Evolution of extreme waves and resonances. Volume I (2020)

• Record Type: Book
• Further Information: Note: Shamil U. Galiev.
• Authors: Galiev, Shamilʹ Usmanovich
• Contents: PART I. Basic equations and ideas; 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 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; 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 the Chapter 4 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 spectre of its solutions; 2.3.1. The one-dimensional version and one hand travelling 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, unstabilities, resonant generation; 2.5.1. Singularities as fields of the Euler’s elastic figures generation; 2.5.2. Instabilities and generation of the Euler’s elastica figures; 2.5.3. 'Dangerous' dividers and self-excitation of the transresonant waves; 2.6. Simple methods for a description of elastica-like waves; 2.6.1. Modelling of unidirectional elasica-like waves; 2.6.2. The model equation for Faraday waves and Euler’s figures; 2.7. Nonlinear effects on transresonant evolution of Euler figures into particle-waves; References PART II. Waves in finite resonators; Chapter 3 Generalisation of the d’Alembert’s solution for nonlinear long waves; 3.1. Resonance of travelling surface waves (site resonance); 3.2. Extreme waves in finite resonators; 3.2.1. Resonance waves in a gas filling closed tube; 3.2.2. Resonant amplification of seismic waves in natural resonators; 3.2.3. Topographic effect: extreme dynamics of Tarzana hill; 3.3. The d' Alembert- type nonlinear resonant solutions: deformable coordinates; 3.3.1. The singular solution of the nonlinear wave equation; 3.3.2. The solutions of the wave equation without the singularity with time; 3.3.3. Some particular cases of the general solution (3.22); 3.4. The d' Alembert- type nonlinear resonant solutions: undeformable coordinates; 3.4.1. The singular solution of the nonlinear wave equations; 3.4.2. Resonant (unsingular in time) solutions of the wave equation; 3.4.3. Special cases of the resonant (unsingular with time) solution; 3.4.4. Illustration to the theory: the site resonance of waves in a long channel; 3.5. Theory of free oscillations of nonlinear wave in resonators; 3.5.1. Theory of free strongly nonlinear wave in resonators; 3.5.2. Comparison of theoretical results; 3.6. Conclusion on this Chapter Chapter 4 Extreme resonant waves: a quadratic nonlinear theory; 4.1. An example of a boundary problem and the equation determining resonant plane waves; 4.1.1. Very small effects of nonlinearity, viscosity and dispersion; 4.1.2. The dispersion effect on linear oscillations; 4.1.3. Fully linear analysis; 4.2. Linear resonance; 4.2.1. Effect of the nonlinearity; 4.2.2. Waves excited very near band boundaries of resonant band; 4.2.3. Effect of viscosity; 4.3. Solutions within and near the shock structure; 4.4. Resonant wave structure: effect of dispersion; 4.5. Quadratic resonances; 4.5.1. Results of calculations and discussion; 4.6. Forced vibrations of a nonlinear elastic layer Chapter 5. Extreme resonant waves: a cubic nonlinear theory; 5.1. Cubically nonlinear effect for closed resonators 5.1.1. Results of calculations: pure cubic nonlinear effect; 5.1.2. Results of calculations: joint cubic and quadratic nonlinear effect; 5.1.3. Instant collapse of waves near resonant band end; 5.1.4. Linear and cubic-nonlinear standing waves in resonators; 5.1.5. Resonant particles, drops, jets, surface craters and bubbles; 5.2. A half-open resonator; 5.2.1. Basic relations; 5.2.2. Governing equation; 5.3 Scenarios of transresonant evolution and comparisons with experiments; 5.4. Effects of cavitation in liquid on its oscillations in resonators Chapter 6 Spherical resonant waves; 6.1. Examples and effects of extreme amplification of spherical waves; 6.2. Nonlinear spherical waves in solids; 6.2.1. Nonlinear acoustics of the homogeneous viscoelastic solid body; 6.2.2. Approximate general solution; 6.2.3. Boundary problem, basic relations and extreme resonant waves; 6.2.4. Analogy with the plane wave, results of calculations and discussion; 6.3. Extreme waves in spherical resonators filling gas or liquid; 6.3.1. Governing equation and its general solution; 6.3.2. Boundary conditions and basic equation for gas sphere; 6.3.3. Structure and trans-resonant evolution of oscillating waves; 6.3.3.1. First scenario (C -B); 6.3.3.2. Second scenario (C = -B); 6.3.4. Discussion; 6.4. Localisation of resonant spherical waves in spherical layer Chapter 7 Extreme Faraday waves; 7.1. Extreme vertical dynamics of weakly-cohesive materials; 7.1.1. Loosening of surface layers due to strongly-nonlinear wave phenomena 7.2. Main ideas of the research; 7.3. Modelling experiments as standing waves; 7.4. Modelling of counterintuitive waves as travelling waves; 7.4.1. Modeling of the Kolesnichenko's experiments; 7.4.2. Modelling of experiments of Bredmose et al; 7.5. Strongly nonlinear waves and ripples; 7.5.1. Experiments of Lei Jiang et al. and discussion of them; 7.5.2. Deep water model; 7.6. Solitons, oscillons and formation of surface patterns; 7.7. Theory and patterns of nonlinear Faraday waves; 7.7.1 Basic equations and relations; 7.7.2. Modeling of certain experimental data; 7.7.3. Two-dimensional patterns; 7.7.4 Historical comments and key result; References PART III. Extreme ocean waves and resonant phenomena; Chapter 8 Long waves, Green's law and topographical resonance; 8.1. Surface ocean waves and vessels 8.2. Observations of the extreme waves; 8.3. Long solitary waves 8.4. KdV-type, Burgers-type, Gardner-type and Camassa-Holm-type equations for the case of the slowly-variable depth; 8.5. Model solutions and the Green law for solitary wave; 8.6. Examples of coastal evolution of the solitary wave; 8.7. Generalizations of the Green’s law; 8.8. Tests for generalised Green’s law; 8.8.1. The evolution of harmonical waves above topographies; 8.8.2. The evolution of a solitary wave over trapezium topographies; 8.8.3. Waves in the channel with a semicircular topographies; 8.9. Topographic resonances and the Euler’s elastica ; Chapter 9 Modelling of the tsunami described by Charles Darwin and coastal waves; 9.1. Darwin’s description of tsunamis generated by coastal earthquakes 9.2. Coastal evolution of tsunami; 9.2.1. Effect of the bottom slope; 9.2.2. The ocean ebb in front of a tsunami; 9.2.3. Effect of the bottom friction; 9.3. Theory of tsunami: basic relations; 9.4. Scenarios of the coastal evolution of tsunami; 9.4.1. Cubic nonlinear scenarios; 9.4.2. Quadratic nonlinear scenario; 9.5. Cubic nonlinear effects: overturning and breaking of waves Chapter 10. Theory of extreme (rogue, catastrophic) ocean waves; 10.1. Oceanic heterogeneities and the occurrence of extreme waves; 10.2. Model of shallow waves; 10.2.1. Simulation of a “hole in the sea” met by the tanker “Taganrogsky Zaliv”; 10.2.2. Simulation of typical extreme ocean waves as shallow waves; 10.3. Solitary ocean waves; 10.4. Nonlinear dispersive relation and extreme waves; 10.4.1. The weakly nonlinear interaction of many small amplitude ocean waves; 10.4.2. The cubic nonlinear
• Edition: 1st
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2020
• Extent: 1 online resource, illustrations (black and white, and colour)
• Subjects: 531.1133015118; Waves -- Mathematical models; Wave-motion, Theory of
• Languages: English
• ISBNs: 9781000064018; 9781000063974; 9781000063998; 9781003038504
• Related ISBNs: 9780367480646
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