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Shallow Water Waves On The Rotating Earth
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Book Synopsis Shallow Water Waves on the Rotating Earth by : Nathan Paldor
Download or read book Shallow Water Waves on the Rotating Earth written by Nathan Paldor and published by Springer. This book was released on 2015-08-12 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes new theoretical advances concerning analytical solutions of the Rotating Shallow Water Equations, which will make it of great interest to graduate students and scientists in the fields of Geophysical Fluid Dynamics, Physical Oceanography, Dynamical Meteorology and Applied Mathematics. The new dispersion relations and meridional amplitude variations of waves derived in this book can be applied to observations in the atmosphere and ocean and also provide alternatives to the Spherical Harmonics basis of global-scale spectral numerical models.
Book Synopsis A Study on the Nonlocal Shallow-water Model Arising from the Full Water Waves with the Coriolis Effect by : Junwei Sun
Download or read book A Study on the Nonlocal Shallow-water Model Arising from the Full Water Waves with the Coriolis Effect written by Junwei Sun and published by . This book was released on 2017 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Equatorial Undercurrent is a significant feature of the geophysical waves near the equator, which is one of the key factors to explain El Niño phenomenon. However, based on [beta]-plane approximation, the classical theory of geophysical waves ignored the vertical structure of the Equatorial Undercurrent. To obtain a better description of the equatorial waves, in this dissertation, I study the rotational-Camassa-Holm (R-CH) equation, which is a mathematical model of long-crested water waves near the equator, propagating mainly in one direction with the effect of Earth's rotation under the f-plane approximation. R-CH equation can be derived by following the formal asymptotic procedures. Such a model equation is analogous to the Camassa-Holm approximation of the two-dimensional incompressible and irrotational Euler equations and has a formal bi-Hamiltonian structure. Its solutions corresponding to physically relevant initial perturbations is more accurate on a much longer time scale. It is shown that the deviation of the free surface can be determined by the horizontal velocity at a certain depth in the second-order approximation. The effects of the Coriolis force caused by the Earth rotation and nonlocal higher nonlinearities on blow-up criteria and wave-breaking phenomena are also investigated.
Book Synopsis Nonlinear Interaction Between Vortex and Wave in Rotating Shallow Water by : Norihiko Sugimoto
Download or read book Nonlinear Interaction Between Vortex and Wave in Rotating Shallow Water written by Norihiko Sugimoto and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This chapter is primarily concerned with the generation of inertia-gravity wave by vortical flows (spontaneous emission) in shallow water system on an f-plane. Sound waves are generated from vortical flows (aeroacoustics). There are many theoretical and numerical works regarding this subject. A shallow water system is equivalent to a two-dimensional adiabatic gas system, if the effect of Earth's rotation is negligibly small. Then gravity waves are analogous to sound waves. While it is widely known that the effect of the Earth's rotation suppresses inertia-gravity wave radiation, there are few studies about spontaneous emission in rotating shallow water. Here, the generation of inertia-gravity waves by unsteady vortical flows is investigated analytically and numerically as an extension of aeroacoustics. A background of this subject is introduced briefly and several recent works including new results are reviewed. Main findings are cyclone-anticyclone asymmetry in spontaneous emission and a local maximum of intensity of gravity waves emitted from anticyclones at intermediate value of the Coriolis parameter f, which are caused by the source originating in the Coriolis acceleration. All different experimental settings show the similar results, suggesting the robustness of these features.
Author :Open University. Oceanography Course Team Publisher :Gulf Professional Publishing ISBN 13 :9780750642811 Total Pages :230 pages Book Rating :4.6/5 (428 download)
Book Synopsis Waves, Tides and Shallow-Water Processes by : Open University. Oceanography Course Team
Download or read book Waves, Tides and Shallow-Water Processes written by Open University. Oceanography Course Team and published by Gulf Professional Publishing. This book was released on 1999 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book begins by describing the characteristics of waves and tides, and their behaviour in shallow water. After outlining the sources of sediment supply to the oceans, some theoretical aspects of sediment movement and deposition by currents are considered. After looking at wave action in the littoral zone, the interplay of tidal currents, river flow and wave action in estuaries and deltas are explored. The final chapter provides an overview of shelf processes."--Amazon.com viewed June 30, 2022.
Book Synopsis A Study on Traveling Wave Solutions in the Shallow-water-type Systems by : Ting Luo
Download or read book A Study on Traveling Wave Solutions in the Shallow-water-type Systems written by Ting Luo and published by . This book was released on 2017 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of water waves reveals the physical principles of many phenomena of scientific and engineering interest. In this dissertation I consider three models: two-component Camassa-Holm system(2CH), generalized two-component Camassa-Holm equation(g2CH) and rotation-Camassa-Holm equation(R-CH). In the first part, we consider the stability of the Camassa-Holm peakons and antipeakons in the dynamics of the two-component Camassa-Holm system. The second part shows that the train of N-smooth traveling waves of this system is dynamically stable to perturbations in energy space with a range of parameters. In the third part, we formally derive the simplified phenomenological models with the Coriolis effect due to the Earth's rotation and justify rigorously that the solutions of these models are well approximated by the solutions of the rotation-Camassa-Holm equation. Furthermore, we demonstrate nonexistence of the Camassa-Holm-type peaked solution and classify various localized traveling-wave solutions to the rotation-Camassa-Holm equation.
Book Synopsis Waves, Tides, and Shallow-water Processes by : Open University. Oceanography Course Team
Download or read book Waves, Tides, and Shallow-water Processes written by Open University. Oceanography Course Team and published by Pergamon. This book was released on 1989 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth Volume of the six Volume Open University set. Each Volume is used by students as a relevant part of the Open University course in the UK, but designed so that it can equally be used as an individual text book. This Volume describes waves, their measurement and characteristics, their behaviour in shallow water and unusual waves. It also considers mainly theoretical aspects of sediment movement and deposition of currents, wave estuaries, and the interaction of waves, tides and river flow in deltas. Concludes with a look at shelf-sea processes and their mineral resources. Each Volume in this set is well laid out and copiously illustrated with full colour photographs, graphs and graphics. Questions to help develop arguments and/or understanding can be found in the text and at the end of each chapter, with worked answers provided at the back of each Volume. Each chapter also concludes with a summary to help consolidate understanding before the next chapter is begun.
Book Synopsis Dispersive Shallow Water Waves by : Gayaz Khakimzyanov
Download or read book Dispersive Shallow Water Waves written by Gayaz Khakimzyanov and published by Springer Nature. This book was released on 2020-09-15 with total page 296 pages. Available in PDF, EPUB and Kindle. 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.
Book Synopsis Free-Surface Flow: by : Nikolaos D. Katopodes
Download or read book Free-Surface Flow: written by Nikolaos D. Katopodes and published by Butterworth-Heinemann. This book was released on 2018-08-30 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: Free-Surface Flow: Shallow-Water Dynamics presents a novel approach to this phenomenon. It bridges the gap between traditional books on open-channel flow and analytical fluid mechanics. Shallow-water theory is established by formal integration of the Navier-Stokes equations, and boundary resistance is developed by a rigorous construction of turbulent flow models for channel flow. In addition, the book presents a comprehensive description of shallow-water waves by mathematical analysis. These methods form the foundation for understanding flood routing, sudden water releases, dam and levee break, sluice gate dynamics and wave-current interaction. Bridges the gap between traditional books on open-channel flow and wave mechanics Presents a comprehensive description of shallow-water waves by characteristic and bicharacteristic analysis Presents techniques for wave control and active flood mitigation
Book Synopsis Atmosphere—Ocean Dynamics by : Adrian E. Gill
Download or read book Atmosphere—Ocean Dynamics written by Adrian E. Gill and published by Elsevier. This book was released on 2016-06-03 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: Atmosphere-Ocean Dynamics deals with a systematic and unified approach to the dynamics of the ocean and atmosphere. The book reviews the relationship of the ocean-atmosphere and how this system functions. The text explains this system through radiative equilibrium models; the book also considers the greenhouse effect, the effects of convection and of horizontal gradients, and the variability in radiative driving of the earth. Equations in the book show the properties of a material element, mass conservation, the balance of scalar quantity (such as salinity), and the mathematical behavior of the ocean and atmosphere. The book also addresses how the ocean-atmosphere system tends to adjust to equilibrium, both in the absence and presence of driving forces such as gravity. The text also explains the effect of the earth's rotation on the system, as well as the application of forced motions such as that produced by wind or temperature changes. The book explains tropical dynamics and the effects of variation of the Coriolis parameter with latitude. The text will be appreciated by meteorologists, environmentalists, students studying hydrology, and people working in general earth sciences.
Book Synopsis Waves, Tides and Shallow-Water Processes by : Open Open University
Download or read book Waves, Tides and Shallow-Water Processes written by Open Open University and published by Elsevier. This book was released on 2013-10-22 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text begins by describing waves, their measurement and characteristics, their behaviour in shallow water, and unusual waves. Next, mainly theoretical aspects are considered of sediment movement and deposition by currents, before discussing wave action in the littoral zone, tidal current action on tidal flat and in estuaries, and the interaction of waves, tides, and river flow in deltas. Finally, we examine shelf-sea processes, including an outline of their mineral resources.
Book Synopsis Introduction to PDEs and Waves for the Atmosphere and Ocean by : Andrew Majda
Download or read book Introduction to PDEs and Waves for the Atmosphere and Ocean written by Andrew Majda and published by American Mathematical Soc.. This book was released on 2003-01-01 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geophysical Waves and Flows by : David E. Loper
Download or read book Geophysical Waves and Flows written by David E. Loper and published by Cambridge University Press. This book was released on 2017-10-26 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Waves and flows are pervasive on and within Earth. This book presents a unified physical and mathematical approach to waves and flows in the atmosphere, oceans, rivers, volcanoes and the mantle, emphasizing the common physical principles and mathematical methods that apply to a variety of phenomena and disciplines. It is organized into seven parts: introductory material; kinematics, dynamics and rheology; waves in non-rotating fluids; waves in rotating fluids; non-rotating flows; rotating flows; and silicate flows. The chapters are supplemented by 47 'fundaments', containing knowledge that is fundamental to the material presented in the main text, organized into seven appendices: mathematics; dimensions and units; kinematics; dynamics; thermodynamics; waves; and flows. This book is an ideal reference for graduate students and researchers seeking an introduction to the mathematics of waves and flows in the Earth system, and will serve as a supplementary textbook for a number of courses in geophysical fluid dynamics.
Book Synopsis State and Evolution of the Baltic Sea, 1952-2005 by : Rainer Feistel
Download or read book State and Evolution of the Baltic Sea, 1952-2005 written by Rainer Feistel and published by John Wiley & Sons. This book was released on 2008-07-21 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a fifty-year study conducted by the Leibniz Institute for Baltic Sea Research, this book brings together a comprehensive summary of their observations and findings. Written by well-known experts, this revealing book concentrates on long-term changes in the Baltic Sea?which can be extrapolated to shed light on the environmental problems of other shelf seas, brackish seas, and large estuaries?thereby contributing to our understanding of water exchange processes, eutrophication, and climatic impacts at the forefront of international concern.
Book Synopsis Ship Hydrodynamics, Water Waves, and Asymptotics by : Fritz Ursell
Download or read book Ship Hydrodynamics, Water Waves, and Asymptotics written by Fritz Ursell and published by World Scientific. This book was released on 1994 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Physics of Lakes by : Kolumban Hutter
Download or read book Physics of Lakes written by Kolumban Hutter and published by Springer Science & Business Media. This book was released on 2011-07-29 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: The overwhelming focus of this 2nd volume of “Physics of Lakes” is adequately expressed by its subtitle “Lakes as Oscillators”. It deals with barotropic and baroclinic waves in homogeneous and stratified lakes on the rotating Earth and comprises 12 chapters, starting with rotating shallow-water waves, demonstrating their classification into gravity and Rossby waves for homogeneous and stratified water bodies. This leads to gravity waves in bounded domains of constant depth, Kelvin, Poincaré and Sverdrup waves, reflection of such waves in gulfs and rectangles and their description in sealed basins as barotropic ‘inertial waves proper’. The particular application to gravity waves in circular and elliptical basins of constant depth leads to the description of Kelvin-type and Poincaré-type waves and their balanced description in basins of arbitrary geometry on the rotating Earth. Consideration of two-, three- and n-layer fluids with sharp interfaces give rise to the description of gravity waves of higher order baroclinicity with experimental corroboration in a laboratory flume and e.g. in Lake of Lugano, Lake Banyoles and Lake Biwa. Barotropic wave modes in Lake Onega with complex geometry show that data and computational output require careful interpretation. Moreover, a summer field campaign in Lake of Lugano and its two-layer modal analysis show that careful statistical analyses of the data are requested to match data with computational results. Three chapters are devoted to topographic Rossby waves. Conditions are outlined for which these waves are negligibly affected by baroclinicity. Three classes of these large period modes are identified: channel modes, so-called Ball modes and bay modes, often with periods which lie very close together. The last chapter deals with an entire class of Chrystal-type equations for barotropic waves in elongated basins which incorporate the effects of the rotation of the Earth.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1953 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Coastal Geology by : Juan A. Morales
Download or read book Coastal Geology written by Juan A. Morales and published by Springer Nature. This book was released on 2022-03-18 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook shows all the existing knowledge about coastal geology and its implications for coastal management. In the last decades, the geological sciences have been supplying exciting information about the coastal systems, not only from its dynamics but also providing a sedimentary concept to understand and interpret the preserved coastal stratigraphical record. Furthermore, recent investigations have been focused on the prevention of coastal hazards like storms, tsunamis, or sea-level fluctuation. This discipline has an increasing interest after the expanding human activities around the coasts worldwide. The present trend is that many of the problems raised by the coast–human interaction must be resolved by using the Integrated Coastal Zone Management. The chapters of this book have a double-level structure. The first part of each chapter contains the necessary information for undergraduate courses studying coastal geology. The second part includes advanced information and examples to be used by graduate students and novel professionals.
