Kolumban Hutter Libri

The second volume of “Physics of Lakes,” subtitled “Lakes as Oscillators,” focuses on barotropic and baroclinic waves in homogeneous and stratified lakes on a rotating Earth. Spanning 12 chapters, it begins with an exploration of rotating shallow-water waves, classifying them into gravity and Rossby waves in various water bodies. The discussion extends to gravity waves in bounded domains of constant depth, covering Kelvin, Poincaré, and Sverdrup waves, as well as their reflections in gulfs and rectangles, and their behavior in sealed basins as barotropic ‘inertial waves proper.’ The application to gravity waves in circular and elliptical basins leads to a description of Kelvin-type and Poincaré-type waves, addressing basins of arbitrary geometry. The text also examines two-, three-, and n-layer fluids with sharp interfaces, detailing higher-order baroclinic gravity waves, supported by experimental evidence from locations such as Lake Lugano, Lake Banyoles, and Lake Biwa. It highlights the need for careful interpretation of data and computational outputs in complex geometries, particularly in Lake Onega. A summer field campaign in Lake Lugano emphasizes the importance of statistical analyses to align data with computational results. The work includes three chapters on topographic Rossby waves, identifying conditions under which baroclinicity has minimal impact and categorizing these waves into channel modes, Ball modes, and bay

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.

The 2nd volume of “Physics of Lakes” focuses on “Lakes as Oscillators,” exploring barotropic and baroclinic waves in both homogeneous and stratified lakes on a rotating Earth. Comprising 12 chapters, it begins with the classification of rotating shallow-water waves into gravity and Rossby waves. The discussion progresses to gravity waves in bounded domains of constant depth, including Kelvin, Poincaré, and Sverdrup waves, as well as their reflections in gulfs and rectangles and their behavior in sealed basins as barotropic ‘inertial waves proper.’ The text delves into gravity waves in circular and elliptical basins, leading to Kelvin-type and Poincaré-type waves and their balanced descriptions in various geometries. It also examines two-, three-, and n-layer fluids with sharp interfaces, detailing higher-order baroclinic gravity waves supported by experimental evidence from lakes like Lugano, Banyoles, and Biwa. The analysis of barotropic wave modes in Lake Onega highlights the need for careful interpretation of data and computational results. A summer field campaign in Lake Lugano emphasizes the importance of statistical analysis to align data with computational findings. Additionally, three chapters focus on topographic Rossby waves, identifying conditions under which baroclinicity has minimal impact and categorizing these waves into channel modes, Ball modes, and bay modes. The final chapter presents Chrystal-type equations

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.

Fluid mechanical concepts are explored in detail, focusing on both ideal and viscous processes. The volume covers fundamental hydrostatics and hydrodynamics, providing an almanac of flow problems for ideal fluids. Exact solutions for various flow configurations are graphically illustrated, addressing both Newtonian and non-Newtonian fluids. It also includes analyses of specific flows, such as Blasius boundary layer flows and the Navier-Stokes equations, while offering critiques of established models like the logarithmic velocity profile.

The book delves into the complexities of continuous bodies, exploring both classical Boltzmann and Cosserat continua, as well as fluid mixtures. It formulates balance laws and deformation measures for systems with trivial and nontrivial angular momentum, addressing multiphase interactions. Thermodynamic principles are applied to Boltzmann-type fluids interacting across various dimensions, with a focus on mass, momentum, energy, and entropy balance. Additionally, it introduces constitutive modeling for different body parts, emphasizing both equilibrium and non-equilibrium processes.

The book presents fluid mechanics and thermodynamics as interconnected disciplines, beginning with an analysis of creeping motion around stationary spheres and progressing through various theories, including Stokes flows and the Oseen correction. It explores 3D creeping flows and granular avalanches, leading to insights on turbulence modeling. The discussion of thermodynamics encompasses the first and second laws and entropy balance. Additionally, it includes applications in gas dynamics and concludes with a chapter on dimensional analysis and physical experiments.

Internal wave dynamics in lakes (and oceans) is an important physical component of geophysical fluid mechanics of ‘quiescent’ water bodies of the Globe. The formation of internal waves requires seasonal stratification of the water bodies and generation by (primarily) wind forces. Because they propagate in basins of variable depth, a generated wave field often experiences transformation from large basin-wide scales to smaller scales. As long as this fission is hydrodynamically stable, nothing dramatic will happen. However, if vertical density gradients and shearing of the horizontal currents in the metalimnion combine to a Richardson number sufficiently small (< ¼), the light epilimnion water mixes with the water of the hypolimnion, giving rise to vertical diffusion of substances into lower depths. This meromixis is chiefly responsible for the ventilation of the deeper waters and the homogenization of the water through the lake depth. These processes are mainly formed as a result of the physical conditions, but they play biologically an important role in the trophicational state of the lake.

KlappentextThis book in two parts delivers a thorough derivation of nonrelativistic interaction models of electromagnetic field theories with thermoelastic solids and viscous fluids, the intention being to derive unique representations for the observable field quantities. Part I, a revised and updated version of LNP 88 „Field Matter Interactions in Thermoelastic Solids,“ investigates the foundations and the equivalence of various formulations of the interaction of the electromagnetic field with thermoelastic solids in the classical continuum physics limit, while Part II extensively surveys two major fields of applications, namely, magnetoelastic instabilities and vibrations, and electrorheological fluids. This volume is intended for and will be useful to students and researchers working on all aspects of electromagneto-mechanical interactions in the materials sciences of complex solids and fluids.

This book is a considerable outgrowth of lecture notes on Mechanics of en vironmentally related systems I, which I hold since more than ten years in the Department of Mechanics at the Darmstadt University of Technology for upper level students majoring in mechanics, mathematics, physics and the classical engineering sciences. These lectures form a canon of courses over three semesters in which I present the foundations of continuum physics (first semester), those of physical oceanography and limnology (second semester) and those of soil, snow and ice physics in the geophysical context (third semester). The intention is to build an understanding of the mathemati cal foundations of the mentioned geophysical research fields combined with a corresponding understanding of the regional, but equally also the global, processes that govern the climate dynamics of our globe. The present book contains the material (and extensions of it) of the first semester; it gives an introduction into continuum thermomechanics, the methods of dimensional analysis and turbulence modeling.