Physics of lakes 1

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This first volume of the treatise on the Physics of Lakes establishes the mathematical and physical foundation needed to understand lake dynamics. It describes various lakes, detailing their morphology and responses to environmental factors. The text begins with basic mathematical concepts, assuming only a foundational knowledge of classical Newtonian physics, and gradually advances to more complex topics. It introduces fundamental equations of Lake Hydrodynamics through ‘primitive equations’ and delves into angular momentum and vorticity. Following these basics, turbulence modeling is explored using Reynolds, Favre, and other non-ergodic filters. The derivation of averaged field equations is discussed, incorporating various closure schemes, including the k-ε model for Boussinesq fluids and early anisotropic schemes. The volume also examines surface gravity waves in the absence of rotation and assesses how mass distribution in water bodies affects internal waves. It concludes with an analysis of wind-induced currents in both homogeneous and stratified waters, alongside the Ekman theory and its extensions. The final chapter compiles formulas for the phenomenological coefficients of water, rounding out this comprehensive introduction to lake physics.