Non Linear Dynamics And Statistical Theories For Basic Geophysical Flows
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Non-linear Dynamics and Statistical Theories for Basic Geophysical Flows by Andrew Majda Pdf
Geophysical fluid dynamics illustrates the rich interplay between mathematical analysis, nonlinear dynamics, statistical theories, qualitative models and numerical simulations. This self-contained introduction will suit a multi-disciplinary audience ranging from beginning graduate students to senior researchers. It is the first book following this approach and contains many recent ideas and results.
Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows by Andrew Majda,Xiaoming Wang Pdf
The general area of geophysical fluid mechanics is truly interdisciplinary. Now ideas from statistical physics are being applied in novel ways to inhomogeneous complex systems such as atmospheres and oceans. In this book, the basic ideas of geophysics, probability theory, information theory, nonlinear dynamics and equilibrium statistical mechanics are introduced and applied to large time-selective decay, the effect of large scale forcing, nonlinear stability, fluid flow on a sphere and Jupiter's Great Red Spot. The book is the first to adopt this approach and it contains many recent ideas and results. Its audience ranges from graduate students and researchers in both applied mathematics and the geophysical sciences. It illustrates the richness of the interplay of mathematical analysis, qualitative models and numerical simulations which combine in the emerging area of computational science.
Peyresq Lectures on Nonlinear Phenomena by Freddy Bouchet Pdf
This book is the third volume of lecture notes from summer schools held in the small village of Peyresq (France). These lectures cover nonlinear physics in a broad sense. They were given over the period 2004 to 2008. The summer schools were organized by the Institut Non Lin(r)aire de Nice (Nice, France), the Laboratoire de Physique Statistique (ENS Paris, France) and the Institut de Recherche de Physique Hors Equilibre (Marseilles, France). The goal of the book is to provide a high-quality overview on the state of the art in nonlinear sciences, and to promote the transfer of knowledge between the various domains in physics dealing with nonlinear phenomen
Peyresq Lectures on Nonlinear Phenomena by Freddy Bouchet,Basile Audoly,Jacques Alexandre Sepulchre Pdf
This book is the third volume of lecture notes from summer schools held in the small village of Peyresq (France). These lectures cover nonlinear physics in a broad sense. They were given over the period 2004 to 2008. The summer schools were organized by the Institut Non Linéaire de Nice (Nice, France), the Laboratoire de Physique Statistique (ENS Paris, France) and the Institut de Recherche de Physique Hors Equilibre (Marseilles, France). The goal of the book is to provide a high-quality overview on the state of the art in nonlinear sciences, and to promote the transfer of knowledge between the various domains in physics dealing with nonlinear phenomena. Contents:Some Examples of Animal Locomotion in Fluids (M Argentina)Applications of Equilibrium Statistical Mechanics to Atmospheres and Oceans (F Bouchet and A Venaille)Stochastic Perturbations of Nonlinear Dispersive Waves (A De Bouard)On Different Aspects of Granular Physics (C Josserand, P-Y Lagrée and D Lhuillier)Relativité générale (General relativity) (M Le Bellac)Bioadhesion (E Perez and F Pincet)Interfacial Growth Phenomena (A Pocheau) Readership: Physicists, mathematicians and biologists. Graduate students, post-docs, lecturers and researchers in nonlinear science. Keywords:BoseâEinstein Condensates;Fluid Dynamics;Complex Fluids;Mixing;Dynamo Effect
Nonlinear Conservation Laws, Fluid Systems and Related Topics by Gui-Qiang Chen Pdf
This book is a collection of lecture notes on Nonlinear Conservation Laws, Fluid Systems and Related Topics delivered at the 2007 Shanghai Mathematics Summer School held at Fudan University, China, by world''s leading experts in the field. The volume comprises five chapters that cover a range of topics from mathematical theory and numerical approximation of both incompressible and compressible fluid flows, kinetic theory and conservation laws, to statistical theories for fluid systems. Researchers and graduate students who want to work in this field will benefit from this essential reference as each chapter leads readers from the basics to the frontiers of the current research in these areas.
Information Theory and Stochastics for Multiscale Nonlinear Systems by Andrew Majda,Rafail V. Abramov,Marcus J. Grote Pdf
This book introduces mathematicians to the fascinating mathematical interplay between ideas from stochastics and information theory and practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena. After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of complex nonlinear systems. After a general discussion, a new elementary model, motivated by issues in climate dynamics, is utilized to develop a self-contained example of stochastic mode reduction. Based on A. Majda's Aisenstadt lectures at the University of Montreal, the book is appropriate for both pure and applied mathematics graduate students, postdocs and faculty, as well as interested researchers in other scientific disciplines. No background in geophysical flows is required. About the authors: Andrew Majda is a member of the National Academy of Sciences and has received numerous honors and awards, including the National Academy of Science Prize in Applied Mathematics, the John von Neumann Prize of the Society of Industrial and Applied Mathematics, the Gibbs Prize of the American Mathematical Society, and the Medal of the College de France. In the past several years at the Courant Institute, Majda and a multi-disciplinary faculty have created the Center for Atmosphere Ocean Science to promote cross-disciplinary research with modern applied mathematics in climate modeling and prediction. R.V. Abramov is a young researcher; he received his PhD in 2002. M. J. Grote received his Ph.D. under Joseph B. Keller at Stanford University in 1995.
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
Nonlinear Climate Dynamics by Henk A. Dijkstra Pdf
This book presents stochastic dynamical systems theory in order to synthesize our current knowledge of climate variability, for graduate students and researchers.
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.
Introduction to Turbulent Dynamical Systems in Complex Systems by Andrew J. Majda Pdf
This volume is a research expository article on the applied mathematics of turbulent dynamical systems through the paradigm of modern applied mathematics. It involves the blending of rigorous mathematical theory, qualitative and quantitative modeling, and novel numerical procedures driven by the goal of understanding physical phenomena which are of central importance to the field. The contents cover general framework, concrete examples, and instructive qualitative models. Accessible open problems are mentioned throughout. Topics covered include: · Geophysical flows with rotation, topography, deterministic and random forcing · New statistical energy principles for general turbulent dynamical systems, with applications · Linear statistical response theory combined with information theory to cope with model errors · Reduced low order models · Recent mathematical strategies for online data assimilation of turbulent dynamical systems as well as rigorous results for finite ensemble Kalman filters The volume will appeal to graduate students and researchers working mathematics, physics and engineering and particularly those in the climate, atmospheric and ocean sciences interested in turbulent dynamical as well as other complex systems.
Climate Change: Multidecadal and Beyond by Chih-Pei Chang,Michael Ghil,Mojib Latif,John M Wallace Pdf
This book focuses on two major challenges in the climate sciences: 1) to describe the decadal-to-centennial variations in instrumental and proxy records; and 2) to distinguish between anthropogenic variations and natural variability. The National Taiwan University invited some of the world's leading experts across the areas of observational analysis, mathematical theory, and modeling to discuss these two issues. The outcome of the meeting is the 23 chapters in this book that review the state of the art in theoretical, observational and modeling research on internal, unforced and externally forced climate variability. The main conclusion of this research is that internal climate variability on decadal and longer time scales is so large that sidestepping it may lead to false estimates of the climate's sensitivity to anthropogenic forcing. Contents:Attribution of Climate Change in the Presence of Internal Variability (John M Wallace, Clara Deser, Brian V Smoliak, and Adam S Phillips)A Mathematical Theory of Climate Sensitivity or, How to Deal With Both Anthropogenic Forcing and Natural Variability? (Michael Ghil)Fluctuation-dissipation Theorem with Application to Climate Change Studies with Seasonal Impact (Xiaoming Wang)Parametrization of Cross-scale Interaction in Multiscale Systems (Jeroen Wouters and Valerio Lucarini)Dynamics of Nonlinear Error Growth and the "Spring Predictability Barrier" for El Niño Predictions (Wansuo Duan and Mu Mu)An Adaptive Approach for Nonlinear and Nonstationary Data Analysis (Norden E Huang)Internal Southern Ocean Centennial Variability: Dynamics, Impacts and Implications for Global Warming (Mojib Latif, Torge Martin, Wonsun Park, and Mohammad H Bordbar)Atlantic Meridional Overturning Circulation and Climate (Rong Zhang)North Atlantic Multi-Decadal Variability — Mechanisms and Predictability (Noel S Keenlyside, Jin Ba, Jennifer Mecking, Nour-Eddine Omrani, Mojib Latif, Rong Zhang, and Rym Msadek)A Review of the Dynamics of Pacific Interdecadal Climate Variability (Zhengyu Liu)Global-Scale Decadal Hyper Modes (Dietmar Dommenget)Evidence for a Recurrent Multi-Decadal Oscillation in Global Temperature and Possible Impacts on 21st Century Climate Projections (Ka-Kit Tung and Jiansong Zhou)Variability of Sea Ice Extent Over Decadal and Longer Timescales (John E Walsh and William L Chapman)Multi-year Prediction and Predictability (Timothy DelSole, Michael K Tippett, and Liwei Jia)Decadal Hydroclimate Variability Across the Americas (Richard Seager)The Interhemispheric Pattern and Long-Term Variations in the Tropical Climate over the 20th and 21st Centuries (John C H Chiang)Climate of China in the Holocene (Wang Shaowu, Wen Xinyu, and Huang Jianbin)North Atlantic Hurricane Activity: Past, Present and Future (Rym Msadek, Gabriel A Vecchi, and Thomas R Knutson)Observed Variations of Western North Pacific Tropical Cyclone Activity on Decadal Time Scales and Longer (Johnny C L Chan)Record-Breaking Increase of Tropical Cyclone Heavy Rainfall in Taiwan in the First Decade of 21st Century (Chih-Pei Chang, Hung-Chi Kuo, and Chung-Hsiung Sui)Multi-Decadal Variability in Indian Summer Monsoon Rainfall Using Proxy Data (Bhupendra N Goswami, Ramesh H Kripalani, Hemant P Borgaonkar, and Bhaskar Preethi)The South-Flood North-Drought Pattern Over Eastern China and the Drying of the Gangetic Plain (Sumant Nigam, Yongjing Zhao, Alfredo Ruiz-Barradas, and Tianjun Zhou)Impacts of Aerosols on the Asian Monsoon — An Interim Assessment (William K M Lau and Kyu-Myong Kim) Readership: Graduate students, academics and researchers in atmospheric sciences, oceanography, mathematics, and climate change. Keywords:Climate Change;Multidecadal Variability;Climate Variability Asia-Pacific Weather
Data-driven modeling and optimization in fluid dynamics: From physics-based to machine learning approaches by Michel Bergmann,Laurent Cordier,Traian Iliescu Pdf
Interactions between waves and mean flows play a crucial role in understanding the long-term aspects of atmospheric and oceanographic modelling. Indeed, our ability to predict climate change hinges on our ability to model waves accurately. This book gives a modern account of the nonlinear interactions between waves and mean flows such as shear flows and vortices. A detailed account of the theory of linear dispersive waves in moving media is followed by a thorough introduction to classical wave–mean interaction theory. The author then extends the scope of the classical theory and lifts its restriction to zonally symmetric mean flows. The book is a fundamental reference for graduate students and researchers in fluid mechanics, and can be used as a text for advanced courses; it will also be appreciated by geophysicists and physicists who need an introduction to this important area in fundamental fluid dynamics and atmosphere-ocean science.
Mathematical Approach to Climate Change and its Impacts by Piermarco Cannarsa,Daniela Mansutti,Antonello Provenzale Pdf
This book presents important recent applied mathematics research on environmental problems and impacts due to climate change. Although there are inherent difficulties in addressing phenomena that are part of such a complex system, exploration of the subject using mathematical modelling is especially suited to tackling poorly understood issues in the field. It is in this spirit that the book was conceived. It is an outcome of the International INDAM Workshop “Mathematical Approach to Climate Change Impacts – MAC2I”, held in Rome in March 2017. The workshop comprised four sessions, on Ecosystems, Hydrology, Glaciology, and Monitoring. The book includes peer-reviewed contributions on research issues discussed during each of these sessions or generated by collaborations among the specialists involved. Accurate parameter determination techniques are explained and innovative mathematical modelling approaches, presented. The book also provides useful material and mathematical problem-solving tools for doctoral programs dealing with the complexities of climate change.
The book introduces readers to and summarizes the current ideas and theories about the basic mechanisms for transport in chaotic flows. Typically no single paradigmatic approach exists as this topic is relevant for fields as diverse as plasma physics, geophysical flows and various branches of engineering. Accordingly, the dispersion of matter in chaotic or turbulent flows is analyzed from different perspectives. Partly based on lecture courses given by the author, this book addresses both graduate students and researchers in search of a high-level but approachable and broad introduction to the topic.
