Evolution of Extreme Waves and Resonances: Volume I

ISBN-13: 9780367480646 / Angielski / Twarda / 2020 / 508 str.

Shamil U. Galiev

Opis

The book generalizes theory of waves on cases of strongly nonlinear waves, multivalued waves and particle-waves. The appearance of these waves in various continuous media and physical fields is explained by resonances and nonlinearity effects.

Recenzje

"Galiev presents a comprehensive theory of extreme waves—unexpectedly appearing and disappearing waves with large amplitudes—a topic gaining attention especially in the last 20 years. Fundamental ingredients in such waves are nonlinearities (geometric or material) and behavior near and past resonance (hence large amplitudes). The theory is applied to ocean waves and optical physics…Some important experiments are drawn from the literature (e.g., Euler's work on the elastica, Darwin's observations on tsunami)."

J. Lambropoulos, Choice Reviews October 2021, USA

Spis treści

PART I. Basic equations and ideasChapter 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 equations1.1.2. Boundary conditions1.1.3. A basic expression for the pressure and a basic strongly nonlinear wave equation 1.2. 2D strongly nonlinear wave equations for a viscous liquid1.2.1. The vertical displacement assumption1.2.2. The 2D Airy-type wave equation1.2.3. 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 equation1.3.2. Three-speed variants of the strongly nonlinear wave equation 1.3.3. Resonant interaction of the gravity and capillary effects in a surface wave1.3.4. Effects of the dispersion1.3.5. Examples of nonlinear wave equations 1.4. Nonlinear equations for gravity waves over the finite-depth ocean1.4.1. Moderate depth 1.4.2. The gravity waves over the deep ocean1.5. Models and basic equations for long waves1.6. Bottom friction and governing equations for long extreme waves1.7. Airy- type equations for capillary waves and remarks to the Chapter 4 Chapter 2 Euler’s figures and extreme waves: examples, equations and unified solutions2.1. Example of Euler's elastica figures 2.2. Examples of fundamental nonlinear wave equations2.3. The nonlinear Klein-Gordon equation and wide spectre of its solutions2.3.1. The one-dimensional version and one hand travelling waves2.3.2. Exact solutions of the nonlinear Klein-Gordon equation2.3.3. The sine-Gordon equation: approximate and exact elastica-like wave solutions2.4. Cubic nonlinear equations describing elastica-like waves 2.5. Elastica-like waves: singularities, unstabilities, resonant generation2.5.1. Singularities as fields of the Euler’s elastic figures generation2.5.2. Instabilities and generation of the Euler’s elastica figures 2.5.3. 'Dangerous' dividers and self-excitation of the transresonant waves2.6. Simple methods for a description of elastica-like waves2.6.1. Modelling of unidirectional elasica-like waves2.6.2. The model equation for Faraday waves and Euler’s figures2.7. Nonlinear effects on transresonant evolution of Euler figures into particle-wavesReferences PART II. Waves in finite resonatorsChapter 3 Generalisation of the d’Alembert’s solution for nonlinear long waves3.1. Resonance of travelling surface waves (site resonance)3.2. Extreme waves in finite resonators3.2.1. Resonance waves in a gas filling closed tube3.2.2. Resonant amplification of seismic waves in natural resonators3.2.3. Topographic effect: extreme dynamics of Tarzana hill3.3. The d' Alembert- type nonlinear resonant solutions: deformable coordinates 3.3.1. The singular solution of the nonlinear wave equation3.3.2. The solutions of the wave equation without the singularity with time3.3.3. 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 equations3.4.2. Resonant (unsingular in time) solutions of the wave equation3.4.3. Special cases of the resonant (unsingular with time) solution3.4.4. Illustration to the theory: the site resonance of waves in a long channel3.5. Theory of free oscillations of nonlinear wave in resonators3.5.1. Theory of free strongly nonlinear wave in resonators3.5.2. Comparison of theoretical results3.6. Conclusion on this Chapter Chapter 4 Extreme resonant waves: a quadratic nonlinear theory4.1. An example of a boundary problem and the equation determining resonant plane waves4.1.1. Very small effects of nonlinearity, viscosity and dispersion4.1.2. The dispersion effect on linear oscillations4.1.3. Fully linear analysis 4.2. Linear resonance4.2.1. Effect of the nonlinearity4.2.2. Waves excited very near band boundaries of resonant band4.2.3. Effect of viscosity4.3. Solutions within and near the shock structure4.4. Resonant wave structure: effect of dispersion4.5. Quadratic resonances4.5.1. Results of calculations and discussion4.6. Forced vibrations of a nonlinear elastic layer Chapter 5. Extreme resonant waves: a cubic nonlinear theory5.1. Cubically nonlinear effect for closed resonators 5.1.1. Results of calculations: pure cubic nonlinear effect5.1.2. Results of calculations: joint cubic and quadratic nonlinear effect5.1.3. Instant collapse of waves near resonant band end5.1.4. Linear and cubic-nonlinear standing waves in resonators5.1.5. Resonant particles, drops, jets, surface craters and bubbles 5.2. A half-open resonator5.2.1. Basic relations5.2.2. Governing equation5.3 Scenarios of transresonant evolution and comparisons with experiments 5.4. Effects of cavitation in liquid on its oscillations in resonators Chapter 6 Spherical resonant waves6.1. Examples and effects of extreme amplification of spherical waves6.2. Nonlinear spherical waves in solids6.2.1. Nonlinear acoustics of the homogeneous viscoelastic solid body6.2.2. Approximate general solution 6.2.3. Boundary problem, basic relations and extreme resonant waves6.2.4. Analogy with the plane wave, results of calculations and discussion 6.3. Extreme waves in spherical resonators filling gas or liquid6.3.1. Governing equation and its general solution6.3.2. Boundary conditions and basic equation for gas sphere6.3.3. Structure and trans-resonant evolution of oscillating waves6.3.3.1. First scenario (C -B)6.3.3.2. Second scenario (C = -B)6.3.4. Discussion6.4. Localisation of resonant spherical waves in spherical layer Chapter 7 Extreme Faraday waves7.1. 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 research7.3. Modelling experiments as standing waves7.4. Modelling of counterintuitive waves as travelling waves7.4.1. Modeling of the Kolesnichenko's experiments7.4.2. Modelling of experiments of Bredmose et al.7.5. Strongly nonlinear waves and ripples7.5.1. Experiments of Lei Jiang et al. and discussion of them7.5.2. Deep water model7.6. Solitons, oscillons and formation of surface patterns7.7. Theory and patterns of nonlinear Faraday waves7.7.1 Basic equations and relations7.7.2. Modeling of certain experimental data 7.7.3. Two-dimensional patterns7.7.4 Historical comments and key resultReferences PART III. Extreme ocean waves and resonant phenomenaChapter 8 Long waves, Green's law and topographical resonance8.1. Surface ocean waves and vessels 8.2. Observations of the extreme waves8.3. Long solitary waves 8.4. KdV-type, Burgers-type, Gardner-type and Camassa-Holm-type equations for the case of the slowly-variable depth8.5. Model solutions and the Green law for solitary wave8.6. Examples of coastal evolution of the solitary wave8.7. 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 topographies8.8.3. Waves in the channel with a semicircular topographies8.9. Topographic resonances and the Euler’s elastica Chapter 9 Modelling of the tsunami described by Charles Darwin and coastal waves9.1. Darwin’s description of tsunamis generated by coastal earthquakes 9.2. Coastal evolution of tsunami9.2.1. Effect of the bottom slope9.2.2. The ocean ebb in front of a tsunami9.2.3. 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 scenarios9.4.2. Quadratic nonlinear scenario9.5. Cubic nonlinear effects: overturning and breaking of waves Chapter 10. Theory of extreme (rogue, catastrophic) ocean waves10.1. Oceanic heterogeneities and the occurrence of extreme waves10.2. Model of shallow waves10.2.1. Simulation of a “hole in the sea” met by the tanker “Taganrogsky Zaliv”10.2.2. Simulation of typical extreme ocean waves as shallow waves10.3. Solitary ocean waves10.4. Nonlinear dispersive relation and extreme waves10.4.1. The weakly nonlinear interaction of many small amplitude ocean waves 10.4.2. The cubic nonlinear interaction of ocean waves and extreme waves formation10.5. Resonant nature of extreme harmonic wave Chapter 11. Wind-induced waves and wind-wave resonance11.1. Effects of wind and current 11.2. Modeling the effect of wind on the waves11.3. Relationships and equations for wind waves in shallow and deep water11.4. Wave equations for unidirectional wind waves11.5. The transresonance evolution of coastal wind waves Chapter 12. Transresonant evolution of Euler’s figures into vortices12.1. Vortices in the resonant tubes12.2. Resonance vortex generation12.3. Simulation of the Richtmyer-Meshkov instability results12.4. Cubic nonlinearity and evolution of waves into vortices12.5. Remarks to extreme water waves (Parts I-III) References PART IV. Modelling of particle-waves, slit experiments and the extreme waves in scalar fieldsChapter 13. Resonances, Euler figures, and particle-waves13.1. Scalar fields and Euler figures13.1.1 Own nonlinear oscillations of a scalar field in a resonator13.1.2. The simplest model of the evolution of Euler’s figures into periodical particle-wave13.2. Some data of exciting experiments with layers of liqud13.3. Stable oscillations of particle-wave configurations13.4. Schrödinger and Klein-Gordon equations13.5. Strongly localised nonlinear sphere-like waves and wave packets13.6. Wave trajectories, wave packets and discussion Chapter 14. Nonlinear quantum waves in the light of recent slit experiments14.1. Introduction14.2. Experiments using different kind of "slits" and the beginning of the discussion14.3. Explanations and discussion of the experimental results14.4. Casimir’s effect14.5. Thin metal layer and plasmons as the synchronizators14.6. Testing of thought experiments14.7. Main thought experiment14.8. Resonant dynamics of particle-wave, vacuum and Universe Chapter 15. Resonant models of origin of particles and the Universe due to quantum perturbations of scalar fields15.1. Basic equation and relations15.2. Basic solutions. Dynamic and quantum effects15.3. Two-dimensional maps of landscapes of the field15.4. Description of quantum perturbations15.4.1. Quantum perturbations and free nonlinear oscillations in the potential well15.4.2. Oscilations of scalar field, granular layer and the Bose-Einstein condensate15.4.3. Simple model of the origin of the particles: mathematics and imaginations15.5. Modelling of quantum actions: theory15.6. Modelling of quantum actions: calculationsReferences

O autorze

Shamil U. Galiev obtained his Ph.D. degree in Mathematics and Physics from Leningrad University in 1971, and, later, a full doctorate (ScD) in Engineering Mechanics from the Academy of Science of Ukraine (1978). He worked in the Academy of Science of former Soviet Union as a researcher, senior researcher, and department chair from 1965 to 1995. From 1984 to 1989, he served as a Professor of Theoretical Mechanics in the Kiev Technical University, Ukraine. Since 1996, he has served as Professor, Honorary Academic of the University of Auckland, New Zealand. Dr. Galiev has published approximately 90 scientific publications, and he is the author of seven books devoted to different complex wave phenomena. From 1965-2014 he has studied different engineering problems connected with dynamics and strength of submarines, rocket systems, and target/projectile (laser beam) systems. Some of these results were published in books and papers. During 1998-2017, he conducted extensive research and publication in the area of strongly nonlinear effects connected with catastrophic earthquakes, giant ocean waves and waves in nonlinear scalar fields. Overall, Dr. Galiev’s research has covered many areas of engineering, mechanics, physics, and mathematics.