Download or read book Variational Formulation of Fluid and Geophysical Fluid Dynamics written by Gualtiero Badin and published by Springer. This book was released on 2017-08-29 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Variational Formulation of Fluid and Geophysical Fluid Dynamics written by Gualtiero Badin and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Geophysical Fluid Dynamics written by Rick Salmon and published by Oxford University Press. This book was released on 1998-02-26 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on Geophysical Fluid Dynamics offers an introduction to several topics in geophysical fluid dynamics, including the theory of large-scale ocean circulation, geostrophic turbulence, and Hamiltonian fluid dynamics. Since each chapter is a self-contained introduction to its particular topic, the book will be useful to students and researchers in diverse scientific fields.
Download or read book Atmospheric and Oceanic Fluid Dynamics written by Geoffrey K. Vallis and published by Cambridge University Press. This book was released on 2006-11-06 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geophysical Fluid Dynamics written by Joseph Pedlosky and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: The content of this book is based, largely, on the core curriculum in geophys ical fluid dynamics which land my colleagues in the Department of Geophysical Sciences at The University of Chicago have taught for the past decade. Our purpose in developing a core curriculum was to provide to advanced undergraduates and entering graduate students a coherent and systematic introduction to the theory of geophysical fluid dynamics. The curriculum and the outline of this book were devised to form a sequence of courses of roughly one and a half academic years (five academic quarters) in length. The goal of the sequence is to help the student rapidly advance to the point where independent study and research are practical expectations. It quickly became apparent that several topics (e. g. , some aspects of potential theory) usually thought of as forming the foundations of a fluid-dynamics curriculum were merely classical rather than essential and could be, however sadly, dispensed with for our purposes. At the same time, the diversity of interests of our students is so great that no curriculum can truly be exhaust ive in such a curriculum period. It seems to me that the best that can be achieved as a compromise is a systematic introduction to some important segment of the total scope of geophysical fluid dynamics which is illustrative of its most fruitful methods.
Download or read book Fundamentals of Geophysical Fluid Dynamics written by James C. McWilliams and published by Cambridge University Press. This book was released on 2006-07-20 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intermediate/advanced textbook which provides concise and accessible introduction to GFD for broad range of students.
Download or read book Mathematical Geophysics written by Jean-Yves Chemin and published by Oxford University Press. This book was released on 2006-04-13 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The Navier-Stokes equations are examined in both incompressible and rapidly rotating forms.
Download or read book Numerical Methods for Fluid Dynamics written by Dale R. Durran and published by Springer Science & Business Media. This book was released on 2010-09-14 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows. The book covers both the essentials of building a numerical model and the more sophisticated techniques that are now available. Finite difference methods, spectral methods, finite element method, flux-corrected methods and TVC schemes are all discussed. Throughout, the author keeps to a middle ground between the theorem-proof formalism of a mathematical text and the highly empirical approach found in some engineering publications. The book establishes a concrete link between theory and practice using an extensive range of test problems to illustrate the theoretically derived properties of various methods. From the reviews: "...the books unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currently actively used in geophysical fluid dynamics." Physics of Atmosphere and Ocean
Download or read book Introduction to Geophysical Fluid Dynamics written by Benoit Cushman-Roisin and published by Academic Press. This book was released on 2011-08-26 with total page 851 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Geophysical Fluid Dynamics provides an introductory-level exploration of geophysical fluid dynamics (GFD), the principles governing air and water flows on large terrestrial scales. Physical principles are illustrated with the aid of the simplest existing models, and the computer methods are shown in juxtaposition with the equations to which they apply. It explores contemporary topics of climate dynamics and equatorial dynamics, including the Greenhouse Effect, global warming, and the El Nino Southern Oscillation. Combines both physical and numerical aspects of geophysical fluid dynamics into a single affordable volume Explores contemporary topics such as the Greenhouse Effect, global warming and the El Nino Southern Oscillation Biographical and historical notes at the ends of chapters trace the intellectual development of the field Recipient of the 2010 Wernaers Prize, awarded each year by the National Fund for Scientific Research of Belgium (FNR-FNRS)
Download or read book An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics written by and published by Elsevier. This book was released on 1980-01-01 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics
Download or read book Mathematical Geophysics written by Jean-Yves Chemin and published by Clarendon Press. This book was released on 2006-04-13 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students, researchers and academics in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The text is divided into four parts, with the first part providing the physical background of the geophysical models to be analysed. Part II is devoted to a self contained proof of the existence of weak (or strong) solutions to the incompressible Navier-Stokes equations. Part III deals with the rapidly rotating Navier-Stokes equations, first in the whole space, where dispersion effects are considered. The case where the domain has periodic boundary conditions is then analysed, and finally rotating Navier-Stokes equations between two plates are studied, both in the case of periodic horizontal coordinates and those in R2. In Part IV the stability of Ekman boundary layers, and boundary layer effects in magnetohydrodynamics and quasigeostrophic equations are discussed. The boundary layers which appear near vertical walls are presented and formally linked with the classical Prandlt equations. Finally spherical layers are introduced, whose study is completely open.
Download or read book Theoretical Geophysical Fluid Dynamics written by Monin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of lectures on geophysical fluid dynamics delivered over many years at the Moscow Institute of Physics and Technology by the author (and, with regard to some parts of the book, by his colleagues). During these lectures the students were advised to read many books, and sometimes individual articles, in order to acquaint themselves with the necessary material, since there was no single book available which provided a sufficiently complete and systematic account (except, perhaps, the volumes on Hydrophysics of the Ocean, Hydrodynamics of the Ocean, and Geodynamics in the ten-volume Oceanology series published by Nauka Press in 1978-1979; these refer, however, specifically to the ocean, and anyway they are much too massive to be convenient for study by students). As far as we know, no text corresponding to our understanding of geophysical fluid dynamics has as yet been published outside the Soviet Union. The present book is designed to fill this gap. Since it is customary to write the preface after the entire book has been completed, the author has an opportunity there to raise some points of possible criticism by the reviewers and readers. First of all, note that this work presents the theoretical fundamentals of geophysical fluid dynamics, and that observational and experimental data (which in the natural sciences are always very copious) are referred to only rarely and briefly.
Download or read book Compatible Finite Element Methods for Geophysical Flows written by Thomas H. Gibson and published by Springer Nature. This book was released on 2019-08-26 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces recently developed mixed finite element methods for large-scale geophysical flows that preserve essential numerical properties for accurate simulations. The methods are presented using standard models of atmospheric flows and are implemented using the Firedrake finite element library. Examples guide the reader through problem formulation, discretisation, and automated implementation. The so-called “compatible” finite element methods possess key numerical properties which are crucial for real-world operational weather and climate prediction. The authors summarise the theory and practical implications of these methods for model problems, introducing the reader to the Firedrake package and providing open-source implementations for all the examples covered. Students and researchers with engineering, physics, mathematics, or computer science backgrounds will benefit from this book. Those readers who are less familiar with the topic are provided with an overview of geophysical fluid dynamics.
Download or read book Fluid Models in Geophysics written by Robert R. Long and published by . This book was released on 1953 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Variational Methods in Fluid Dynamics written by Henry Karl Voigt and published by . This book was released on 1965 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geophysical Fluid Dynamics I written by Emin Özsoy and published by Springer Nature. This book was released on 2020-01-16 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fluid Dynamics in Action written by Paolo Glorioso and published by . This book was released on 2016 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we formulate an effective field theory for nonlinear dissipative fluid dynamics. The formalism incorporates an action principle for the classical equations of motion as well as a systematic approach to thermal and quantum fluctuations around the classical motion of fluids. The dynamical degrees of freedom are Stuckelberg-like fields associated with diffeomorphisms and gauge transformations, and are related to the conservation of the stress tensor and a U(1) current if the fluid possesses a charge. This inherently geometric construction gives rise to an emergent "fluid space-time", similar to the Lagrangian description of fluids. We develop the variational formulation based on symmetry principles defined on such fluid space-time. Through a prescribed correspondence, the dynamical fields are mapped to the standard fluid variables, such as temperature, chemical potential and velocity. This allows to recover the standard equations of fluid dynamics in the limit where fluctuations are negligible. Demanding the action to be invariant under a discrete transformation, which we call local KMS, guarantees that the correlators of the stress tensor and the current satisfy the fluctuation-dissipation theorem. Local KMS invariance also automatically ensures that the constitutive relations of the conserved quantities satisfy the standard constraints implied e.g. by the second law of thermodynamics, and leads to a new set of constraints which we call generalized Onsager relations. Requiring the above properties to hold beyond tree-level leads to introducing fermionic partners of the original degrees of freedom, and to an emergent supersymmetry. We also outline a procedure for obtaining the effective field theory for fluid dynamics by applying the holographic Wilsonian renormalization group to systems with a gravity dual.
