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Nonlinear Dynamics Of Rotating Shallow Water

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Nonlinear Dynamics of Rotating Shallow Water Methods and Advances

Nonlinear Dynamics of Rotating Shallow Water  Methods and Advances Book
Author : Anonim
Publisher : Elsevier
Release : 2007-04-03
ISBN : 9780080489469
Language : En, Es, Fr & De

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Book Description :

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)

Rotating Shallow Water

Rotating Shallow Water Book
Author : Alana McKenzie
Publisher : Unknown
Release : 2007
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Rotating shallow water is traditionally the first model encountered in the study of geophysical fluid dynamics. Its simplicity and applicability at large scales make it a favourable starting point for understanding midlatitude atmospheric behaviour. The linearized model reveals two principal dynamical features - fast time-scale wave disturbances, and slow time-scale balanced flow. Textbook analysis typically includes linear wave properties, and the leading order balanced dynamics of quasigeostrophy. We seek to further understand the successes and limitations of rotating shallow water in modelling geophysical fluid dynamics. In this study, nonlinear wave dynamics are restricted to uniform potential vorticity. This reduced set of equations enables the computational analysis of nonlinear waves, devoid of balanced dynamics. Additionally, balanced dynamics are investigated beyond quasigeostrophy to include small Rossby number corrections. As anticipated, an asymmetry between cyclone and anticyclone vortices emerges; the biases are consistent with similar models, and contradict atmospheric behaviour.

Fronts Waves and Vortices in Geophysical Flows

Fronts  Waves and Vortices in Geophysical Flows Book
Author : Jan-Bert Flor
Publisher : Springer
Release : 2010-06-01
ISBN : 364211587X
Language : En, Es, Fr & De

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Book Description :

Most well known structures in planetary atmospheres and the Earth’s oceans are jets or fronts interacting with vortices on a wide range of scales. The transition from one state to another, such as in unbalanced or adjustment flows, involves the generation of waves as well as the interaction of coherent structures with these waves. This book presents a fluid mechanics perspective to the dynamics of fronts and vortices and their interaction with waves in geophysical flows. It provides a basic physical background for modeling coherent structures in a geophysical context, and it gives essential information on advanced topics such as spontaneous wave emission and wavemomentum transfer in geophysical flows. Based on a set of lectures by leading specialists, this text is targeted at graduate students, researchers and engineers in geophysics and environmental fluid mechanics.

Geophysical Fluid Dynamics

Geophysical Fluid Dynamics Book
Author : Vladimir Zeitlin
Publisher : Oxford University Press
Release : 2018-02-15
ISBN : 0198804334
Language : En, Es, Fr & De

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Book Description :

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.

Dispersive Shallow Water Waves

Dispersive Shallow Water Waves Book
Author : Gayaz Khakimzyanov,Denys Dutykh,Zinaida Fedotova,Oleg Gusev
Publisher : Springer Nature
Release : 2020
ISBN : 3030462676
Language : En, Es, Fr & De

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Book Description :

This monograph presents cutting-edge research on dispersive wave modelling, and the numerical methods used to simulate the propagation and generation of long surface water waves. Including both an overview of existing dispersive models, as well as recent breakthroughs, the authors maintain an ideal balance between theory and applications. From modelling tsunami waves to smaller scale coastal processes, this book will be an indispensable resource for those looking to be brought up-to-date in this active area of scientific research. Beginning with an introduction to various dispersive long wave models on the flat space, the authors establish a foundation on which readers can confidently approach more advanced mathematical models and numerical techniques. The first two chapters of the book cover modelling and numerical simulation over globally flat spaces, including adaptive moving grid methods along with the operator splitting approach, which was historically proposed at the Institute of Computational Technologies at Novosibirsk. Later chapters build on this to explore high-end mathematical modelling of the fluid flow over deformed and rotating spheres using the operator splitting approach. The appendices that follow further elaborate by providing valuable insight into long wave models based on the potential flow assumption, and modified intermediate weakly nonlinear weakly dispersive equations. Dispersive Shallow Water Waves will be a valuable resource for researchers studying theoretical or applied oceanography, nonlinear waves as well as those more broadly interested in free surface flow dynamics.

Vortex Structures in Fluid Dynamic Problems

Vortex Structures in Fluid Dynamic Problems Book
Author : Hector Perez-De-Tejada
Publisher : BoD – Books on Demand
Release : 2017-03-01
ISBN : 9535129430
Language : En, Es, Fr & De

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Book Description :

The contents of the book cover topics on vortex dynamics in a variety of flow problems and describe observational measurements and their interpretation. The book contains 13 chapters that first include vortices in the earth and planetary sciences related to vortices in the Venus plasma wake and also on tropical cyclones and on rotating shallow water in the earth's atmosphere. Vortices in fluid problems include airplane wake vortices, vorticity evolution in free-shear flows, together with axisymmetric flows with swirl, as well as thermal conductivities in fluid layers. Vortices in relativistic fluids, in magnetic disks, solitons and vortices, and relaxation for point vortices were also examined. Other chapters describe conditions in a vortex bioreactor and in vortex yarn structures.

Waves in Flows

Waves in Flows Book
Author : Tomáš Bodnár
Publisher : Springer Nature
Release : 2021-09-18
ISBN : 3030678458
Language : En, Es, Fr & De

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Book Description :

Download Waves in Flows book written by Tomáš Bodnár, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Dynamics of the Equatorial Ocean

Dynamics of the Equatorial Ocean Book
Author : John P. Boyd
Publisher : Springer
Release : 2017-09-25
ISBN : 3662554763
Language : En, Es, Fr & De

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Book Description :

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.

Handbook of Geomathematics

Handbook of Geomathematics Book
Author : Willi Freeden,M. Zuhair Nashed,Thomas Sonar
Publisher : Springer Science & Business Media
Release : 2010-08-13
ISBN : 364201545X
Language : En, Es, Fr & De

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Book Description :

During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as spaceborne data of better and better quality explain the strong need of new mathematical structures, tools, and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The ‘Handbook Geomathematics’ as a central reference work in this area comprises the following scientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic, and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.

Handbook of Differential Equations Evolutionary Equations

Handbook of Differential Equations  Evolutionary Equations Book
Author : C.M. Dafermos,Milan Pokorny
Publisher : Elsevier
Release : 2009-04-29
ISBN : 9780080932590
Language : En, Es, Fr & De

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Book Description :

Handbook of Differential Equations: Evolutionary Equations is the last text of a five-volume reference in mathematics and methodology. This volume follows the format set by the preceding volumes, presenting numerous contributions that reflect the nature of the area of evolutionary partial differential equations. The book is comprised of five chapters that feature the following: • A thorough discussion of the shallow-equations theory, which is used as a model for water waves in rivers, lakes and oceans. It covers the issues of modeling, analysis and applications. • Evaluation of the singular limits of reaction-diffusion systems, where the reaction is fast compared to the other processes; and applications that range from the theory of the evolution of certain biological processes to the phenomena of Turing and cross-diffusion instability • Detailed discussion of numerous problems arising from nonlinear optics, at the high-frequency and high-intensity regime • Geometric and diffractive optics, including wave interactions • Presentation of the issues of existence, blow-up and asymptotic stability of solutions, from the equations of solutions to the equations of linear and non-linear thermoelasticity • Answers to questions about unique space, such as continuation and backward uniqueness for linear second-order parabolic equations. Research mathematicians, mathematics lecturers and instructors, and academic students will find this book invaluable. - Review of new results in the area - Continuation of previous volumes in the handbook series covering evolutionary PDEs - New content coverage of DE applications

Nonlinear Topics in Ocean Physics

Nonlinear Topics in Ocean Physics Book
Author : A.R. Osborne
Publisher : Elsevier
Release : 1991-07-04
ISBN : 0444597824
Language : En, Es, Fr & De

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Book Description :

The main fields presented at this school were mesoscale and large scale flows, and nonlinear wave dynamics. The resulting proceedings present the latest developments in these fields.

Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows

Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows Book
Author : Andrew Majda,Xiaoming Wang
Publisher : Cambridge University Press
Release : 2006-05-11
ISBN : 1139452274
Language : En, Es, Fr & De

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Book Description :

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.

IUTAM Symposium on Turbulence in the Atmosphere and Oceans

IUTAM Symposium on Turbulence in the Atmosphere and Oceans Book
Author : David Dritschel
Publisher : Springer Science & Business Media
Release : 2010-12-09
ISBN : 9789400703605
Language : En, Es, Fr & De

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Book Description :

The text of the Persian poet Rum ̄ ̄ ?, written some eight centuries ago, and reproduced at the beginning of this book is still relevant to many of our pursuits of knowledge, not least of turbulence. The text illustrates the inability people have in seeing the whole thing, the ‘big picture’. Everybody looks into the problem from his/her vi- point, and that leads to disagreement and controversy. If we could see the whole thing, our understanding would become complete and there would be no cont- versy. The turbulent motion of the atmosphere and oceans, at the heart of the observed general circulation, is undoubtedly very complex and dif?cult to understand in its entirety. Even ‘bare’ turbulence, without rotation and strati?cation whose effects are paramount in the atmosphere and oceans, still poses great fundamental ch- lenges for understanding after a century of research. Rotating strati?ed turbulence is a relatively new research topic. It is also far richer, exhibiting a host of distinct wave types interacting in a complicated and often subtle way with long-lived - herent structures such as jets or currents and vortices. All of this is tied together by basic ?uid-dynamical nonlinearity, and this gives rise to a multitude of phen- ena: spontaneous wave emission, wave-induced transport, both direct and inverse energy scale cascades, lateral and vertical anisotropy, fronts and transport barriers, anomalous transport in coherent vortices, and a very wide range of dynamical and thermodynamical instabilities.

Modeling Atmospheric and Oceanic Flows

Modeling Atmospheric and Oceanic Flows Book
Author : Thomas von Larcher,Paul D. Williams
Publisher : John Wiley & Sons
Release : 2014-10-30
ISBN : 1118855922
Language : En, Es, Fr & De

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Book Description :

Modeling Atmospheric and Oceanic Flows: Insights from Laboratory Experiments and Numerical Simulations provides a broad overview of recent progress in using laboratory experiments and numerical simulations to model atmospheric and oceanic fluid motions. This volume not only surveys novel research topics in laboratory experimentation, but also highlights recent developments in the corresponding computational simulations. As computing power grows exponentially and better numerical codes are developed, the interplay between numerical simulations and laboratory experiments is gaining paramount importance within the scientific community. The lessons learnt from the laboratory–model comparisons in this volume will act as a source of inspiration for the next generation of experiments and simulations. Volume highlights include: Topics pertaining to atmospheric science, climate physics, physical oceanography, marine geology and geophysics Overview of the most advanced experimental and computational research in geophysics Recent developments in numerical simulations of atmospheric and oceanic fluid motion Unique comparative analysis of the experimental and numerical approaches to modeling fluid flow Modeling Atmospheric and Oceanic Flows will be a valuable resource for graduate students, researchers, and professionals in the fields of geophysics, atmospheric sciences, oceanography, climate science, hydrology, and experimental geosciences.

Nonlinear Processes in Geophysical Fluid Dynamics

Nonlinear Processes in Geophysical Fluid Dynamics Book
Author : O.U. Velasco Fuentes,J. Sheinbaum,J. Ochoa
Publisher : Springer Science & Business Media
Release : 2011-06-27
ISBN : 9401000743
Language : En, Es, Fr & De

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Book Description :

A Tribute to the Scientific Work of Pedro Ripa

Nonlinear Dynamics And Chaos Proceedings Of The Fourth Physics Summer School

Nonlinear Dynamics And Chaos  Proceedings Of The Fourth Physics Summer School Book
Author : Dewar Robert L,Henry B I
Publisher : World Scientific
Release : 1992-01-24
ISBN : 9814555738
Language : En, Es, Fr & De

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Book Description :

The importance of equational axioms emerged initially with the axiomatic approach to Boolean algebras, groups, and rings, and later in lattices. This unique research monograph systematically presents minimal equational axiom-systems for various lattice-related algebras, regardless of whether they are given in terms of “join and meet” or other types of operations such as ternary operations. Each of the axiom-systems is coded in a handy way so that it is easy to follow the natural connection among the various axioms and to understand how to combine them to form new axiom systems.A new topic in this book is the characterization of Boolean algebras within the class of all uniquely complemented lattices. Here, the celebrated problem of E V Huntington is addressed, which — according to G Gratzer, a leading expert in modern lattice theory — is one of the two problems that shaped a century of research in lattice theory. Among other things, it is shown that there are infinitely many non-modular lattice identities that force a uniquely complemented lattice to be Boolean, thus providing several new axiom systems for Boolean algebras within the class of all uniquely complemented lattices. Finally, a few related lines of research are sketched, in the form of appendices, including one by Dr Willian McCune of the University of New Mexico, on applications of modern theorem-proving to the equational theory of lattices.

Structure And Dynamics Of Nonlinear Waves In Fluids Proceedings Of The Iutam isimm Symposium

Structure And Dynamics Of Nonlinear Waves In Fluids  Proceedings Of The Iutam isimm Symposium Book
Author : Kirchgassner K,Mielke Alexander
Publisher : World Scientific
Release : 1995-08-31
ISBN : 9814549770
Language : En, Es, Fr & De

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Book Description :

This symposium brought together mechanicians, physicists and applied mathematicians to discuss the interdisciplinary topic of nonlinear wave motion, which displays effects that give rise to a multitude of unanswered questions. Nonlinear waves in fluids in particular display all the prominent nonlinear phenomena such as chaos, turbulence and pattern formation. Amongst the topics emphasized in these proceedings are: travelling fronts, solitary waves and periodic waves (dissipative and conservative); temporal and spatial asymptotics of perturbations of waves; bifurcations, stability and local dynamics of waves; interaction between different waves, and between waves and the mean flow; wave breaking, nonlinear effects on focussing and diffraction; modulation and envelope equations (their derivation and validity); and numerical and experimental results.

Introduction to Nonlinear Dynamics for Physicists

Introduction to Nonlinear Dynamics for Physicists Book
Author : H. D. I. Abarbanel,M. I. Rabinovich,Mikhael M. Sushchik
Publisher : World Scientific
Release : 1993
ISBN : 9789810214104
Language : En, Es, Fr & De

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Book Description :

This series of lectures aims to address three main questions that anyone interested in the study of nonlinear dynamics should ask and ponder over. What is nonlinear dynamics and how does it differ from linear dynamics which permeates all familiar textbooks? Why should the physicist study nonlinear systems and leave the comfortable territory of linearity? How can one progress in the study of nonlinear systems both in the analysis of these systems and in learning about new systems from observing their experimental behavior? While it is impossible to answer these questions in the finest detail, this series of lectures nonetheless successfully points the way for the interested reader. Other useful problems have also been incorporated as a study guide. By presenting both substantial qualitative information about phenomena in nonlinear systems and at the same time sufficient quantitative material, the author hopes that readers would learn how to progress on their own in the study of such similar material hereon.

Rossby Vortices Spiral Structures Solitons

Rossby Vortices  Spiral Structures  Solitons Book
Author : Mikhail V. Nezlin,Evgenii N. Snezhkin
Publisher : Springer Science & Business Media
Release : 2013-11-11
ISBN : 364288122X
Language : En, Es, Fr & De

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Book Description :

This book can be looked upon in more ways than one. On the one hand, it describes strikingly interesting and lucid hydrodynamic experiments done in the style of the "good old days" when the physicist needed little more than a piece of string and some sealing wax. On the other hand, it demonstrates how a profound physical analogy can help to get a synoptic view on a broad range of nonlinear phenomena involving self-organization of vortical structures in planetary atmo spheres and oceans, in galaxies and in plasmas. In particular, this approach has elucidated the nature and the mechanism of such grand phenomena as the Great of galaxies. A number of our Red Spot vortex on Jupiter and the spiral arms predictions concerning the dynamics of spiral galaxies are now being confirmed by astronomical observations stimulated by our experiments. This book is based on the material most of which was accumulated during 1981-88 in close cooperation with our colleagues, experimenters from the Plasma Physics Department of the Kurchatov Atomic Energy Institute (S. V. Antipov, A. S. Trubnikov, AYu. Rylov, AV. Khutoretsky) and astrophysics theoreticians from the Astronomical Council of the USSR Academy of Sciences (AM. Frid man) and from the Volgograd State University (AG. Morozov). To all of them we wish to express our gratitude. Whenever we speak of "our experiments", the participation of the entire team is implied.