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published_or_final_version / abstract / Mechanical Engineering / Doctoral / Doctor of Philosophy

Thermal and fingering convection in a horizontal porous layer underlying a fluid layer was studied using linear stability analysis, experiment (for the thermal convection case only), and nonlinear simulation. For the thermal convection case, the linear analysis shows that when the fluid layer is thin, convection is largely confined to the porous layer. When the fluid layer thickness exceeds 15% of the porous layer thickness, convection is localized in the fluid layer and the critical wavelength is dramatically reduced. Experimental investigations were then conducted in a test box 24 cm x 12 cm x 4 cm high to substantiate the predictions. The ratio of the thickness of the fluid layer to that of the porous layer, d, varied from 0 to 1. The results were in good agreement with predictions. To investigate supercritical convection, a nonlinear computational study was carried out. It was found that for d ≤ 0.13, the Nusselt number increases sharply with the thermal Rayleigh number, whereas at larger values of d, the increase is more moderate. Heat transfer rates predicted for d = 0.1 and 0.2 are in good agreement with the experimental results. For salt-finger convection at R(m) ≤ 1, the critical value of the solute Rayleigh number R(sm) decreases as d increases; the convection is unicellular. For 5 ≤ R(m) ≤ 10, the critical R(sm) initially decreases with d, and then remains almost constant for larger values of d; multicellular convection prevails at high d. For 20 ≤ R(m) ≤ 50, the critical R(sm) first decreases and then increases as d increases from 0 to 0.1. When d > 0.1, the critical R(sm) decreases slowly with d and remains almost constant for d ≥ 0.4. In the nonlinear computations for R(m) = 1, periodic convection sets in at a value of R(sm) between ten and eleven times the critical value. For the case of R(m) = 50, an aperiodic oscillation occurs when R(sm) is between four and five times the critical value. For the superposed layer cases d = 1 and 0.5, the convection characteristics are similar to those of thermal convection when R(m) = 0.01. For R(m) = 1, it was found that the onset of salt-finger convection is oscillatory. For R(m) = 50, the nonlinear code failed to obtain satisfactory results.

In this thesis, we attempt to address some of these questions. First, we have devised a scheme to extract information of the plumes from simultaneous velocity and temperature measurements. Our method makes explicit use of the physical intuition that the velocity of the buoyant structures, e.g. plumes, should be related to the temperature fluctuation, in some apriori unknown manner as they are generated by buoyancy. Our scheme involves a decomposition of the local velocity measurement into two parts. The part that is correlated with some function of the temperature fluctuation measured at the same time is taken as the velocity of the plumes. Applying this scheme to measurements taken at the center and near the sidewall of the convection cell where the dominant buoyant structures are plumes, we have found the temperature dependence of the plume velocity at these two locations and understood our results from the equations of motion. Using these results of the temperature dependence of the plume velocity, we (i) conclude that heat is not mainly transported through the central region of the convection cell and (ii) obtain a relation between the scaling behavior of the plume velocity structure functions and the temperature structure functions that is different from what is implied by Bolgiano-Obukhov scaling. Then we have studied the possible effects of the large-scale mean circulation on the velocity and temperature statistics using simplified shell models of turbulent convection. We have introduced a large-scale mean flow into two shell models and found that its presence does not change the scaling behavior of velocity and temperature. / In turbulent thermal convection, velocity and temperature measurements taken at a point display complex fluctuations in time. On the other hand, visualization of the flow reveals recurring coherent structures. One prominent flow structure is a plume, which is generated from the thermal boundary layers by buoyancy. Another flow structure is a large-scale mean circulation that spans the entire convection cell. At least two strategies can be employed to study turbulent thermal convection or turbulent flows in general. One is to analyze and understand the fluctuations of the local measurements. The other is to characterize the coherent structures and study and understand their dynamics. These two approaches are not independent but provide complementary knowledge of the flows. Interesting questions hence include whether and how information about the ordered flow structures can be extracted from the fluctuating local measurements and how the presence of the ordered flow structures might affect the statistics of the fluctuations. / Guo, Hao = 热对流湍流中的统计特性与结构 / 郭昊. / "January 2007." / Source: Dissertation Abstracts International, Volume: 68-09, Section: B, page: 6036. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 62-66). / 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. / Title and abstract in English and Chinese. / School code: 1307. / Guo, Hao = Re dui liu tuan liu zhong de tong ji te xing yu jie gou / Guo Hao.

Ni, Rui = 關于Kolmogorov常數以及湍流熱對流中能量耗散率、加速度統計、環流反轉研究 / 倪睿. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 105-119). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Ni, Rui = Guan yu Kolmogorov chang shu yi ji tuan liu re dui liu zhong neng liang hao san lu, jia su du tong ji, huan liu fan zhuan yan jiu / Ni Rui.