Brandt, Martin B.C. 2011. Imaging the African Superplume – Upper mantle, Tomography and Moment tensor. Ph.D. thesis, Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa. The African Superplume, African Superswell and East African Rift System are amongst the most prominent geophysical features on Earth, but the structure, evolution and interaction between these features is controversial. In my thesis I conducted a range of investigations in an effort to better understand these issues. The thesis presents the investigations into the structure and expressions of these features. These include: (I) A study of the upper mantle shear velocity structure beneath southern Africa to investigate the source of the buoyancy that has powered the Superswell; (II) Statistical hypothesis testing of middle-mantle shear velocity tomographic models to evaluate evidence for links between the Superplume and low velocity features in/near the transition zone; and (III) Computation of three new regional moment tensors for South Africa to assess crustal stress in the Kalahari craton, and its link with mantle structure and dynamics. Waveform data were obtained for the study on the upper mantle shear velocity structure and the moment tensor inversions from the Southern African Seismic Experiment Kaapvaal craton array. For the statistical hypothesis testing on global tomography images, new travel-time data from both global and AfricaArray stations were added to Grand’s global shear velocity data set. The principal findings of this study are summarized below. I. The upper mantle shear velocity structure beneath the Kalahari craton is similar to that of other shields, except for slightly slower velocities from 110–220 km depth. The difference may be due to higher temperatures or a decrease in magnesium number (Mg#). If the slower velocities in the deep lithosphere are due solely to a temperature anomaly, then slightly less than half of the unusually high elevation of the Kalahari craton can be explained by shallow buoyancy from a depleted hot lithosphere. Decreasing the Mg# of the lower lithosphere would increase density and counteract higher temperatures. If an excess temperature of 90 K over a 110 km depth range and a corresponding decrease in Mg# of -2 between the Kalahari and the other cratons are assumed, this would match the seismic velocity difference but would result in essentially no buoyancy difference. We conclude that the high elevation of the Kalahari craton can only be partially supported by shallow mantle buoyancy and must have a deeper source. We determined a thickness of 250±30 km for the mantle transition zone below eastern southern Africa, which is similar to the global average, but the corresponding velocity gradient is less steep than in standard global models (PREM and IASP91). Velocity jumps of 0.16±0.1 km/s (eastern) and 0.21±0.1 km/s (central) across the 410 km discontinuity were found. Our results indicate a thermal or chemical anomaly in the mantle transition zone, but this cannot be quantified due to uncertainty. II. Statistical hypothesis testing on our global tomography images indicated that the African Superplume rises from the core-mantle boundary to at least 1150 km depth, and the upper mantle slow-velocity anomaly extends from the base of the lithosphere to below the mantle transition zone. The model that links the African Superplume with the slow-velocity anomaly in the upper mantle under eastern Africa has an equal probability to an alternative hypothesis with a thin slow-velocity “obstruction zone” at 850 to 1000 km depth. III. Finally, we calculated three regional moment tensors for South Africa and made progress towards resolving the discrepancy between the local and moment magnitudes we observe for the region. Moment tensors/focal mechanisms in southern Africa change from normal faulting (extension) in the northeast near the East African Rift to strike-slip faulting in the southwest. This confirms previous studies stating that not only eastern Africa, but also southern Africa is being actively uplifted by lithospheric modification at its base and/or the African Superplume.

Tam Wai Shing = 穩態環流的熱傳送與縱橫比之關係及其與湍流狀態的瑞利-伯纳德對流之聯繫 / 譚偉誠. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 59-61). / Text in English; abstracts in English and Chinese. / Tam Wai Shing = Wen tai huan liu de re chuan song yu zong heng bi zhi guan xi ji qi yu tuan liu zhuang tai de Ruili-Bonade dui liu zhi lian xi / Tan Weicheng. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Review of the theoretical studies of heat transport by turbulent convection --- p.5 / Chapter 2.1 --- The marginal stability arguments --- p.7 / Chapter 2.2 --- Chicago mixing zone model --- p.7 / Chapter 2.3 --- Shraiman and Siggia theory --- p.10 / Chapter 2.4 --- Grossmann and Lohse Theory --- p.12 / Chapter 2.4.1 --- Estimation of the kinetic dissipation --- p.13 / Chapter 2.4.2 --- Estimation of the thermal dissipation --- p.14 / Chapter 2.4.3 --- The four regimes --- p.15 / Chapter 3 --- Aspect-ratio dependence: The problem studied --- p.19 / Chapter 3.1 --- The velocity field --- p.21 / Chapter 3.1.1 --- Incompressible flow --- p.21 / Chapter 3.1.2 --- Large-scale circulating flow --- p.21 / Chapter 3.1.3 --- No-slip boundary conditions --- p.22 / Chapter 3.2 --- The functions f(x) and g(y) --- p.23 / Chapter 3.3 --- Boundary conditions for the temperature field --- p.23 / Chapter 3.4 --- Important parameters in the numerical calculation --- p.24 / Chapter 4 --- The numerical calculations --- p.31 / Chapter 5 --- Results and discussions --- p.34 / Chapter 5.1 --- Nu-Г Relationship --- p.38 / Chapter 5.2 --- Nu - Pe Relationship --- p.41 / Chapter 6 --- Implications for heat transport by Rayleigh-Benard convection --- p.49 / Chapter 6.1 --- Nu-Ra relationship --- p.50 / Chapter 6.2 --- Comparison with recent experimental results --- p.52 / Chapter 7 --- Conclusions --- p.57 / Bibliography --- p.59

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Civil Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography : leaves 231-234. / Ph.D.

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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.

Direct real-space multi-point measurements of the velocity and temperature fields were carried out in various places of the convection cell. In the central region of the cell it is found that both velocity and temperature exhibit the same scaling behavior that one would find for the velocity and for a passive scalar in homogeneous and isotropic Navier-Stokes turbulence. Near the cell's sidewall where thermal plumes abound, vertical velocity and temperature exhibit different scalings. A model, taking into account both buoyancy and energy dissipation, is proposed and its predictions agree well with the sidewall experimental results. / This thesis aims to address three key issues in convectioe thermal turbulence: heat transport, statistics of turbulent fluctuations of the velocity and temperature fields, and flow dynamics. / Through measurement of 2D velocity at different cross sections of the cylindrical cell with Gamma = 1, we investigate the 3D flow structures and dynamics of turbulent thermal convection. Our result reveals how thermal plumes synchronize their emissions and organize their motions spatially between the top and bottom plates, leading to an oscillatory motion in the bulk region of the fluid. In Gamma = 0.5 small cell, we successfully identified the relationship between 2D instantaneous velocity map and the time-averaged 3D flow pattern. This experiment also showed that a particular value of Nu can be unambiguously associated with a specific large-scale flow mode in the convection cell. By taking into account the effects of the evolution in the circulation path of the mean wind and of the counterflow, we provide a solution to the riddle about the scaling exponent dispersion of the Reynolds number Re with Ra and show that the scaling exponent has a universal value of 0.5. / To study the confinement effect on heat transport at high levels of turbulence, we conducted high precision measurements of the Nusselt number Nu as a function of the Rayleigh number Ra in a 1 m diameter cylindrical cell filled with water with aspect ratio Gamma = 0.67, l, 2, 5, 10, 20. The measurements were conducted at the Prandtl number Pr ≃ 4 with Ra varying from 1 x 10 7 to 5 x 1012. It is found that Nuinfinity can be described by a combination of two power laws for all aspect ratios, and that the asymptotic large Gamma behavior may have been reached for Gamma ≥ 10. By studying the statistics of temperature fluctuations inside the conducting plates, we found that the product of temperature skewness and the skewness of temperature time derivative may be used to quantify the intensity of plume emissions. / Sun Chao = 熱湍流對流的實驗研究 / 孙超. / "July 2006." / Adviser: Keqing Xia. / Source: Dissertation Abstracts International, Volume: 68-03, Section: B, page: 1697. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (p. 132-140). / 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. / School code: 1307. / Sun Chao = Re tuan liu dui liu de shi yan yan jiu / Sun Chao.

Qi, Pengfei = 湍流熱對流中速度場結構函數和流動循環的實驗研究 / 齊鵬飛. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 65-69). / Abstracts in English and Chinese. / Qi, Pengfei = Tuan liu re dui liu zhong su du chang jie gou han shu he liu dong xun huan de shi yan yan jiu / Qi Pengfei. / Abstract --- p.i / 摘要 --- p.ii / Acknowledgements --- p.iii / Contents --- p.iv / List of Figures --- p.vi / List of Tables --- p.X / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- What is turbulence? --- p.1 / Chapter 1.2 --- Why study turbulence and experimentally? --- p.2 / Chapter 1.3 --- Turbulent Rayleigh-Benard convection --- p.4 / Chapter 1.4 --- Basic equations and characteristic parameters --- p.S / Chapter 1.4.1 --- Continuity equation --- p.5 / Chapter 1.4.2 --- Momentum equation (Navier-Stokes equation) --- p.5 / Chapter 1.4.3 --- Energy equation --- p.7 / Chapter 1.4.4 --- Averaged equations --- p.9 / Chapter 1.4.5 --- Characteristic parameters --- p.10 / Chapter 1.5 --- Statistical properties in small-scale turbulence --- p.13 / Chapter 1.5.1 --- Phenomenological description and Kolmogorov hypotheses --- p.14 / Chapter 1.5.2 --- Local structure of the velocity fluctuations --- p.15 / Chapter 1.6 --- Large-scale circulation --- p.17 / Chapter 1.7 --- Motivation and Organizations of this thesis --- p.19 / Chapter 1.7.1 --- B059 scaling --- p.19 / Chapter 1.7.2 --- Large-scale circulation --- p.19 / Chapter 1.7.3 --- Organization of the thesis --- p.20 / Chapter 1.8 --- Some words to my experiment and further expectation --- p.21 / Chapter Chapter 2 --- Experimental apparatus and techniques --- p.27 / Chapter 2.1 --- Rectangle cell --- p.27 / Chapter 2.2 --- The power supply and cooler --- p.28 / Chapter 2.3 --- Thermistor and multimeter --- p.29 / Chapter 2.4 --- Particle image velocimetry (PIV) technology --- p.30 / Chapter 2.4.1 --- Seeding particles --- p.31 / Chapter 2.4.2 --- Light source and light-sheet optics --- p.33 / Chapter 2.4.3 --- Imaging system --- p.34 / Chapter 2.4.4 --- Control system --- p.34 / Chapter 2.4.5 --- Analysis method --- p.35 / Chapter Chapter 3 --- Small-scale properties in rectangular cell --- p.37 / Chapter 3.1 --- Introduction --- p.37 / Chapter 3.2 --- Experimental condition --- p.37 / Chapter 3.3 --- Homogeneity --- p.39 / Chapter 3.4 --- Isotropy --- p.40 / Chapter 3.5 --- Scaling of structure function --- p.42 / Chapter Chapter 4 --- Large-scale circulation --- p.51 / Chapter 4.1 --- Introduction --- p.51 / Chapter 4.2 --- Experimental condition and limitation --- p.54 / Chapter 4.3 --- Statistical properties of large-scale circulation period --- p.56 / Chapter 4.4 --- Scaling of the Reynolds number --- p.59 / Chapter 4.5 --- Oscillation period --- p.60 / Chapter Chapter 5 --- Conclusion --- p.63 / Chapter 5.1 --- Small-scale properties in rectangular cell --- p.63 / Chapter 5.2 --- Large-scale circulation --- p.63 / Reference --- p.65

Graduation date: 1993

A droplet may be prevented from wetting a solid surface by the existence of a lubricating film of air, driven by theromcapillary convection, between liquid and solid surfaces. The noncontact nature and the load-carrying capability of a nonwetting droplet lead to potential engineering applications, e.g., low-friction bearings. The present research consists of two thrusts. The first is aimed at quantifying nonwetting-system failures (film and pinning) triggered by application of a mechanical load, gaining insights to failure mechanisms. Experimental results show that film failure occurs over a wide range of droplet volumes when the temperature difference between the droplet and the plate, the driving potential of the free-surface motion, is small. Interferometric observations reveal flow instability just prior to film failure, with the growth of a nonaxisymmetric disturbance on a free surface (m = 1). Pinning failure becomes more prevalent as the temperature difference is increased, stabilizing the film flow. As part of the present investigation, a system was devised, allowing an oscillating free-surface to be reconstructed from a series of interferograms. The dynamic responses of the free surface reveal mode coupling, with harmonics of the input frequency excited through nonlinearity. The second thrust of the research succeeded in levitating and translating a droplet using the mechanism of permanent nonwetting. In this scheme, the droplet is heated by a CO2 laser and is placed above a cooled glass surface in order to drive the lubricating film that supports the weight of the drop. Furthermore, the position of the droplet can be controlled by moving the heating location, which leads to an asymmetry of the flow fields, driving air from the cooler-end of the droplet and propelling it towards the heat source. These demonstrations suggest the techniques potential use as a liquid-delivery scheme in a Lab-On-a-Chip system. Modeling is carried out to estimate propulsive forces on the droplet and to explain oscillatory behavior observed when excessive heating is applied on the drop. The concept to sandwich a droplet between two plates, a necessary configuration for levitating smaller droplets (less than mm-scale), is also discussed.

Thin liquid layers have been proposed for heat extraction and protection of the solid surfaces of divertors in magnetic fusion reactors. A number of conceptual designs for plasma-facing components (PFC) use stationary and flowing liquid layers as a renewable first wall for reactor chambers to remove heat and shield solid surfaces from damaging radiation while maintaining acceptable plasma purity levels. Such liquid-protected PFC have the potential to make fusion more commercially attractive by increasing reactor lifetimes and decreasing failure rates. The results of this research will help identify the parameter ranges for successful operation of such protection schemes. This thesis investigates the thermocapillary behavior of axisymmetric horizontal liquid layers with initial heights from 0.27 to 3.0 mm. A negative radial temperature gradient is imposed at the bottom of the liquid layer. Experimental, numerical and asymptotic analyses were carried out for thin layers where buoyancy forces are negligible. A novel asymptotic solution for this axisymmetric geometry was derived from the previous two-dimensional long-wave analysis by Sen et al. (1982). A numerical simulation using the level contour reconstruction method was used to follow the evolution of the liquid-gas interface above an axisymmetric non-isothermal solid surface. Experimental validation of the theoretical and numerical studies was performed using silicone oils of various viscosities (μ = 0.48 × 10-2 9.6 × 10-2 N s/m2). Two measurement techniques, a needle contact method and laser-confocal displacement method, were employed to obtain height profiles for applied temperature differences up to 65°C. Finally, reflectance shadowgraphy was used to visualize free-surface deformation and classify flow regimes in thick layers, where the assumptions of negligible buoyancy and axisymmetric flow are no longer valid. The results of this investigation will allow designers to determine operating windows for successful implementation of liquid-protected PFC.