Author: Gualtiero Badin
Publisher: Springer
ISBN: 3319596950
Category : Science
Languages : en
Pages : 224
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Book Description
This book describes the derivation of the equations of motion of fluids as well as the dynamics of ocean and atmospheric currents on both large and small scales through the use of variational methods. In this way the equations of Fluid and Geophysical Fluid Dynamics are re-derived making use of a unifying principle, that is Hamilton’s Principle of Least Action. The equations are analyzed within the framework of Lagrangian and Hamiltonian mechanics for continuous systems. The analysis of the equations’ symmetries and the resulting conservation laws, from Noether’s Theorem, represent the core of the description. Central to this work is the analysis of particle relabeling symmetry, which is unique for fluid dynamics and results in the conservation of potential vorticity. Different special approximations and relations, ranging from the semi-geostrophic approximation to the conservation of wave activity, are derived and analyzed. Thanks to a complete derivation of all relationships, this book is accessible for students at both undergraduate and graduate levels, as well for researchers. Students of theoretical physics and applied mathematics will recognize the existence of theoretical challenges behind the applied field of Geophysical Fluid Dynamics, while students of applied physics, meteorology and oceanography will be able to find and appreciate the fundamental relationships behind equations in this field.
Author: Gualtiero Badin
Publisher:
ISBN: 9783319596969
Category : Fluid dynamics
Languages : en
Pages :
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Book Description
Author: Geoffrey K. Vallis
Publisher: Cambridge University Press
ISBN: 1139459961
Category : Science
Languages : en
Pages : 772
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Book Description
Fluid dynamics is fundamental to our understanding of the atmosphere and oceans. Although many of the same principles of fluid dynamics apply to both the atmosphere and oceans, textbooks tend to concentrate on the atmosphere, the ocean, or the theory of geophysical fluid dynamics (GFD). This textbook provides a comprehensive unified treatment of atmospheric and oceanic fluid dynamics. The book introduces the fundamentals of geophysical fluid dynamics, including rotation and stratification, vorticity and potential vorticity, and scaling and approximations. It discusses baroclinic and barotropic instabilities, wave-mean flow interactions and turbulence, and the general circulation of the atmosphere and ocean. Student problems and exercises are included at the end of each chapter. Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation will be an invaluable graduate textbook on advanced courses in GFD, meteorology, atmospheric science and oceanography, and an excellent review volume for researchers. Additional resources are available at www.cambridge.org/9780521849692.
Author: Emin Özsoy
Publisher: Springer Nature
ISBN: 3030169731
Category : Science
Languages : en
Pages : 296
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Book Description
This textbook develops a fundamental understanding of geophysical fluid dynamics by providing a mathematical description of fluid properties, kinematics and dynamics as influenced by earth’s rotation. Its didactic value is based on elaborate treatment of basic principles, derived equations, exemplary solutions and their interpretation. Both starting graduate students and experienced scientists can closely follow the mathematical development of the basic theory applied to the flow of uniform density fluids on a rotating earth, with (1) basic physics introducing the "novel" effects of rotation for flows on planetary scales, (2) simplified dynamics of shallow water and quasi-geostrophic theories applied to a variety of steady, unsteady flows and geophysical wave motions, demonstrating the restoring effects of Coriolis acceleration, earth’s curvature (beta) and topographic steering, (3) conservation of vorticity and energy at geophysical scales, and (4) specific applications to help demonstrate the ability to create and solve new problems in this very rich field. A comprehensive review of the complex geophysical flows of the ocean and the atmosphere is closely knitted with this basic description, intended to be developed further in the second volume that addresses density stratified geophysical fluid dynamics.
Author: Emin Özsoy
Publisher: Springer Nature
ISBN: 3030749347
Category : Science
Languages : en
Pages : 332
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Book Description
This book develops a fundamental understanding of geophysical fluid dynamics based on a mathematical description of the flows of inhomogeneous fluids. It covers these topics: 1. development of the equations of motion for an inhomogeneous fluid 2. review of thermodynamics 3. thermodynamic and kinetic energy equations 4. equations of state for the atmosphere and the ocean, salt, and moisture effects 5. concepts of potential temperature and potential density 6. Boussinesq and quasi-geostrophic approximations 7. conservation equations for vorticity, mechanical and thermal energy instability theories, internal waves, mixing, convection, double-diffusion, stratified turbulence, fronts, intrusions, gravity currents Graduate students will be able to learn and apply the basic theory of geophysical fluid dynamics of inhomogeneous fluids on a rotating earth, including: 1. derivation of the governing equations for a stratified fluid starting from basic principles of physics 2. review of thermodynamics, equations of state, isothermal, adiabatic, isentropic changes 3. scaling of the equations, Boussinesq approximation, applied to the ocean and the atmosphere 4. examples of stratified flows at geophysical scales, steady and unsteady motions, inertia-gravity internal waves, quasi-geostrophic theory 5. vorticity and energy conservation in stratified fluids 6.boundary layer convection in stratified containers and basins
Author: Joseph M. Powers
Publisher: Cambridge University Press
ISBN: 1009028081
Category : Technology & Engineering
Languages : en
Pages : 722
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Book Description
Providing a modern approach to classical fluid mechanics, this textbook presents an accessible and rigorous introduction to the field, with a strong emphasis on both mathematical exposition and physical problems. It includes a consistent treatment of a broad range of fluid mechanics topics, including governing equations, vorticity, potential flow, compressible flow, viscous flow, instability, and turbulence. It has enhanced coverage of geometry, coordinate transformations, kinematics, thermodynamics, heat transfer, and nonlinear dynamics. To round out student understanding, a robust emphasis on theoretical fundamentals and underlying mathematical details is provided, enabling students to gain confidence and develop a solid framework for further study. Included also are 180 end-of-chapter problems, with full solutions and sample course syllabi available for instructors. With sufficient coverage for a one- or two-semester sequence, this textbook provides an ideal flexible teaching pathway for graduate students in aerospace, mechanical, chemical, and civil engineering, and applied mathematics.
Author: Carsten Eden
Publisher: Springer
ISBN: 3030057046
Category : Computers
Languages : en
Pages : 323
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Book Description
This book describes a recent effort combining interdisciplinary expertise within the Collaborative Research Centre “Energy transfers in atmosphere and ocean” (TRR-181), which was funded by the German Research Foundation (DFG). Energy transfers between the three dynamical regimes – small-scale turbulence, internal gravity waves and geostrophically balanced motion – are fundamental to the energy cycle of both the atmosphere and the ocean. Nonetheless, they remain poorly understood and quantified, and have yet to be adequately represented in today’s climate models. Since interactions between the dynamical regimes ultimately link the smallest scales to the largest ones through a range of complex processes, understanding these interactions is essential to constructing atmosphere and ocean models and to predicting the future climate. To this end, TRR 181 combines expertise in applied mathematics, meteorology, and physical oceanography. This book provides an overview of representative specific topics addressed by TRR 181, ranging from - a review of a coherent hierarchy of models using consistent scaling and approximations, and revealing the underlying Hamiltonian structure - a systematic derivation and implementation of stochastic and backscatter parameterisations - an exploration of the dissipation of large-scale mean or eddying balanced flow and ocean eddy parameterisations; and - a study on gravity wave breaking and mixing, the interaction of waves with the mean flow and stratification, wave-wave interactions and gravity wave parameterisations to topics of a more numerical nature such as the spurious mixing and dissipation of advection schemes, and direct numerical simulations of surface waves at the air-sea interface. In TRR 181, the process-oriented topics presented here are complemented by an operationally oriented synthesis focusing on two climate models currently being developed in Germany. In this way, the goal of TRR 181 is to help reduce the biases in and increase the accuracy of atmosphere and ocean models, and ultimately to improve climate models and climate predictions.
Author: Andrew N. Staniforth
Publisher: Cambridge University Press
ISBN: 1108968724
Category : Science
Languages : en
Pages : 820
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Book Description
Combining rigorous theory with practical application, this book provides a unified and detailed account of the fundamental equations governing atmospheric and oceanic fluid flow on which global, quantitative models of weather and climate prediction are founded. It lays the foundation for more accurate models by making fewer approximations and imposing dynamical and thermodynamical consistency, moving beyond the assumption that the Earth is perfectly spherical. A general set of equations is developed in a standard notation with clearly stated assumptions, limitations, and important properties. Some exact, non-linear solutions are developed to promote further understanding and for testing purposes. This book contains a thorough consideration of the fundamental equations for atmospheric and oceanic models, and is therefore invaluable to both theoreticians and numerical modellers. It also stands as an accessible source for reference purposes.
Author: Amir A. Aliabadi
Publisher: Springer Nature
ISBN: 3030954110
Category : Technology & Engineering
Languages : en
Pages : 296
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Book Description
This textbook explains turbulent flows using an introductory but fundamental approach to teaching the core principles, striking a balance between theoretical and practical aspects of the topic without overwhelming the reader with mathematical detail. It is aimed at students in various engineering disciplines—mechanical, civil, environmental—and the geosciences. It is divided in five parts. Part 1 provides the fundamentals of turbulence, main hypotheses, and analysis tools; Part 2 illustrates various measurement techniques used to study turbulent flows; Part 3 explains the modelling and simulation frameworks to study turbulent flows; Part 4 describes brief applications of turbulence in engineering and sciences; and Part 5 presents basic statistical, mathematical, and numerical tools. Elucidates the theory behind turbulence in a concise yet rigorous manner Combines theoretical, computational, experimental, and applied aspects of the topic Reinforces concepts with practice problems at the end of each chapter Provides brief chapters on statistics, mathematics, and numerical techniques
Author: Geoffrey K. Vallis
Publisher: Cambridge University Press
ISBN: 1108586856
Category : Science
Languages : en
Pages : 368
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Book Description
This is a modern, introductory textbook on the dynamics of the atmosphere and ocean, with a healthy dose of geophysical fluid dynamics. It will be invaluable for intermediate to advanced undergraduate and graduate students in meteorology, oceanography, mathematics, and physics. It is unique in taking the reader from very basic concepts to the forefront of research. It also forms an excellent refresher for researchers in atmospheric science and oceanography. It differs from other books at this level in both style and content: as well as very basic material it includes some elementary introductions to more advanced topics. The advanced sections can easily be omitted for a more introductory course, as they are clearly marked in the text. Readers who wish to explore these topics in more detail can refer to this book's parent, Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation, now in its second edition.
