A Theoretical Study of Boundary Layers in Rayleigh-Bénard Convection and Vertical Convection

Thermal convection is ubiquitous in nature and in engineering problems. In this thesis, two common model systems of thermal convection: Rayleigh-Benard convection (RBC) and vertical convection (VC) will be studied. Particularly, we will focus on the turbulent regime in which boundary layers (BLs) are developed near solid boundaries. In BLs, temperature and velocity gradients perpendicular to the boundaries are large and BLs are thus important for turbulent heat and momentum transport.In this thesis, we will carry out a theoretical study of the BLs in RBC and VC. This thesis consists of two parts. In the first part, the complete set of BL equations [Ching et al., Phys. Rev. Research 1, 033037 (2019)] derived for RBC will be reviewed and further analysis will be presented. In the regime where horizontal pressure gradient is negligible, analytical expressions of the heat transfer and velocity BL thickness are obtained in the limit of large and small Prandtl number. By solving the BL equations numerically, the velocity and temperature profiles are obtained. In the second part, a set of BL equations will be derived for VC by generalizing the approach used to study RBC. Theoretical analysis and numerical results of heat transfer, velocity BL thickness and velocity of the large-scale circulation are presented. We will discuss the velocity and temperature profiles obtained as well.在大自然及工程問題中，對流是一常見現象。在這篇論文，我們會研究兩個對流系統的常見模型體系，分別是瑞立-貝納德對流(RBC)及垂直對流(VC)。我們會集中研究於湍流的情況。邊界層(BLs)在邊界處形成。在內的溫度和速度的法向梯度相對大，因此邊界層對於熱及動量的傳播有重大影響。在這篇論文，我們會對RBC及VC的邊界層作出理論性研究。這篇 論文分為兩部分。在第一部分，我們會先回顧發表於[Ching et al., Phys. Rev. Research 1, 033037 (2019)]關於RBC的邊界層公式，繼而再作出進一步的分析。當壓強梯度在水平方向可被忽略時，我們推導出在大與小普朗特數的極限下，關於熱傳播及速度邊界層厚度的解析解。透過數值計算，我們獲得平均溫度及速度的分佈。在第二部分，我們利用同樣的方法研究VC，並推導出對於VC的邊界層公式。透過理論分析及數值計算，我們獲得有關熱傳播、邊界層厚度及大規模環流速度的結果。我們同時亦獲得平均溫度及速度的分佈。TAI, Ngan Cheung.M.Phil. Chinese University of Hong Kong 2021.Includes bibliographical references (leaves )Abstracts in English and Chinese.Title from PDF title page (viewed on ...