THESIS
2017

xvii, 114 pages : illustrations (some color) ; 30 cm

**Abstract**
We report a combined experimental and theoretical study of turbulent Rayleigh-Bénard convection (RBC) in a horizontal thin disk cell and an upright cylindrical cell filled with water and glycerine aqueous solution. The aim of the thesis work is to study the effects of turbulent fluctuations on four aspects of the statistical and dynamic properties
of the temperature field and flow patterns in RBC. The Grossmann-Lohse (GL) model serves as the main theoretical framework describing the global heat transport and large-scale dynamics in RBC [2–5]. This framework, however, is a mean field model and does not take turbulent fluctuations into account, which play an important role in determining the temperature fluctuations and flow evolution in reality. For example, the mean temperature profil...[

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We report a combined experimental and theoretical study of turbulent Rayleigh-Bénard convection (RBC) in a horizontal thin disk cell and an upright cylindrical cell filled with water and glycerine aqueous solution. The aim of the thesis work is to study the effects of turbulent fluctuations on four aspects of the statistical and dynamic properties
of the temperature field and flow patterns in RBC. The Grossmann-Lohse (GL) model serves as the main theoretical framework describing the global heat transport and large-scale dynamics in RBC [2–5]. This framework, however, is a mean field model and does not take turbulent fluctuations into account, which play an important role in determining the temperature fluctuations and flow evolution in reality. For example, the mean temperature profile θ(z) as a function of distance z away from the conducting plate is usually assumed to have the Prandtl-Blasius-Pohlhausen (PBP) form for a laminar boundary layer (BL), which has no fluctuation and the heat transfer within it is maintained by molecular diffusion. In our experiment, the measured θ(z) along the central axis of the convection cell is found to deviate systematically from the PBP form, and its functional form agrees well with the BL equation recently derived by Shishkina
et al [1]. This deviation originates from fluctuations in the thermal BL, which also gives rise to a non-zero temperature variance profile η(z). The measured η(z) is found to have a scaling form η(z/δ) in the BL region, when the distance z is normalized by the thermal BL thickness δ. Based on the new experimental findings, we derive a BL equation for η(z) and excellent agreement is obtained between the experimental results and theory.

Our understanding of the temperature variance profile is then extended to the mixing zone outside the thermal BL, in which turbulent convection becomes dominant and the convective flow forms a large-scale circulation (LSC). In the mixing zone, the measured θ(z) remains approximately constant, but the measured η(z) is found to scale with the cell height H and has a power law form, η(z) ∼ (z/H)

^{ϵ}, with the obtained values of ϵ being close to -1. A new equation for η(z) is derived, which has a power law solution in good agreement with the experimental results. To give a
complete description of the temperature fluctuation T′ from its time-averaged mean value, I investigated its probability density function P(T′). As RBC is a system far from equilibrium, the measured P(T′) is highly non-Gaussian and has an exponential tail for large temperature fluctuations. In the mixing zone, the measured P(T′) is found to have a characteristic behaviour for the thermal plumes emitted from the
thermal BL intermittently. By introducing a Gaussian source representing the turbulent background and an exponential source representing the thermal plumes, an analytic expression for P(T′) is derived, which describes well the measured P(T′) in different
regions of the convection cell.

I also systematically studied the random reveral events of the large scale flow in the thin disk cell, which are rare but large fluctuations in this system. Using the shadow-graphic technique, the net heat flux accumulation/loss in the closed convection cell is measured. It is found that the net heat flux passing through the convection system is not instantaneously balanced but is balanced only over a long period of time. Two distinct states are identified, one is a small heat accumulation over a long period with a steady LSC and another is a large heat release over a short period of convective quake, which destroys the LSC. We find that the distribution function of the large convective quake amplitude has an exponential form, and the distribution of the time intervals between adjacent quakes also has the same exponential form. By introducing two sensitivity parameters representing the asymmetry between the top and bottom BLs, I generalized the two coupled nonlinear delayed equations proposed by Villermaux [6] and obtained three different types of solutions. The numerical results are consistent with the experimental findings, demonstrating that these solutions indeed capture the essential physics of the convective quake event. Our work thus provides a complete and self-consistent framework for understanding the effect of turbulent fluctuations on the temperature field and dynamics of the flow patterns in RBC. Such an understanding is relevant to many geophysical flows and various practical applications of turbulent thermal convection.

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