Download or read book A Mathematical Theory Of Large scale Atmosphere ocean Flow written by Michael John Priestley Cullen and published by World Scientific. This book was released on 2006-01-18 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book counteracts the current fashion for theories of “chaos” and unpredictability by describing a theory that underpins the surprising accuracy of current deterministic weather forecasts, and it suggests that further improvements are possible. The book does this by making a unique link between an exciting new branch of mathematics called “optimal transportation” and existing classical theories of the large-scale atmosphere and ocean circulation. It is then possible to solve a set of simple equations proposed many years ago by Hoskins which are asymptotically valid on large scales, and use them to derive quantitative predictions about many large-scale atmospheric and oceanic phenomena. A particular feature is that the simple equations used have highly predictable solutions, thus suggesting that the limits of deterministic predictability of the weather may not yet have been reached. It is also possible to make rigorous statements about the large-scale behaviour of the atmosphere and ocean by proving results using these simple equations and applying them to the real system allowing for the errors in the approximation. There are a number of other titles in this field, but they do not treat this large-scale regime.

Download or read book A Mathematical Theory of Large scale Atmosphere ocean Flow written by Michael J. P. Cullen and published by Imperial College Press. This book was released on 2006 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book counteracts the current fashion for theories of OC chaosOCO and unpredictability by describing a theory that underpins the surprising accuracy of current deterministic weather forecasts, and it suggests that further improvements are possible. The book does this by making a unique link between an exciting new branch of mathematics called OC optimal transportationOCO and existing classical theories of the large-scale atmosphere and ocean circulation. It is then possible to solve a set of simple equations proposed many years ago by Hoskins which are asymptotically valid on large scales, and use them to derive quantitative predictions about many large-scale atmospheric and oceanic phenomena. A particular feature is that the simple equations used have highly predictable solutions, thus suggesting that the limits of deterministic predictability of the weather may not yet have been reached. It is also possible to make rigorous statements about the large-scale behaviour of the atmosphere and ocean by proving results using these simple equations and applying them to the real system allowing for the errors in the approximation. There are a number of other titles in this field, but they do not treat this large-scale regime. Contents: The Governing Equations and Asymptotic Approximations to Them; Solution of the Semi-Geostrophic Equations in Plane Geometry; Solution of the Semi-Geostrophic Equations in More General Cases; Properties of Semi-Geostrophic Solutions; Application of Semi-Geostrophic Theory to the Predictability of atmospheric Flows. Readership: Researchers and graduate students in atmosphere/ocean dynamics with some mathematical background."

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 Introduction to PDEs and Waves for the Atmosphere and Ocean written by Andrew Majda and published by American Mathematical Soc.. This book was released on 2003 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a leading specialist in the area of atmosphere/ocean science (AOS), the book presents an excellent introduction to this important topic. The goals of these lecture notes, based on courses presented by the author at the Courant Institute of Mathematical Sciences, are to introduce mathematicians to the fascinating and important area of atmosphere/ocean science (AOS) and, conversely, to develop a mathematical viewpoint on basic topics in AOS of interest to the disciplinary AOS community, ranging from graduate students to researchers. The lecture notes emphasize the serendipitous connections between applied mathematics and geophysical flows in the style of modern applied mathematics, where rigorous mathematical analysis as well as asymptotic, qualitative, and numerical modeling all interact to ease the understanding of physical phenomena. Reading these lecture notes does not require a previous course in fluid dynamics, although a serious reader should supplement these notes with material such The book is intended for graduate students and researchers working in interdisciplinary areas between mathematics and AOS. It is excellent for supplementary course reading or independent study.

Download or read book The Theory of Large Scale Ocean Circulation written by R. M. Samelson and published by Cambridge University Press. This book was released on 2011-06-27 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mounting evidence that human activities are substantially modifying the Earth's climate brings a new imperative to the study of the ocean's large-scale circulation. This textbook provides a concise but comprehensive introduction to the theory of large-scale ocean circulation, as it is currently understood and established. Students and instructors will benefit from the carefully chosen chapter-by-chapter exercises. This advanced textbook is invaluable for graduate students and researchers in the fields of oceanic, atmospheric and climate sciences, and other geophysical scientists, as well as physicists and mathematicians with a quantitative interest in the planetary fluid environment.

Download or read book Geophysical Fluid Dynamics II written by Emin Özsoy and published by Springer Nature. This book was released on 2021-08-13 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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 The Mathematics Of Large scale Atmosphere And Ocean written by Michael John Priestley Cullen and published by World Scientific. This book was released on 2021-06-04 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: The high predictability of the atmosphere and ocean depends on the existence of a 'slow manifold', which contains the solutions of equations describing only large-scale motions. This unique compendium succinctly describes major recent advances in showing that these equations can be solved independently.The book is a new edition of a similar book published 15 years ago. The explanation of the mathematical techniques has been expanded. Many new theoretical results are included. Illustrations derived from production atmosphere and ocean models are also incorporated to cover the full range between rigorous mathematics and state-of-the-art numerical modelling.The author is a dynamical meteorologist with long experience and international standing. The mathematical results in the book were proved by many of the world's leading analysts. The results come from the Met Office Unified Model, which is one of the world's leading weather and climate models.Related Link(s)

Download or read book Ocean Circulation in Three Dimensions written by Barry A. Klinger and published by Cambridge University Press. This book was released on 2019-03-14 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: An innovative survey of large-scale ocean circulation that links observations, conceptual models, numerical models, and theories.

Download or read book Atmosphere Ocean and Climate Dynamics written by John Marshall and published by Academic Press. This book was released on 1965-01-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: For advanced undergraduate and beginning graduate students in atmospheric, oceanic, and climate science, Atmosphere, Ocean and Climate Dynamics is an introductory textbook on the circulations of the atmosphere and ocean and their interaction, with an emphasis on global scales. It will give students a good grasp of what the atmosphere and oceans look like on the large-scale and why they look that way. The role of the oceans in climate and paleoclimate is also discussed. The combination of observations, theory and accompanying illustrative laboratory experiments sets this text apart by making it accessible to students with no prior training in meteorology or oceanography.* Written at a mathematical level that is appealing for undergraduates andbeginning graduate students* Provides a useful educational tool through a combination of observations andlaboratory demonstrations which can be viewed over the web* Contains instructions on how to reproduce the simple but informativelaboratory experiments* Includes copious problems (with sample answers) to help students learn thematerial.

Download or read book Atmospheric Frontal Dynamics written by Mankin Mak and published by Cambridge University Press. This book was released on 2017-11-16 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Atmospheric Frontal Dynamics is the first book to present a self-contained and comprehensive coverage of the ubiquitous surface and upper-level fronts, which are boundaries separating two air masses of different densities. Atmospheric fronts are a product of interaction between planetary, synoptic, meso and small scales of motions. They are uniquely important in weather forecasting since many meteorological phenomena are closely associated with them. The discussions of the multifaceted aspects of basic frontal dynamics are based on illustrative analyses of a hierarchy of semi-geostrophic frontal models performed in physical, as opposed to geostrophic, coordinates. Such analyses enable us to systematically and quantitatively delineate the physical nature of different types of fronts in a relatively straightforward manner. They are further supplemented by two illustrative analyses using a state-of-the-art model. 'Learning-by-doing' is the guiding principle behind the book, making it an asset to both students and instructors in atmospheric science and meteorology.

Download or read book Mathematics Of Planet Earth A Primer written by Jochen Broecker and published by World Scientific. This book was released on 2017-07-27 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Planet Earth (MPE) was started and continues to be consolidated as a collaboration of mathematical science organisations around the world. These organisations work together to tackle global environmental, social and economic problems using mathematics.This textbook introduces the fundamental topics of MPE to advanced undergraduate and graduate students in mathematics, physics and engineering while explaining their modern usages and operational connections. In particular, it discusses the links between partial differential equations, data assimilation, dynamical systems, mathematical modelling and numerical simulations and applies them to insightful examples.The text also complements advanced courses in geophysical fluid dynamics (GFD) for meteorology, atmospheric science and oceanography. It links the fundamental scientific topics of GFD with their potential usage in applications of climate change and weather variability. The immediacy of examples provides an excellent introduction for experienced researchers interested in learning the scope and primary concepts of MPE.

Download or read book Fundamentals of Numerical Weather Prediction written by Jean Coiffier and published by Cambridge University Press. This book was released on 2011-12-01 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical models have become essential tools in environmental science, particularly in weather forecasting and climate prediction. This book provides a comprehensive overview of the techniques used in these fields, with emphasis on the design of the most recent numerical models of the atmosphere. It presents a short history of numerical weather prediction and its evolution, before describing the various model equations and how to solve them numerically. It outlines the main elements of a meteorological forecast suite, and the theory is illustrated throughout with practical examples of operational models and parameterizations of physical processes. This book is founded on the author's many years of experience, as a scientist at Météo-France and teaching university-level courses. It is a practical and accessible textbook for graduate courses and a handy resource for researchers and professionals in atmospheric physics, meteorology and climatology, as well as the related disciplines of fluid dynamics, hydrology and oceanography.

Download or read book Partial Differential Equations and Geometric Measure Theory written by Alessio Figalli and published by Springer. This book was released on 2018-05-23 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods. The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered. The lectures, given during the course "Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2–7, 2014, should help to encourage further research in the area. The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.

Download or read book Acta Numerica 2009 written by Arieh Iserles and published by Cambridge University Press. This book was released on 2009-05-28 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: A high-impact, prestigious, annual publication featuring invited surveys by subject leaders: essential reading for all practitioners and researchers.

Download or read book Analysis of Monge Amp re Equations written by Nam Q. Le and published by American Mathematical Society. This book was released on 2024-03-07 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic analysis of the Monge–Ampère equation, the linearized Monge–Ampère equation, and their applications, with emphasis on both interior and boundary theories. Starting from scratch, it gives an extensive survey of fundamental results, essential techniques, and intriguing phenomena in the solvability, geometry, and regularity of Monge–Ampère equations. It describes in depth diverse applications arising in geometry, fluid mechanics, meteorology, economics, and the calculus of variations. The modern treatment of boundary behaviors of solutions to Monge–Ampère equations, a very important topic of the theory, is thoroughly discussed. The book synthesizes many important recent advances, including Savin's boundary localization theorem, spectral theory, and interior and boundary regularity in Sobolev and Hölder spaces with optimal assumptions. It highlights geometric aspects of the theory and connections with adjacent research areas. This self-contained book provides the necessary background and techniques in convex geometry, real analysis, and partial differential equations, presents detailed proofs of all theorems, explains subtle constructions, and includes well over a hundred exercises. It can serve as an accessible text for graduate students as well as researchers interested in this subject.

Download or read book Geophysical Fluid Dynamics written by Vladimir Zeitlin and published by Oxford University Press. This book was released on 2018-02-02 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geophysical fluid dynamics examines the dynamics of stratified and turbulent motion of fluids in the ocean and outer core, and of gases in the atmosphere. This book explains key notions and fundamental processes of the dynamics of large- and medium-scale atmospheric and oceanic motions from the unifying viewpoint of the rotating shallow water model. The model plays a distinguished role in geophysical fluid dynamics. It has been used for about a century for conceptual understanding of various phenomena, for elaboration of approaches and methods to be used later in more complete models, for development and testing of numerical codes, and for many other purposes. In spite of its simplicity, the model grasps essential features of the complete "primitive equations" models, being their vertically averaged version, and gives an intuitive representation and clear vision of principal dynamical processes. This book is a combination of a course on geophysical fluid dynamics (Part 1), with explanations and illustrations of fundamentals, and problems, as well as a more advanced treatise of a range of principal dynamical phenomena (Part 2), including recently arisen approaches and applications (Part 3). Mathematics and physics underlying dynamical phenomena are explained, with necessary demonstrations. Yet, an important goal of the book is to develop the reader's physical intuition and qualitative insights.