# Nonlinear Dynamics Of Rotating Shallow Water

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## Nonlinear Dynamics of Rotating Shallow Water Methods and Advances

Author | : Anonim |

Publsiher | : Elsevier |

Total Pages | : 400 |

Release | : 2007-04-03 |

ISBN | : 9780080489469 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Nonlinear Dynamics of Rotating Shallow Water Methods and Advances Book Excerpt:**

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)

## Geophysical Fluid Dynamics

Author | : Vladimir Zeitlin |

Publsiher | : Oxford University Press |

Total Pages | : 512 |

Release | : 2018-02-15 |

ISBN | : 0198804334 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Geophysical Fluid Dynamics 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.

## Fronts Waves and Vortices in Geophysical Flows

Author | : Jan-Bert Flor |

Publsiher | : Springer |

Total Pages | : 192 |

Release | : 2010-06-01 |

ISBN | : 364211587X |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Fronts Waves and Vortices in Geophysical Flows Book Excerpt:**

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.

## Dispersive Shallow Water Waves

Author | : Gayaz Khakimzyanov,Denys Dutykh,Zinaida Fedotova,Oleg Gusev |

Publsiher | : Springer Nature |

Total Pages | : 284 |

Release | : 2020-09-15 |

ISBN | : 3030462676 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Dispersive Shallow Water Waves Book Excerpt:**

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

Author | : Hector Perez-De-Tejada |

Publsiher | : BoD – Books on Demand |

Total Pages | : 280 |

Release | : 2017-03-01 |

ISBN | : 9535129430 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Vortex Structures in Fluid Dynamic Problems Book Excerpt:**

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

Author | : Tomáš Bodnár,Giovanni P. Galdi,Šárka Nečasová |

Publsiher | : Springer Nature |

Total Pages | : 353 |

Release | : 2021-04-29 |

ISBN | : 3030678458 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Waves in Flows Book Excerpt:**

This volume offers an overview of the area of waves in fluids and the role they play in the mathematical analysis and numerical simulation of fluid flows. Based on lectures given at the summer school “Waves in Flows”, held in Prague from August 27-31, 2018, chapters are written by renowned experts in their respective fields. Featuring an accessible and flexible presentation, readers will be motivated to broaden their perspectives on the interconnectedness of mathematics and physics. A wide range of topics are presented, working from mathematical modelling to environmental, biomedical, and industrial applications. Specific topics covered include: Equatorial wave–current interactions Water–wave problems Gravity wave propagation Flow–acoustic interactions Waves in Flows will appeal to graduate students and researchers in both mathematics and physics. Because of the applications presented, it will also be of interest to engineers working on environmental and industrial issues.

## Dynamics of the Equatorial Ocean

Author | : John P. Boyd |

Publsiher | : Springer |

Total Pages | : 517 |

Release | : 2017-09-25 |

ISBN | : 3662554763 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Dynamics of the Equatorial Ocean Book Excerpt:**

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 Topics in Ocean Physics

Author | : A.R. Osborne |

Publsiher | : Elsevier |

Total Pages | : 1032 |

Release | : 1991-07-04 |

ISBN | : 0444597824 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Nonlinear Topics in Ocean Physics Book Excerpt:**

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.

## Rotating Shallow Water

Author | : Alana McKenzie |

Publsiher | : Unknown |

Total Pages | : 168 |

Release | : 2007 |

ISBN | : 1928374650XXX |

Category | : Fluid dynamics |

Language | : EN, FR, DE, ES & NL |

**Rotating Shallow Water Book Excerpt:**

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.

## Handbook of Differential Equations Evolutionary Equations

Author | : C.M. Dafermos,Milan Pokorny |

Publsiher | : Elsevier |

Total Pages | : 534 |

Release | : 2009-04-29 |

ISBN | : 9780080932590 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Handbook of Differential Equations Evolutionary Equations Book Excerpt:**

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

## Handbook of Geomathematics

Author | : Willi Freeden,M. Zuhair Nashed,Thomas Sonar |

Publsiher | : Springer Science & Business Media |

Total Pages | : 612 |

Release | : 2010-08-13 |

ISBN | : 364201545X |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Handbook of Geomathematics Book Excerpt:**

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.

## IUTAM Symposium on Turbulence in the Atmosphere and Oceans

Author | : David Dritschel |

Publsiher | : Springer Science & Business Media |

Total Pages | : 298 |

Release | : 2010-12-09 |

ISBN | : 9400703600 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**IUTAM Symposium on Turbulence in the Atmosphere and Oceans Book Excerpt:**

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.

## Physical and Mathematical Modeling of Earth and Environment Processes

Author | : V. I. Karev |

Publsiher | : Springer Nature |

Total Pages | : 135 |

Release | : 2022 |

ISBN | : 3030995046 |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Physical and Mathematical Modeling of Earth and Environment Processes Book Excerpt:**

## Introduction to Turbulent Transfer of Particles Temperature and Magnetic Fields

Author | : Igor Rogachevskii |

Publsiher | : Cambridge University Press |

Total Pages | : 300 |

Release | : 2021-08-05 |

ISBN | : 1316518604 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Introduction to Turbulent Transfer of Particles Temperature and Magnetic Fields Book Excerpt:**

Introducing key concepts in turbulent transport with an overview of analytical and statistical tools to advanced graduates and researchers.

## Modeling Atmospheric and Oceanic Flows

Author | : Thomas von Larcher,Paul D. Williams |

Publsiher | : John Wiley & Sons |

Total Pages | : 368 |

Release | : 2014-10-30 |

ISBN | : 1118855922 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Modeling Atmospheric and Oceanic Flows Book Excerpt:**

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 Dynamics Of Ocean Waves Proceedings Of The Symposium

Author | : Shlesinger Michael F,Ramberg S E,Brandt A |

Publsiher | : World Scientific |

Total Pages | : 228 |

Release | : 1992-08-31 |

ISBN | : 9814554529 |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Nonlinear Dynamics Of Ocean Waves Proceedings Of The Symposium Book Excerpt:**

The Standard Model of elementary particles, although very successful, contains various elements that are put in by hand. Understanding their origin requires going beyond the model and searching for “new physics”. The present book elaborates on one particular proposal concerning such physics. While the original conception is 50 years old, it has not lost its appeal over time. Its basic idea is that space — an arena of events treated in the Standard Model as a classical background — is a concept which emerges from a strictly discrete quantum layer in the limit of large quantum numbers. This book discusses an extension of this view by replacing space with phase space. It combines the results of the author's research papers and places them in much broader philosophical and phenomenological contexts, thus providing further arguments in favor of the proposed alternative. The book should be of interest to the philosophically-minded readers who are willing to contemplate unorthodox ideas on the very nature of the world.

## Mathematics of Complexity and Dynamical Systems

Author | : Robert A. Meyers |

Publsiher | : Springer Science & Business Media |

Total Pages | : 1858 |

Release | : 2011-10-05 |

ISBN | : 1461418054 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Mathematics of Complexity and Dynamical Systems Book Excerpt:**

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

## Nonlinear Dynamics Materials Theory and Experiments

Author | : Mustapha Tlidi,Marcel. G. Clerc |

Publsiher | : Springer |

Total Pages | : 361 |

Release | : 2015-11-14 |

ISBN | : 3319248715 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Nonlinear Dynamics Materials Theory and Experiments Book Excerpt:**

This book presents recent advances, new ideas and novel techniques related to the field of nonlinear dynamics, including localized pattern formation, self-organization and chaos. Various natural systems ranging from nonlinear optics to mechanics, fluids and magnetic are considered. The aim of this book is to gather specialists from these various fields of research to promote cross-fertilization and transfer of knowledge between these active research areas. In particular, nonlinear optics and laser physics constitute an important part in this issue due to the potential applications for all-optical control of light, optical storage, and information processing. Other possible applications include the generation of ultra-short pulses using all-fiber cavities.

## Proceedings of the International School of Physics Enrico Fermi

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 135 |

Release | : 1991 |

ISBN | : 1928374650XXX |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Proceedings of the International School of Physics Enrico Fermi Book Excerpt:**

## Scientific and Technical Aerospace Reports

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 135 |

Release | : 1995 |

ISBN | : 1928374650XXX |

Category | : Aeronautics |

Language | : EN, FR, DE, ES & NL |

**Scientific and Technical Aerospace Reports Book Excerpt:**