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Author: Nathan Paldor
Publisher: Springer
ISBN: 3319202618
Category : Science
Languages : en
Pages : 83
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Book Description
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.
Author: Nathan Paldor
Publisher: Springer
ISBN: 3319202618
Category : Science
Languages : en
Pages : 83
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Book Description
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.
Author: Junwei Sun
Publisher:
ISBN:
Category : Coriolis force
Languages : en
Pages : 78
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Book Description
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.
Author: Open University. Oceanography Course Team
Publisher: Pergamon
ISBN:
Category : Science
Languages : en
Pages : 196
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Book Description
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.
Author: Norihiko Sugimoto
Publisher:
ISBN:
Category : Science
Languages : en
Pages :
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Book Description
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: Ting Luo
Publisher:
ISBN:
Category : Nonlinear wave equations
Languages : en
Pages : 131
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Book Description
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.
Author: Open University. Oceanography Course Team
Publisher: Gulf Professional Publishing
ISBN: 9780750642811
Category : Science
Languages : en
Pages : 230
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Book Description
"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.
Author: Nikolaos D. Katopodes
Publisher: Butterworth-Heinemann
ISBN: 0128154888
Category : Technology & Engineering
Languages : en
Pages : 850
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Book Description
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
Author: Manuel G. Velarde
Publisher: Springer
ISBN: 3319719343
Category : Science
Languages : en
Pages : 610
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Book Description
This book commemorates the 70th birthday of Eugene Morozov, the noted Russian observational oceanographer. It contains many contributions reflecting his fields of interest, including but not limited to tidal internal waves, ocean circulation, deep ocean currents, and Arctic oceanography. Special attention is paid to studies on internal waves and especially those on tidal internal waves in the Global Ocean. These papers describe the most important open problems concerning experimental studies of internal waves and their theoretical, numerical, and laboratory modeling. Further contributions investigate the physics of surface waves and their interaction with internal waves. Here, the focus is on describing interaction processes between internal waves and deep currents in the ocean, especially currents of Antarctic Bottom Water in abyssal fractures. They also touch on the problem of oceanic circulation and related processes in fjords, including those occurring under sea ice. Given its breadth of coverage, the book will appeal to anyone interested in a survey of ocean dynamics, ranging from historic perspectives to modern research topics.
Author: Gayaz Khakimzyanov
Publisher: Springer Nature
ISBN: 3030462676
Category : Mathematics
Languages : en
Pages : 296
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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.
Author: Open Open University
Publisher: Elsevier
ISBN: 1483292711
Category : Science
Languages : en
Pages : 192
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Book Description
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.
