A Mathematical Theory of Large-scale Atmosphere/ocean Flow
A Mathematical Theory of Large-scale Atmosphere/ocean Flow

Author: Michael J. P. Cullen

Publisher: World Scientific

Published: 2006

Total Pages: 274

ISBN-13: 186094518X

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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.

A Mathematical Theory of Large-scale Atmosphere/ocean Flow
A Mathematical Theory of Large-scale Atmosphere/ocean Flow

Author: Michael J. P. Cullen

Publisher: Imperial College Press

Published: 2006

Total Pages: 274

ISBN-13: 1860949193

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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."

Atmospheric and Oceanic Fluid Dynamics
Atmospheric and Oceanic Fluid Dynamics

Author: Geoffrey K. Vallis

Publisher: Cambridge University Press

Published: 2006-11-06

Total Pages: 772

ISBN-13: 1139459961

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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.

Introduction to PDEs and Waves for the Atmosphere and Ocean
Introduction to PDEs and Waves for the Atmosphere and Ocean

Author: Andrew Majda

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 210

ISBN-13: 9780821829547

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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.

The Theory of Large-Scale Ocean Circulation
The Theory of Large-Scale Ocean Circulation

Author: R. M. Samelson

Publisher: Cambridge University Press

Published: 2011-06-27

Total Pages: 209

ISBN-13: 1139499009

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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.

Geophysical Fluid Dynamics II
Geophysical Fluid Dynamics II

Author: Emin Özsoy

Publisher: Springer Nature

Published: 2021-08-13

Total Pages: 332

ISBN-13: 3030749347

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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

Geophysical Fluid Dynamics I
Geophysical Fluid Dynamics I

Author: Emin Özsoy

Publisher: Springer Nature

Published: 2020-01-16

Total Pages: 296

ISBN-13: 3030169731

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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.

The Mathematics Of Large-scale Atmosphere And Ocean
The Mathematics Of Large-scale Atmosphere And Ocean

Author: Michael John Priestley Cullen

Publisher: World Scientific

Published: 2021-06-04

Total Pages: 411

ISBN-13: 9811240167

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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)

Ocean Circulation in Three Dimensions
Ocean Circulation in Three Dimensions

Author: Barry A. Klinger

Publisher: Cambridge University Press

Published: 2019-03-14

Total Pages: 491

ISBN-13: 0521768438

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An innovative survey of large-scale ocean circulation that links observations, conceptual models, numerical models, and theories.

Atmospheric Frontal Dynamics
Atmospheric Frontal Dynamics

Author: Mankin Mak

Publisher: Cambridge University Press

Published: 2017-11-16

Total Pages: 209

ISBN-13: 1108547362

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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.