Physics of Lakes

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This first volume in the treatise on the Physics of Lakes focuses on the mathematical and physical foundations necessary for understanding lakes. It describes various lakes, detailing their morphology and responses to environmental factors. The text emphasizes the importance of mathematics in lake physics, beginning with a straightforward introduction that assumes only basic knowledge of classical Newtonian physics. It progresses in complexity, starting with fundamental equations of Lake Hydrodynamics in the form of ‘primitive equations’ and advancing to angular momentum and vorticity. Following these fundamentals, turbulence modeling is introduced, covering Reynolds, Favre, and other non-ergodic filters. The derivation of averaged field equations is discussed, including closure schemes such as the k-ε model for Boussinesq fluids and early anisotropic models. The book also examines surface gravity waves without rotation and the impact of mass distribution within water bodies, leading to an exploration of internal waves. Additionally, it addresses the vertical structure of wind-induced currents in both homogeneous and stratified waters, along with Ekman theory and its extensions. The volume concludes with a chapter summarizing formulas for the phenomenological coefficients of water.