| Description |
1 online resource (865 p.) |
| Series |
Modeling of Extreme Waves in Technology and Nature Ser |
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Modeling of Extreme Waves in Technology and Nature Ser
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| Contents |
Cover -- Volume 01 -- Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- Acknowledgments -- Author -- Part I An Example of a Unified Theory of Extreme Waves -- Chapter 1 Lagrangian Description of Surface Water Waves -- 1.1 The Lagrangian Form of the Hydrodynamics Equations: The Balance Equations, Boundary Conditions, and a Strongly Nonlinear Basic Equation -- 1.1.1 Balance and State Equations -- 1.1.2 Boundary Conditions -- 1.1.3 A Basic Expression for the Pressure and a Basic Strongly Nonlinear Wave Equation |
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1.2 2D Strongly Nonlinear Wave Equations for a Viscous Liquid -- 1.2.1 The Vertical Displacement Assumption -- 1.2.2 The 2D Airy-Type Wave Equation -- 1.2.3 The Generation of the Green-Naghdi-Type Equation -- 1.3 A Basic Depth-Averaged 1D Model Using a Power Approximation -- 1.3.1 The Strongly Nonlinear Wave Equation -- 1.3.2 Three-Speed Variants of the Strongly Nonlinear Wave Equation -- 1.3.3 Resonant Interaction of the Gravity and Capillary Effects in a Surface Wave -- 1.3.4 Effects of the Dispersion -- 1.3.5 Examples of Nonlinear Wave Equations |
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1.4 Nonlinear Equations for Gravity Waves over the Finite-Depth Ocean -- 1.4.1 Moderate Depth -- 1.4.2 The Gravity Waves Over the Deep Ocean -- 1.5 Models and Basic Equations for Long Waves -- 1.6 Bottom Friction and Governing Equations for Long Extreme Waves -- 1.7 Airy-Type Equations for Capillary Waves and Remarks to This Chapter -- Chapter 2 Euler's Figures and Extreme Waves: Examples, Equations, and Unified Solutions -- 2.1 Example of Euler's Elastica Figures -- 2.2 Examples of Fundamental Nonlinear Wave Equations -- 2.3 The Nonlinear Klein-Gordon Equation and Wide Spectra of Its Solutions |
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2.3.1 The One-Dimensional Version and One-Hand Traveling Waves -- 2.3.2 Exact Solutions of the Nonlinear Klein-Gordon Equation -- 2.3.3 The Sine-Gordon Equation: Approximate and Exact Elastica-Like Wave Solutions -- 2.4 Cubic Nonlinear Equations Describing Elastica-Like Waves -- 2.5 Elastica-Like Waves: Singularities, Instabilities, Resonant Generation -- 2.5.1 Singularities as Fields of Euler's Elastica Figures Generation -- 2.5.2 Instabilities and Generation of Euler's Elastica Figures -- 2.5.3 "Dangerous" Dividers and Self-Excitation of the Transresonant Waves |
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2.6 Simple Methods for a Description of Elastica-Like Waves -- 2.6.1 Modeling of Unidirectional Elastica-Like Waves -- 2.6.2 The Model Equation for the Faraday Waves and Euler's Figures -- 2.7 Nonlinear Effects on Transresonant Evolution of Euler's Figures into Particle-Waves -- References -- Part II Waves in Finite Resonators -- Chapter 3 Generalization of d'Alembert's Solution for Nonlinear Long Waves -- 3.1 Resonance of Traveling Surface Waves (Site Resonance) -- 3.2 Extreme Waves in Finite Resonators -- 3.2.1 Resonance Waves in a Gas Filling Closed Tube |
| Notes |
Description based upon print version of record |
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3.2.2 Resonant Amplification of Seismic Waves in Natural Resonators |
| Form |
Electronic book
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| ISBN |
9781351059381 |
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1351059386 |
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