Introduction To Pdes And Waves For The Atmosphere And Ocean

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Introduction to PDEs and Waves for the Atmosphere and Ocean

Andrew Majda
Introduction to PDEs and Waves for the Atmosphere and Ocean Book PDF

Author : Andrew Majda
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 54,9 Mb
Release : 2003
Category : Atmosphere
ISBN : 0821829548

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Introduction to PDEs and Waves for the Atmosphere and Ocean by Andrew Majda Pdf

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.

Introduction to PDEs and Waves for the Atmosphere and Ocean

Andrew Majda
Introduction to PDEs and Waves for the Atmosphere and Ocean Book PDF

Author : Andrew Majda
Publisher : American Mathematical Soc.
Page : 252 pages
File Size : 52,9 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0821883496

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Introduction to PDEs and Waves for the Atmosphere and Ocean by Andrew Majda Pdf

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.

Waves in the Ocean and Atmosphere

Joseph Pedlosky
Waves in the Ocean and Atmosphere Book PDF

Author : Joseph Pedlosky
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 48,9 Mb
Release : 2013-04-17
Category : Science
ISBN : 9783662051313

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Waves in the Ocean and Atmosphere by Joseph Pedlosky Pdf

A study of the fundamental theory of waves appropriate for first year graduate students in oceanography, meteorology and associated sciences. Starting with an elementary overview of the basic wave concept, specific wave phenomena are then examined, including: surface gravity waves, internal gravity waves, lee waves, waves in the presence of rotation, and geostrophic adjustment. Each wave topic is used to introduce either a new technique or concept in general wave theory. Emphasis is placed on connectivity between the various subjects and on the physical interpretation of the mathematical results. The book contains numerous exercises at the end of the respective chapters.

Energy Transfers in Atmosphere and Ocean

Carsten Eden,Armin Iske
Energy Transfers in Atmosphere and Ocean Book PDF

Author : Carsten Eden,Armin Iske
Publisher : Springer
Page : 312 pages
File Size : 54,5 Mb
Release : 2019-01-23
Category : Computers
ISBN : 9783030057046

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Energy Transfers in Atmosphere and Ocean by Carsten Eden,Armin Iske Pdf

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.

The Mathematics Of Large-scale Atmosphere And Ocean

Michael John Priestley Cullen
The Mathematics Of Large scale Atmosphere And Ocean Book PDF

Author : Michael John Priestley Cullen
Publisher : World Scientific
Page : 411 pages
File Size : 55,6 Mb
Release : 2021-06-04
Category : Science
ISBN : 9789811240164

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The Mathematics Of Large-scale Atmosphere And Ocean by Michael John Priestley Cullen Pdf

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)

Geophysical Fluid Dynamics II

Emin Özsoy
Geophysical Fluid Dynamics II Book PDF

Author : Emin Özsoy
Publisher : Springer Nature
Page : 332 pages
File Size : 52,7 Mb
Release : 2021-08-13
Category : Science
ISBN : 9783030749347

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Geophysical Fluid Dynamics II by Emin Özsoy Pdf

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

Intraseasonal Variability in the Atmosphere-Ocean Climate System

William K.-M. Lau,Duane E. Waliser
Intraseasonal Variability in the Atmosphere Ocean Climate System Book PDF

Author : William K.-M. Lau,Duane E. Waliser
Publisher : Springer Science & Business Media
Page : 614 pages
File Size : 42,8 Mb
Release : 2011-10-25
Category : Science
ISBN : 9783642139147

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Intraseasonal Variability in the Atmosphere-Ocean Climate System by William K.-M. Lau,Duane E. Waliser Pdf

Improving the reliability of long-range forecasts of natural disasters, such as severe weather, droughts and floods, in North America, South America, Africa and the Asian/Australasian monsoon regions is of vital importance to the livelihood of millions of people who are affected by these events. In recent years the significance of major short-term climatic variability, and events such as the El Nino/Southern Oscillation in the Pacific, with its worldwide effect on rainfall patterns, has been all to clearly demonstrated. Understanding and predicting the intra-seasonal variability (ISV) of the ocean and atmosphere is crucial to improving long range environmental forecasts and the reliability of climate change projects through climate models. In the second edition of this classic book on the subject, the authors have updated the original chapters, where appropriate, and added a new chapter that includes short subjects representing substantial new development in ISV research since the publication of the first edition.

Nonlinear Partial Differential Equations

Helge Holden,Kenneth H. Karlsen
Nonlinear Partial Differential Equations Book PDF

Author : Helge Holden,Kenneth H. Karlsen
Publisher : Springer Science & Business Media
Page : 369 pages
File Size : 40,9 Mb
Release : 2012-01-14
Category : Mathematics
ISBN : 9783642253614

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Nonlinear Partial Differential Equations by Helge Holden,Kenneth H. Karlsen Pdf

The topic of the 2010 Abel Symposium, hosted at the Norwegian Academy of Science and Letters, Oslo, was Nonlinear Partial Differential Equations, the study of which is of fundamental importance in mathematics and in almost all of natural sciences, economics, and engineering. This area of mathematics is currently in the midst of an unprecedented development worldwide. Differential equations are used to model phenomena of increasing complexity, and in areas that have traditionally been outside the realm of mathematics. New analytical tools and numerical methods are dramatically improving our understanding of nonlinear models. Nonlinearity gives rise to novel effects reflected in the appearance of shock waves, turbulence, material defects, etc., and offers challenging mathematical problems. On the other hand, new mathematical developments provide new insight in many applications. These proceedings present a selection of the latest exciting results by world leading researchers.

Dynamics of the Equatorial Ocean

John P. Boyd
Dynamics of the Equatorial Ocean Book PDF

Author : John P. Boyd
Publisher : Springer
Page : 517 pages
File Size : 47,9 Mb
Release : 2017-09-25
Category : Science
ISBN : 9783662554760

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Dynamics of the Equatorial Ocean by John P. Boyd Pdf

This book is the first comprehensive introduction to the theory of equatorially-confined waves and currents in the ocean. Among the topics treated are inertial and shear instabilities, wave generation by coastal reflection, semiannual and annual cycles in the tropic sea, transient equatorial waves, vertically-propagating beams, equatorial Ekman layers, the Yoshida jet model, generation of coastal Kelvin waves from equatorial waves by reflection, Rossby solitary waves, and Kelvin frontogenesis. A series of appendices on midlatitude theories for waves, jets and wave reflections add further material to assist the reader in understanding the differences between the same phenomenon in the equatorial zone versus higher latitudes.

Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances

Anonim
Nonlinear Dynamics of Rotating Shallow Water Methods and Advances Book PDF

Author : Anonim
Publisher : Elsevier
Page : 401 pages
File Size : 49,6 Mb
Release : 2007-04-03
Category : Science
ISBN : 9780080489469

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Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances by Anonim Pdf

The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of atmosphere and ocean dynamics at the synoptic scale, especially in its two- (or multi-) layer version. The book describes recent advances in understanding (in the framework of RSW and related models) of some fundamental GFD problems, such as existence of the slow manifold, dynamical splitting of fast (inertia-gravity waves) and slow (vortices, Rossby waves) motions, nonlinear geostrophic adjustment and wave emission, the role of essentially nonlinear wave phenomena. The specificity of the book is that analytical, numerical, and experimental approaches are presented together and complement each other. Special attention is paid on explaining the methodology, e.g. multiple time-scale asymptotic expansions, averaging and removal of resonances, in what concerns theory, high-resolution finite-volume schemes, in what concerns numerical simulations, and turntable experiments with stratified fluids, in what concerns laboratory simulations. A general introduction into GFD is given at the beginning to introduce the problematics for non-specialists. At the same time, recent new results on nonlinear geostrophic adjustment, nonlinear waves, and equatorial dynamics, including some exact results on the existence of the slow manifold, wave breaking, and nonlinear wave solutions are presented for the first time in a systematic manner. · Incorporates analytical, numerical and experimental approaches in the geophysical fluid dynamics context· Combination of essentials in GFD, of the description of analytical, numerical and experimental methods (tutorial part), and new results obtained by these methods (original part)· Provides the link between GFD and mechanics (averaging method, the method of normal forms); GFD and nonlinear physics (shocks, solitons, modons, anomalous transport, periodic nonlinear waves)

Stochastic Transport in Upper Ocean Dynamics II

Bertrand Chapron,Dan Crisan,Darryl Holm,Etienne Mémin,Anna Radomska
Stochastic Transport in Upper Ocean Dynamics II Book PDF

Author : Bertrand Chapron,Dan Crisan,Darryl Holm,Etienne Mémin,Anna Radomska
Publisher : Springer Nature
Page : 347 pages
File Size : 50,5 Mb
Release : 2023-11-04
Category : Mathematics
ISBN : 9783031400940

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Stochastic Transport in Upper Ocean Dynamics II by Bertrand Chapron,Dan Crisan,Darryl Holm,Etienne Mémin,Anna Radomska Pdf

This open access proceedings volume brings selected, peer-reviewed contributions presented at the Third Stochastic Transport in Upper Ocean Dynamics (STUOD) 2022 Workshop, held virtually and in person at the Imperial College London, UK, September 26–29, 2022. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography.

Algebraic Approaches to Partial Differential Equations

Xiaoping Xu
Algebraic Approaches to Partial Differential Equations Book PDF

Author : Xiaoping Xu
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 53,6 Mb
Release : 2013-04-23
Category : Mathematics
ISBN : 9783642368745

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Algebraic Approaches to Partial Differential Equations by Xiaoping Xu Pdf

This book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac equations, the KdV equation, the KP equation, the nonlinear Schrodinger equation, the Davey and Stewartson equations, the Boussinesq equations in geophysics, the Navier-Stokes equations and the boundary layer problems. In order to solve them, I have employed the grading technique, matrix differential operators, stable-range of nonlinear terms, moving frames, asymmetric assumptions, symmetry transformations, linearization techniques and special functions. The book is self-contained and requires only a minimal understanding of calculus and linear algebra, making it accessible to a broad audience in the fields of mathematics, the sciences and engineering. Readers may find the exact solutions and mathematical skills needed in their own research.

Atmospheric and Oceanic Fluid Dynamics

Geoffrey K. Vallis
Atmospheric and Oceanic Fluid Dynamics Book PDF

Author : Geoffrey K. Vallis
Publisher : Cambridge University Press
Page : 772 pages
File Size : 52,8 Mb
Release : 2006-11-06
Category : Science
ISBN : 9781139459969

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Atmospheric and Oceanic Fluid Dynamics by Geoffrey K. Vallis Pdf

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.

Models for Tropical Climate Dynamics

Boualem Khouider
Models for Tropical Climate Dynamics Book PDF

Author : Boualem Khouider
Publisher : Springer
Page : 303 pages
File Size : 51,9 Mb
Release : 2019-07-03
Category : Mathematics
ISBN : 9783030177751

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Models for Tropical Climate Dynamics by Boualem Khouider Pdf

This book is a survey of the research work done by the author over the last 15 years, in collaboration with various eminent mathematicians and climate scientists on the subject of tropical convection and convectively coupled waves. In the areas of climate modelling and climate change science, tropical dynamics and tropical rainfall are among the biggest uncertainties of future projections. This not only puts at risk billions of human beings who populate the tropical continents but it is also of central importance for climate predictions on the global scale. This book aims to introduce the non-expert readers in mathematics and theoretical physics to this fascinating topic in order to attract interest into this difficult and exciting research area. The general thyme revolves around the use of new deterministic and stochastic multi-cloud models for tropical convection and convectively coupled waves. It draws modelling ideas from various areas of mathematics and physics and used in conjunction with state-of-the-art satellite and in-situ observations and detailed numerical simulations. After a review of preliminary material on tropical dynamics and moist thermodynamics, including recent discoveries based on satellite observations as well as Markov chains, the book immerses the reader into the area of models for convection and tropical waves. It begins with basic concepts of linear stability analysis and ends with the use of these models to improve the state-of-the-art global climate models. The book also contains a fair amount of exercises that makes it suitable as a textbook complement on the subject.

Modern Climatology

Shih-Yu (Simon) Wang,Robert Gillies
Modern Climatology Book PDF

Author : Shih-Yu (Simon) Wang,Robert Gillies
Publisher : BoD – Books on Demand
Page : 402 pages
File Size : 51,7 Mb
Release : 2012-03-09
Category : Science
ISBN : 9789535100959

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Modern Climatology by Shih-Yu (Simon) Wang,Robert Gillies Pdf

Climatology, the study of climate, is no longer regarded as a single discipline that treats climate as something that fluctuates only within the unchanging boundaries described by historical statistics. The field has recognized that climate is something that changes continually under the influence of physical and biological forces and so, cannot be understood in isolation but rather, is one that includes diverse scientific disciplines that play their role in understanding a highly complex coupled "whole system" that is the earth's climate. The modern era of climatology is echoed in this book. On the one hand it offers a broad synoptic perspective but also considers the regional standpoint, as it is this that affects what people need from climatology. Aspects on the topic of climate change - what is often considered a contradiction in terms - is also addressed. It is all too evident these days that what recent work in climatology has revealed carries profound implications for economic and social policy; it is with these in mind that the final chapters consider acumens as to the application of what has been learned to date.