime of RBC, the convective rolls exhibit complex spatial and temporal dynamics. We study the dynamics of SDC through local defect formations between convective rolls as well as the topological rearrangements of these rolls at a global scale. A laser based thermal actuation system is developed to reproducibly impose initial states for the fluid flow and construct ensembles of trajectories in the neighborhood of defect nucleation. This is used to extract the modes and their growth rates, characterizing the linear manifold corresponding to defect nucleation. The linear manifold corresponding to instabilities resulting in defect formation is key to building efficient schemes to control the dynamics exhibited. We also develop the use of computational homology as a tool to study spatially extended dynamical systems. A quantitative measure of the topological features of patterns is shown to provide insights into the underlying dynamics not easily uncovered otherwise. In the case of RBC, the homology of the patterns is seen to indicate asymmetries between hot and cold regions of the flow, stochastic evolution at a global scale as well as bifurcations occurring well into the turbulent regime of the flow.

Many problems in applied mathematics involve simulating the evolution of a system using differential equations with known initial conditions. But what if one records observations and seeks to determine the causal factors which produced them? This is known as an inverse problem. Some prominent inverse problems include data assimilation and parameter recovery, which use partial observations of a system of evolutionary, dissipative partial differential equations to estimate the state of the system and relevant physical parameters (respectively). Recently a set of procedures called nudging algorithms have shown promise in performing simultaneous data assimilation and parameter recovery for the Lorentz equations and the Kuramoto-Sivashinsky equation. This work applies these algorithms and extensions of them to the case of Rayleigh-B\'enard convection, one of the most ubiquitous and commonly-studied examples of turbulent flow. The performance of various parameter update formulas is analyzed through direct numerical simulation. Under appropriate conditions and given the correct parameter update formulas, convergence is also established, and in one case, an analytical proof is obtained.

No description available.

No description available.