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The subject of convection in fluid and porous media is investigated. Particular attention is paid to penetrative convection. The first two chapters are devoted to penetrative convection when fluid overlies and saturates a porous medium. Penetrative convection is described by a quadratic equation of state in the first instance and via internal heating in the second. Linear instability analyses are performed in both cases. A surprising and striking array of streamlines are presented at the onset of convection. The streamlines exhibit novel behaviour when physical parameters of the problem are varied. Penetrative convection in a horizontally isotropic porous layer is discussed next. Again penetrative convection is described by a quadratic equation of state and internal heating. The internally heated model is dealt with primarily as it yields a global nonlinear stability bound. The two models are shown to be mathematically adjoint and the nonlinear stability results compared with previously published linear ones. Good agreement between the two is seen. The effect of convection on the evolution of under-ice meltponds is investigated next. Linear and nonlinear analyses are employed to yield instability and global stability results respectively. Discrepancy between the two is found and the region of possible subcritical instabilities is presented. Finally convection in a porous medium is investigated via a cubic equation of state. It is found that unconditional nonlinear stability results can be established if Forchheimer theory is introduced. The results are compared to previously published linear ones and it is shown that the linear theory essentially captures the physics involved.

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Turbulent mixing of chemical elements by convection has fundamental effects on the evolution of stars. The standard algorithm at present, mixing-length theory (MLT), is intrinsically local, and must be supplemented by extensions with adjustable parameters. As a step toward reducing this arbitrariness, we compare asteroseismically inferred internal structures of two Kepler slowly pulsating B stars (SPBs; M similar to 3.25M circle dot.) to predictions of 321D turbulence theory, based upon well-resolved, truly turbulent three-dimensional simulations that include boundary physics absent from MLT. We find promising agreement between the steepness and shapes of the theoretically predicted composition profile outside the convective region in 3D simulations and in asteroseismically constrained composition profiles in the best 1D models of the two SPBs. The structure and motion of the boundary layer, and the generation of waves, are discussed.

Measurements of radiogenic isotopes can in principle constrain the melting, melt migration, and solid state convection that occurs in the Earth's mantle, but to do so requires suitable quantitative models. A new statistical model is introduced to better understand the observed heterogeneity in isotopic ratios 143Nd/144Nd, 87Sr/86Sr, 176Hf/177Hf,208Pb/204Pb, 206Pb/204Pb and 207Pb/204Pb measured on mid-ocean ridge basalt. The model is highly idealised, analytically tractable, and contains the essential physical processes involved: radioactive decay, the stirring and recycling of mantle convection, partial melting, and the mixing of melts. Comparison of the modelled heterogeneity with that observed constrains model parameters, which in turn constrains aspects of mantle convection and melting. The model provides a new interpretation of the 2.0 Ga lead-lead pseudo-isochron age in terms of an age distribution of mantle material. Simple equations relate the pseudo-isochron age to the rate of melting and decay constants. These equations are different from, but related to and more general than, those found previously for standard geochemical box models. The results are in good agreement with numerical simulations of mantle convection. The 2.0 Ga pseudo-isochron age is shown to infer a 0.5 Ga average time scale for melting of mantle material. Geochemical and geological evidence suggests that melt travels to the surface via a network of channels under the ridge. Motivated by this, the fluid dynamical problem of a open melt conduit surrounded by a deformable porous medium is studied. Previous work has shown that the conduit supports solitary waves of elevation, with a region of trapped melt travelling with the wave. The new analysis comes to a different conclusion, showing that the solitary wave is instead one of depression, without a region of trapped melt.

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Xiao Yi-fei = 瑞利-伯纳德对流中的局域热传导的测量 / 肖毅腓. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 85-89). / Text in English; abstracts in English and Chinese. / Xiao Yi-fei = Ruili-Bonade dui liu zhong de ju yu re chuan dao de ce liang / Xiao Yifei. / Abstract (in Chinese) --- p.i / Abstract (in English) --- p.ii / Acknowledgements --- p.iii / Table of Contents --- p.iv / List of Figures --- p.vi / List of Tables --- p.xi / Chapter Chapter 1 --- Theory and Some Physical Picture in Raleigh-Benard convection --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Rayleigh-Benard Convection and its dominated element --- p.3 / Chapter 1.2.1 --- Free convection Equation --- p.3 / Chapter 1.2.2 --- Heat transfer equation in Experiment --- p.6 / Chapter 1.2.3 --- Physical Picture of Plumes --- p.8 / Chapter 1.2.4 --- Large Scale Structure and Plumes --- p.9 / Chapter Chapter 2 --- Experimental Setup and Instrumentation --- p.11 / Chapter 2.1 --- The convection Cell for the experiment --- p.11 / Chapter 2.2 --- Temperature probe and its calibration --- p.14 / Chapter 2.3 --- Principle of Wheatstone electrical Bridge --- p.17 / Chapter 2.4 --- The Principle of Laser Doppler Velocimetry (LDV) --- p.21 / Chapter 2.4.1 --- Features of LDV / Chapter 2.4.2 --- Measurement position in Simultaneous Measurement Velocity and Temperature --- p.25 / Chapter 2.4.3 --- Data analysis of LDV --- p.27 / Chapter Chapter 3 --- Measurement of Local Heat Flux --- p.31 / Chapter 3.1 --- Simultaneous measurement velocity in Different Distance --- p.31 / Chapter 3.2 --- Treatment of Heat Flux Signals --- p.40 / Chapter 3.2.1 --- Sampling Clock of Heat Flux --- p.40 / Chapter 3.2.1 --- Expanding j Relative to Mean wind and Local Fluctuation Term --- p.44 / Chapter 3.2.3 --- "Temperature, Velocity and Heat Flux's Corrections" --- p.46 / Chapter 3.3 --- Conclusions --- p.50 / Chapter Chapter 4 --- Result and Discussion --- p.51 / Chapter 4.1 --- Spatial structure of Heat Flux --- p.51 / Chapter 4.1.1 --- Ra-dependent Spatial Structure for Flow Along the LSC plane --- p.51 / Chapter 4.1.2 --- Ra-dependent Spatial Structure for Flow Perpendicular to the LSC plane --- p.58 / Chapter 4.1.3 --- Comparisons of Jz and Jzfluc --- p.62 / Chapter 4.2 --- Fluctuations of Local Heat Flux --- p.65 / Chapter 4.2.1 --- At Cell Center --- p.65 / Chapter 4.2.2 --- Near Sidewall --- p.70 / Chapter 4.3 --- Conclusions --- p.80 / Chapter Chapter 5 --- Conclusions and Future Work --- p.81 / Chapter 5.1 --- Conclusions --- p.81 / Chapter 5.2 --- Perspective for Further Investigation --- p.84 / Reference --- p.85 / List of Figures / Chapter 1.1 --- Typical temperature profile along z-direction (From lower plate to upper) --- p.7 / Chapter 2.1 --- Sketch of the convection cell for simultaneous measurement temperature and velocity --- p.12 / Chapter 2.2 --- The setup of temperature probe calibration --- p.15 / Chapter 2.3 --- A typical temperature calibrate Resistance vs. Temperature --- p.16 / Chapter 2.4 --- The Wheatstone bridge and the differential amplifier: R0=10.0 kΩ; R1=R2=R3=Rf=5.0 kΩ; Rv is used to balance the bridge --- p.18 / Chapter 2.5 --- Schematic diagram Principle of the LDV --- p.22 / Chapter 2.6 --- Measuring volume of Laser Doppler Velocimetry --- p.24 / Chapter 2.7 --- Velocity (m/s) vs. Transit Time (ms) --- p.28

Sun Chao = 热湍流对流中的自组织结构 / 孫超. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 73-75). / Text in English; abstracts in English and Chinese. / Sun Chao = Re tuan liu dui liu zhong de zi zu zhi jie gou / Sun Chao. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Structures and dynamics of the global velocity field --- p.1 / Chapter 1.2 --- Persistence of the mean wind at very-high Rayleigh numbers --- p.2 / Chapter 1.3 --- Scaling of the wind velocity --- p.3 / Chapter 1.4 --- The present work and organization of the thesis --- p.4 / Chapter 2 --- Experimental setup and measurement techniques --- p.6 / Chapter 2.1 --- The setup of the convection system --- p.7 / Chapter 2.1.1 --- Convection Cell --- p.7 / Chapter 2.1.2 --- The Power Supply and the Refrigerated Recirculator --- p.12 / Chapter 2.1.3 --- The Temperature Probes --- p.12 / Chapter 2.1.4 --- Thermostat --- p.14 / Chapter 2.2 --- Particle Image Velocimetry --- p.16 / Chapter 2.2.1 --- Laser --- p.18 / Chapter 2.2.2 --- CCD --- p.20 / Chapter 2.2.3 --- Synchronizer --- p.21 / Chapter 2.2.4 --- Tracer Particles --- p.22 / Chapter 2.2.5 --- The light path --- p.25 / Chapter 2.2.6 --- Basic Principles of the technique --- p.25 / Chapter 2.3 --- PIV measurement in turbulent thermal covection --- p.35 / Chapter 3 --- 12 --- p.38 / Chapter 3.1 --- Time-averaged velocity field --- p.38 / Chapter 3.2 --- Statistical quantities of velocity field --- p.53 / Chapter 3.3 --- Instant velocity field --- p.59 / Chapter 3.4 --- Velocity in the plane perpendicular to LSC --- p.63 / Chapter 4 --- Conclusions and Further work --- p.69 / Chapter 4.1 --- Conclusions --- p.69 / Chapter 4.2 --- Perspective for further investigation --- p.71 / Bibliography --- p.73