1st Edition

Modeling of Extreme Waves in Technology and Nature, Two Volume Set

    862 Pages 20 Color & 435 B/W Illustrations
    by CRC Press

    862 Pages 20 Color & 435 B/W Illustrations
    by CRC Press

    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 formation and propagation of extreme waves of various physical and mechanical nature (surface, elastoplastic, fracture, thermal, evaporation) in liquid and solid media, and in structural elements contacting with bubbly and cryogenic liquids are considered analytically and numerically. The occurrence of tsunamis, giant ocean waves, turbulence, and different particle-waves is described as resonant natural phenomena.

    Nonstationary and periodic waves are considered using models of continuum. The change in the state of matter is taken into account using wide-range determining equations.

    The desire for the simplest and at the same time general description of extreme wave phenomena that takes the reader to the latest achievements of science is the main thing that characterizes this book and is revolutionary for wave theory. A description of a huge number of observations, experimental data, and calculations is also given.

    Chapter 1. Models of continuum

    1.1. The system of equations of mechanics continuous medium
    1.2. State (constitutive) equations for elastic and elastic-plastic bodies
    1.3. The equations of motion and the wide range equations of state of an inviscid fluid
    1.4. Simplest example of fracture of media within rarefaction zones
    1.4.1. The state equation for bubbly liquid
    1.4.2. Fracture (cold boiling) of water during seaquakes   
    1.4.3. Model of fracture (cold boiling) of bubbly liquid
    1.5. Models of moment and momentless shells
    1.5.1. 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 waves

    2.1. Models of dynamic failure of solid media
    2.1.1. Phenomenological approach
    2.1.2. Microstructural approach
    2.2. Models of interacting voids (bubbles, pores)
    2.3. Pores on porous materials
    2.4. Mathematical model of materials containing pores

    Chapter 3. Models of dynamic failure of weakly-cohesived media (WCM)

    3.1. Introduction
    3.1.1. Examples of gassy material properties
    3.1.2. Behavior of weakly-cohesive geomaterials within of extreme  waves
    3.2. Modelling of gassy media
    3.2.1. State equation for mixture of condensed matter/gas 
    3.2.2. Strongly nonlinear model of the state equation for gassy media
    3.2.3. The Tait-like form of the state equation
    3.2.4. Wave equations for gassy materials
    3.3. Effects of bubble oscillations on the one-dimensional governing equations
    3.3.1. Differential form of the state equation
    3.3.2. The strongly nonlinear wave equation for bubbly media
    3.4. Linear acoustics of bubbly media
    3.4.1. Three speed wave equations
    3.4.2. Two speed wave equations
    3.4.3. One-speed wave equations
    3.4.4. Influence of viscous properties on the sound speed of  magma-like media
    3.5. Examples of observable extreme waves of WCM
    3.5.1. Mount St Helens eruption
    3.5.2. The volcano Santiaguito eruptions
    3.6. 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 Schrödinger equations
    3.7. Strongly nonlinear Airy-type equations and remarks to the Chapters  1-3

    Chapter 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 equations
    4.1.2. Boundary conditions
    4.1.3. A basic expression for the pressure and a basic strongly nonlinear wave equation 
    4.2. 2D strongly nonlinear wave equations for a viscous liquid
    4.2.1. The vertical displacement assumption
    4.2.2. The 2D Airy-type wave equation
    4.2.3.  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 equation
    4.3.2.  Three-speed variants of the strongly nonlinear wave equation 
    4.3.3.  Resonant interaction of the gravity and capillary effects in a surface wave
    4.3.4. Effects of the dispersion
    4.3.5.  Examples of  nonlinear wave equations
    4.4. Nonlinear equations for gravity waves over the finite-depth ocean
    4.4.1. Moderate depth
    4.4.2.  The gravity waves over the deep ocean 
    4. 5.  Models and basic equations for long waves
     4.6. Bottom friction and governing equations for long extreme waves
    4. 7.  Airy- type equations for capillary waves and remarks to the Chapter 4

    Chapter 5.  Euler’s figures and extreme waves: examples, equations and unified solutions

    5.1.  Example of Euler's elastica figures
    5.2.  Examples of fundamental nonlinear wave equations
    5.3.  The nonlinear Klein-Gordon equation and wide spectre of its solutions
    5.3.1  The one dimensional version and one hand travelling waves
    5.3.2.  Exact solutions of the nonlinear Klein-Gordon equation
    5.3.3. The sine-Gordon equation: approximate and exact elastica-like wave solutions
    5.4. Cubic nonlinear equations describing elastica-like waves
    5.5. Elastica-like waves: singularities, unstabilities, resonant generation
    5. 5. 1.  Singularities  as fields of the Euler’s elastic figures generation
    5. 5. 2.  Instabilities and  generation of the Euler’s elastica figures
    5. 5. 3.  'Dangerous' dividers and self-excitation of the transresonant waves
    5. 6.  Simple methods for a description of elastica-like waves
    5. 6. 1.  Modelling of unidirectional elasica-like waves
    5. 6. 2. The model equation for Faraday waves and Euler’s figures
    5.7. Nonlinear effects on transresonant evolution of Euler figures into particle-waves


    PART II.  Waves in finite resonators

    Chapter 6.  Generalisation of the d’Alembert’s  solution  for nonlinear long waves

    6.1. Resonance of travelling surface waves (site resonance)
    6.2.  Extreme waves in finite resonators
    6. 2. 1. Resonance waves in a gas filling closed tube
    6. 2. 2.  Resonant amplification of seismic waves in natural resonators
    6. 2. 3. Topographic effect: extreme dynamics of Tarzana hill
    6. 3. The d' Alembert- type nonlinear resonant solutions: deformable coordinates
    6.3.1. The singular solution of the nonlinear wave equation
    6.3.2.  The solutions of the wave equation without the singularity with time
    6.3.3.  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 equations
    6. 4. 2.  Resonant (unsingular in time) solutions of the wave equation
    6. 4. 3. Special cases of the resonant (unsingular with time ) solution
    6. 4. 4. Illustration to the theory: the site resonance of waves in a long channel
    6. 5.  Theory of  free oscillations of nonlinear wave in resonators
    6. 5. 1. Theory of  free strongly nonlinear wave in resonators
    6. 5. 2. Comparison of theoretical results
    6. 6. Conclusion on this Chapter

    Chapter 7.  Extreme resonant waves: a quadratic nonlinear theory

    7.1.  An example of a boundary problem and the equation determining resonant plane waves
    7.1.1.  Very small effects of nonlinearity, viscosity and dispersion
    7.1.2. The dispersion effect on linear oscillations
    7.1.3. Fully linear analysis
    7.2.  Linear resonance
    7. 2. 1.  Effect of the nonlinearity
    7. 2. 2.     Waves excited very near band  boundaries of  resonant band
    7. 2. 3. Effect of viscosity
    7. 3.  Solutions within and near the shock structure
    7.4. Resonant wave structure: effect of dispersion
    7. 5. Quadratic resonances
    7. 5. 1. Results of calculations and discussion
    7.6. Forced vibrations of a nonlinear elastic layer

    Chapter 8. Extreme resonant waves: a cubic nonlinear theory

    8. 1.  Cubically nonlinear effect for closed resonators  
    8. 1. 1.  Results of calculations: pure cubic nonlinear effect
    8. 1. 2.  Results of calculations: joint cubic and quadratic  nonlinear effect
    8. 1. 3.  Instant collapse of waves near resonant band end
    8. 1. 4.  Linear and cubic-nonlinear standing waves in resonators
    8. 1. 5.  Resonant particles, drops, jets, surface craters and bubbles
    8. 2. A half-open resonator
    8. 2.1. Basic relations
    8. 2.2. Governing equation
    8.3  Scenarios of transresonant evolution and comparisons with experiments
    8. 4. Effects of cavitation in liquid on its oscillations in resonators

    Chapter 9. Spherical resonant waves

    9.1. Examples and effects of extreme amplification of spherical waves
    9. 2. Nonlinear spherical waves in solids
    9.2.1. Nonlinear acoustics of the homogeneous viscoelastic solid body
    9. 2.2. Approximate general solution
    9. 2.3.  Boundary problem,  basic relations and extreme resonant waves
    9.2.4. Analogy  with the plane wave, results of calculations and discussion
    9.3. Extreme waves in spherical resonators filling gas or liquid
    9.3.1.  Governing equation and  its general solution
    9.3.2.  Boundary conditions and basic equation for gas sphere
    9. 3.3. Structure and trans-resonant evolution of oscillating waves First scenario (C -B) Second scenario (C = -B)
    9.3.4.  Discussion
    9. 4. Localisation of resonant spherical waves in spherical layer

    Сhapter 10. Extreme Faraday waves

    10. 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 research
    10. 3.  Modelling experiments as standing waves
    10.4. Modelling of counterintuitive waves as travelling waves
    10. 4. 1. Modeling of  the Kolesnichenko's experiments
    10. 4. 2. Modelling of experiments of  Bredmose et al.
    10. 5.  Strongly nonlinear waves and ripples
    10.5. 1. Experiments of  Lei Jiang et al.  and discussion of them
    10. 5. 2.  Deep water model
    10. 6. Solitons, oscillons and formation of surface patterns
    10.7. Theory and patterns of nonlinear Faraday waves
    10. 7.1  Basic equations and relations
    10. 7.2. Modeling of certain experimental data
          10.7.3. Two-dimensional patterns
    10. 7.4 Historical comments and key result

    PART III. Extreme ocean waves, resonances and phenomena

    Chapter  11. Long waves, Green's law and topographical resonance

    11.1. Surface ocean waves and vessels 
    11.2.  Observations of the extreme waves
    11.3. Long solitary waves 
    11. 4.  KdV-type, Burgers-type, Gardner-type and Camassa-Holm-type equations for the case of the slowly-variable depth
    11. 5. Model solutions and the Green law for solitary wave
    11. 6.  Examples of coastal evolution of the solitary wave
    11. 7.  Generalizations of the Green’s law
    11. 8. Tests for generalisated Green’s law
    11. 8. 1.  The evolution of harmonical waves above topographies
    11. 8. 2.  The evolution of a solitary wave over trapezium topographies
    11. 8. 3. Waves in the channel with a semicircular topographies
    11. 9.  Topographic resonances and the Euler’s elastica

    Chapter 12. Modelling of the tsunami described by Charles Darwin and coastal waves

    12.1.  Darwin’s description of tsunamis generated by coastal earthquakes 
    12.2.  Coastal evolution of tsunami
    12.2.1. Effect of the bottom slope
    12. 2. 2. The ocean ebb in front of a tsunami
    12. 2. 3. Effect of the bottom friction
    12 .3.  Theory of tsunami: basic relations
    12.4.  Scenarios  of  the coastal  evolution of tsunami
    12.4.1. Cubic nonlinear scenarios
    12.4.2. Quadratic nonlinear scenario
    12. 5. Cubic nonlinear effects: overturning and breaking of waves

    Chapter 13.  Theory of extreme (rogue, catastrophic) ocean waves

    13. 1. Oceanic heterogeneities  and the occurrence of extreme waves
    13. 2. Model of shallow waves
    13. 2. 1.  Simulation of a “hole in the sea” met by the  tanker “Taganrogsky Zaliv”
    13. 2. 2.  Simulation of typical extreme ocean waves as  shallow waves
    13.3.  Solitary ocean waves
    13. 4.  Nonlinear dispersive relation and extreme waves
    13. 4.1. The weakly nonlinear interaction of many small amplitude ocean waves
    13. 4.2. The cubic nonlinear interaction of ocean waves and extreme waves formation
    13. 5. Resonant nature of extreme harmonic wave 

    Chapter 14.  Wind -induced waves and wind-wave resonance

    14.1. Effects of wind and current
    14.2. Modeling the effect of wind on the waves
    14. 3. Relationships and equations for wind waves in shallow and deep water
    14. 4. Wave equations for unidirectional wind waves
    14.5. The transresonance evolution of coastal wind waves

    Chapter 15. Transresonant evolution of  Euler’s figures into vortices

    15.1. Vortices in the resonant tubes
    15.2. Resonance vortex generation
    15.3.  Simulation of the Richtmyer-Meshkov instability results
    15.4. Cubic nonlinearity and evolution of waves into vortices
    15.5. Remarks to extreme water waves (Parts I-II) 

    Part IV.  Counterintuitive behaviour CIB of structural elements after impact loads

    Chapter 16. Experimental data

    16. 1. Introduction and method of impact loading
    16. 2. CIB of circular plates: results and discussion
    16. 3. CIB of rectangular plates and shallow caps
    16.3.1.  Discussion of CIB of  shallow caps
    16.3.2. Cap/ permeable membrane system
    16.3.3.  CIB  of  panels

    Chapter 17.  CIB of plates and shallow shells: theory and calculations

    17. 1. Distinctive features of CIB of plates and shallow shells
    17.1. 1.   Investigation techniques                   
    17. 1.2.   Results and discussion: plates , spherical caps and cylindrical panels
    17. 2. Influences of  atmosphere and cavitation on CIB
    17. 2. 1. Theoretical models
    17. 2. 2.  Calculation details   
    17. 2. 3.  Results and discussion                    

    PART V. Extreme waves and structural elements

    Chapter 18.  Extreme effects and waves in impact loaded hydrodeformable systerms
    18.1. Introduction 
    18.2. Underwater explosions and  the cavitation wave: experiments
    18. 3.  Experimental studies of formation and propagation of the cavitation waves
     18. 3.1.  Elastic plate/underwater wave interaction
    18. 3.2.  Elastoplastic plate/underwater wave interaction
    18.4. Extreme underwater wave and plate interaction
    18. 4. 1. Effects of deformability
    18. 4. 2. Effects of cavitation on the plate surface
    18. 4. 3. Effects of cavitation in the liquid volume on the plate-liquid interaction
    18. 4. 4. Effects of plasticity
    18. 5. Modelling of extreme wave cavitation and cool boiling in tanks
    18. 5. 1. Impact loading of tank
    18. 5. 2. Impact loading of liquid in tank

    Chapter 19. Shells and cavitation (cool boiling) waves   

    19. 1. Interaction of a cylindrical shell with shock wave in liquid
    19. 2. Extreme waves in cylindrical elastic container
    19. 2. 1. Effects of cavitation and cool boiling on the interation of shells
    19. 2. 2. Features of bubble dynamics and their effect on shells
    19. 3. Extreme wave phenomena in the hydro - gas-elastic system
    19. 4. Effects of boiling of liquids within rarefaction waves on the transient deformation of hydroelastic systems
    19. 5. A method of solving transient three-dimensional problems of hydroelasticity for cavitating and boiling liquids
    19.5.1. Governing equations
    19.5.2.  Numerical method
    19.5.3. Results and discussion

    Chapter  20.  Interaction of extreme underwater waves with structures

    20.1. Fracture and cavitation waves in thin plate/underwater explosion system
    20.2. Fracture and cavitation waves in plate/underwater explosion system
    20.3. Generation of cavitation waves after tank bottom buckling
    20. 4. Transient interaction of a stiffened spherical  dome with underwater shock waves
    20. 4. 1.  The problem and method of solution
    20. 4. 2. Numeric method of problem solution
    20. 4. 3. Results of calculations
    20. 5.  Extreme amplification of waves at vicinity of the stiffening rib

    PART VI. Extreme waves excited by impact  of  heat, radiation or mass

     Chapter  21. Formation and amplification of heat waves

    21.1. Linear analysis. Influence of hyperbolicity
    21.2. Forming and amplifing of nonlinear heat waves
    21.3. Strongly nonlinearity of thermodynamic function as a cause of formation of cooling shock wave

    Chapter 22.  Extreme waves excited by radiation

    22.1. Impulsive deformation and destruction of bodies at temperatures below the melting point
    22.1.1. Thermoelastic waves excited by long-wave radiation
    22.1.2. Thermo-elastic waves excited by short-wave radiation
    22.1.3. Stress  and  fracture waves in metals during rapid bulk heating
    22.1.4. Optimization of the outer laser–induced spalling
    22.2. Effects of melting of material under impulse loading
    22.2.1. Mathematical model of fracture under thermal force loading
    22.2.2. Algorithm and results
    22.3.  Modelling  of  fracture, melting, vaporization and phase transition
    22. 3.1.  Calculations: effects of temperature
    22.3.2. Calculations: effects of vaporization
    22.3.3.  Calculations: effect of vaporization on spalling
    22.4.  Two dimensional fracture and evaporation
    22.5. Fracture of solid by radiation pulses as a method of ensuring safety in space
    22.5. 1. Introduction
    22.5. 2. Mathematical formulation of the problem
    22.5. 3. Calculation results and comparison  with experiments
    22.5. 4. Special features  of  fracture by spalling
    22.5. 5. Efficiency  of laser fracture
    22.5.6. Discussion and conclusion

    Chapter. 23.  The melting waves in front of a massive perforator

    23.1. Experimental investigation
    23. 2. Numerical modeling.
    23. 3. Results of the calculation and discussion

    Part VII. Modelling of particle-wave,  slit experiments and the origin of the Universe

    Chapter 24. Resonances, Euler figures and particle-waves

    24.1. Scalar fields and Euler figures
    24.1.1  Own nonlinear oscillations of a scalar field in a resonator
    24.1.2.  The simplest model of the evolution of Euler’s figures into periodical particle-wave
    24.2. Some data of  exciting experiments with layers of liqud
    24. 3. Stable oscillations of particle-wave configurations
    24.4.  Schrödinger  and Klein-Gordon equations
    24.5.  Strongly localised nonlinear sphere-like waves and wave packets
    24.6. Wave trajectories, wave packets and discussion

    Chapter 25. Nonlinear quantum waves in the light of recent slit experiments

    25.1.  Introduction
    25. 2. Experiments using different kind of "slits" and the beginning of the discussion
    25.3. Explanations and discussion of the experimental results
    25.4.  Casimir’s effect
    25.5.  Thin metal layer and plasmons as the synchronizators
    25.6. Testing of thought experiments
    25.7. Main thought experiment
    25. 8.  Resonant dynamics of particle-wave, vacuum and Universe

    Chapter 26. Resonant models of origin of particles and the Universe due to quantum perturbations of scalar fields

    26.1. Basic equation and relations
    26.2. Basic solutions. Dynamic and quantum effects
    26.3. Two-dimensional maps of landscapes of the field
    26.4. Description of quantum perturbations
    26.4.1. Quantum perturbations and free nonlinear oscillations in the potential well
    26.4.2. Oscilations of scalar field, granular layer and the Bose-Einstein condensate
    26.4.3. Simple model of the origin of the particles: mathematics and imaginations
    26.5. Modelling of quantum actions:  theory
    26.6. Modelling of quantum actions:  calculations


    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 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 did 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.