Modeling of extreme waves in technology and nature /
Modeling of Extreme Waves in Technology and Nature is a two-volume set, comprising Evolution of Extreme Waves and Resonances (Volume I) and Extreme Waves and Shock-Excited Processes in Structures and Space Objects (Volume II). The theory of waves is generalized on cases of extreme waves. The formati...
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| Format: | eBook |
| Language: | English |
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Boca Raton, FL :
CRC Press,
2022.
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| Series: | Modeling of Extreme Waves in Technology and Nature
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| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Chapter 1. Models of continuum1.1. The system of equations of mechanics continuous medium1.2. State (constitutive) equations for elastic and elastic-plastic bodies1.3. The equations of motion and the wide range equations of state of an inviscid fluid1.4. Simplest example of fracture of media within rarefaction zones1.4.1. The state equation for bubbly liquid1.4.2. Fracture (cold boiling) of water during seaquakes 1.4.3. Model of fracture (cold boiling) of bubbly liquid1.5. Models of moment and momentless shells1.5.1. Shallow shells and the Kirchhoff - Love hypotheses 1.5.2. The Timoshenko theory of thin shells and momentless shells Chapter 2. The dynamic destruction of some materials in tension waves2.1. Models of dynamic failure of solid media2.1.1. Phenomenological approach2.1.2. Microstructural approach2.2. Models of interacting voids (bubbles, pores)2.3. Pores on porous materials2.4. Mathematical model of materials containing poresChapter 3. Models of dynamic failure of weakly-cohesived media (WCM)3.1. Introduction3.1.1. Examples of gassy material properties3.1.2. Behavior of weakly-cohesive geomaterials within of extreme waves3.2. Modelling of gassy media3.2.1. State equation for mixture of condensed matter/gas 3.2.2. Strongly nonlinear model of the state equation for gassy media3.2.3. The Tait-like form of the state equation3.2.4. Wave equations for gassy materials3.3. Effects of bubble oscillations on the one-dimensional governing equations3.3.1. Differential form of the state equation3.3.2. The strongly nonlinear wave equation for bubbly media3.4. Linear acoustics of bubbly media3.4.1. Three speed wave equations3.4.2. Two speed wave equations3.4.3. One-speed wave equations3.4.4. Influence of viscous properties on the sound speed of magma-like media3.5. Examples of observable extreme waves of WCM3.5.1. Mount St Helens eruption3.5.2. The volcano Santiaguito eruptions3.6. Nonlinear acoustic of bubble media 3.6.1. Low frequency waves: Boussinesq and long wave equations 3.6.2. High frequency waves: Klein-Gordon and Schr©œdinger equations3.7. Strongly nonlinear Airy-type equations and remarks to the Chapters 1-3Chapter 4. Lagrangian description of surface water waves 4.1. The Lagrangian form of the hydrodynamics equations: the balance equations, boundary conditions, and a strongly nonlinear basic equation 4.1.1. Balance and state equations4.1.2. Boundary conditions4.1.3. A basic expression for the pressure and a basic strongly nonlinear wave equation 4.2. 2D strongly nonlinear wave equations for a viscous liquid4.2.1. The vertical displacement assumption4.2.2. The 2D Airy-type wave equation4.2.3. The generation of the Green-Naghdi-type equation 4.3. A basic depth-averaged 1D model using a power approximation 4.3.1. The strongly nonlinear wave equation4.3.2. Three-speed variants of the strongly nonlinear wave equation 4.3.3. Resonant interaction of the gravity and capillary effects in a surface wave4.3.4. Effects of the dispersion4.3.5. Examples of nonlinear wave equations 4.4. Nonlinear equations for gravity waves over the finite-depth ocean4.4.1. Moderate depth 4.4.2. The gravity waves over the deep ocean 4. 5. Models and basic equations for long waves4.6. Bottom friction and governing equations for long extreme waves4. 7. Airy- type equations for capillary waves and remarks to the Chapter 4Chapter 5. Euler<U+00CC><U+0081>⁰₉s figures and extreme waves: examples, equations and unified solutions5.1. Example of Euler's elastica figures 5.2. Examples of fundamental nonlinear wave equations5.3. The nonlinear Klein-Gordon equation and wide spectre of its solutions5.3.1 The one dimensional version and one hand travelling waves5.3.2. Exact solutions of the nonlinear Klein-Gordon equation5.3.3. The sine-Gordon equation: approximate and exact elastica-like wave solutions5.4. Cubic nonlinear equations describing elastica-like waves 5.5. Elastica-like waves: singularities, unstabilities, resonant generation5. 5. 1. Singularities as fields of the Euler<U+00CC><U+0081>⁰₉s elastic figures generation5. 5. 2. Instabilities and generation of the Euler<U+00CC><U+0081>⁰₉s elastica figures 5. 5. 3. 'Dangerous' dividers and self-excitation of the transresonant waves5. 6. Simple methods for a description of elastica-like waves5. 6. 1. Modelling of unidirectional elasica-like waves5. 6. 2. The model equation for Faraday waves and Euler<U+00CC><U+0081>⁰₉s figures5.7. Nonlinear effects on transresonant evolution of Euler figures into particle-wavesReferencesPART II. Waves in finite resonatorsChapter 6. Generalisation of the d<U+00CC><U+0081>⁰₉Alembert<U+00CC><U+0081>⁰₉s solution for nonlinear long waves6.1. Resonance of travelling surface waves (site resonance)6.2. Extreme waves in finite resonators6. 2. 1. Resonance waves in a gas filling closed tube6. 2. 2. Resonant amplification of seismic waves in natural resonators6. 2. 3. Topographic effect: extreme dynamics of Tarzana hill6. 3. The d' Alembert- type nonlinear resonant solutions: deformable coordinates 6.3.1. The singular solution of the nonlinear wave equation6.3.2. The solutions of the wave equation without the singularity with time6.3.3. Some particular cases of the general solution (6.22) 6.4. The d' Alembert- type nonlinear resonant solutions: undeformable coordinates 6.4.1. The singular solution of the nonlinear wave equations6. 4. 2. Resonant (unsingular in time) solutions of the wave equation6. 4. 3. Special cases of the resonant (unsingular with time ) solution6. 4. 4. Illustration to the theory: the site resonance of waves in a long channel6. 5. Theory of free oscillations of nonlinear wave in resonators6. 5. 1. Theory of free strongly nonlinear wave in resonators6. 5. 2. Comparison of theoretical results6. 6. Conclusion on this ChapterChapter 7. Extreme resonant waves: a quadratic nonlinear theory7.1. An example of a boundary problem and the equation determining resonant plane waves7.1.1. Very small effects of nonlinearity, viscosity and dispersion7.1.2. The dispersion effect on linear oscillations7.1.3. Fully linear analysis 7.2. Linear resonance7. 2. 1. Effect of the nonlinearity7. 2. 2. Waves excited very near band boundaries of resonant band7. 2. 3. Effect of viscosity7. 3. Solutions within and near the shock structure7.4. Resonant wave structure: effect of dispersion7. 5. Quadratic resonances7. 5. 1. Results of calculations and discussion7.6. Forced vibrations of a nonlinear elastic layerChapter 8. Extreme resonant waves: a cubic nonlinear theory8. 1. Cubically nonlinear effect for closed resonators 8. 1. 1. Results of calculations: pure cubic nonlinear effect8. 1. 2. Results of calculations: joint cubic and quadratic nonlinear effect8. 1. 3. Instant collapse of waves near resonant band end8. 1. 4. Linear and cubic-nonlinear standing waves in resonators8. 1. 5. Resonant particles, drops, jets, surface craters and bubbles 8. 2. A half-open resonator8. 2.1. Basic relations8. 2.2. Governing equation8.3 Scenarios of transresonant evolution and comparisons with experiments 8. 4. Effects of cavitation in liquid on its oscillations in resonatorsChapter 9. Spherical resonant waves9.1. Examples and effects of extreme amplification of spherical waves9. 2. Nonlinear spherical waves in solids9.2.1. Nonlinear acoustics of the homogeneous viscoelastic solid body9. 2.2. Approximate general solution 9. 2.3. Boundary problem, basic relations and extreme resonant waves9.2.4. Analogy with the plane wave, results of calculations and discussion 9.3. Extreme waves in spherical resonators filling gas or liquid9.3.1. Governing equation and its general solution9.3.2. Boundary conditions and basic equation for gas sphere9. 3.3. Structure and trans-resonant evolution of oscillating waves9.3.3.1. First scenario (C <U+00CC><U+0090>²℗Đ-B)9.3.3.2. Second scenario (C = -B)9.3.4. Discussion9. 4. Localisation of resonant spherical waves in spherical layer Chapter 10. Extreme Faraday waves10. 1. Extreme vertical dynamics of weakly-cohesive materials 10. 1.1. Loosening of surface layers due to strongly-nonlinear wave phenomena 10.2 . Main ideas of the research10. 3. Modelling experiments as standing waves10.4. Modelling of counterintuitive waves as travelling waves10. 4. 1. Modeling of the Kolesnichenko's experiments10. 4. 2. Modelling of experiments of Bredmose et al.10.
- 5. Strongly nonlinear waves and ripples10.5. 1. Experiments of Lei Jiang et al. and discussion of them10. 5. 2. Deep water model10. 6. Solitons, oscillons and formation of surface patterns10.7. Theory and patterns of nonlinear Faraday waves10. 7.1 Basic equations and relations10. 7.2. Modeling of certain experimental data 10.7.3. Two-dimensional patterns10. 7.4 Historical comments and key resultReferencesPART III. Extreme ocean waves, resonances and phenomenaChapter 11. Long waves, Green's law and topographical resonance11.1. Surface ocean waves and vessels 11.2. Observations of the extreme waves11.3. Long solitary waves 11. 4. KdV-type, Burgers-type, Gardner-type and Camassa-Holm-type equations for the case of the slowly-variable depth11. 5. Model solutions and the Green law for solitary wave11. 6. Examples of coastal evolution of the solitary wave11. 7. Generalizations of the Green⁰́₉s law 11. 8. Tests for generalisated Green⁰́₉s law 11. 8. 1. The evolution of harmonical waves above topographies 11. 8. 2. The evolution of a solitary wave over trapezium topographies11. 8. 3. Waves in the channel with a semicircular topographies11. 9. Topographic resonances and the Euler⁰́₉s elasticaChapter 12. Modelling of the tsunami described by Charles Darwin and coastal waves