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

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
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 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
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
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
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 Nonlinearity
4.2.2 Waves Excited Very Near 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 Transresonant 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 Localization 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 Modeling Experiments as Standing Waves
7.4 Modeling of Counterintuitive Waves as Travelling Waves
7.4.1 Modeling of the Kolesnichenko’s Experiments
7.4.2 Modeling 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 Varying 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 Generalized Green’s Law
8.8.1 The Evolution of Harmonic 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 Modeling of a 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 Interaction of Ocean Waves and Extreme Waves Formation
10.5 Resonant Nature of Extreme Harmonic Wave
Chapter 11 Wind-Induced Waves and Wind–Wave Resonance
11.1 Effects of Wind and Current
11.2 Modeling the Effect of Wind on the Waves
11.3 Relationships and Equations for Wind Waves in Shallow and Deep Water
11.4 Wave Equations for Unidirectional Wind Waves
11.5 The Transresonance Evolution of Coastal Wind Waves
Chapter 12 Transresonant Evolution of Euler’s Figures into Vortices
12.1 Vortices in the Resonant Tubes
12.2 Resonance Vortex Generation
12.3 Simulation of the Richtmyer–Meshkov Instability Results
12.4 Cubic Nonlinearity and Evolution of Waves into Vortices
12.5 Remarks to Extreme Water Waves (Parts I–III)
References
Part IV Modeling of Particle–Waves, Slit Experiments, and the Extreme Waves in Scalar Fields
Chapter 13 Resonances, Euler’s Figures, and Particle-Waves
13.1 Scalar Fields and Euler’s Figures
13.1.1 Own Nonlinear Oscillations of a Scalar Field in a Resonator
13.1.2 The Simplest Model of the Evolution of Euler’s Figures into Periodical Particle-Wave
13.2 Some Data of Exciting Experiments with Layers of Liquid
13.3 Stable Oscillations of Particle–Wave Configurations
13.4 Schrödinger and Klein–Gordon Equations
13.5 Strongly Localized Nonlinear Sphere-Like Waves and Wave Packets
13.6 Wave Trajectories, Wave Packets, and Discussion
Chapter 14 Nonlinear Quantum Waves in the Light of Recent Slit Experiments
14.1 Introduction
14.2 Experiments Using Different Kinds of “Slits” and the Beginning of the Discussion
14.3 Explanations and Discussion of the Experimental Results
14.4 Casimir’s Effect
14.5 Thin Metal Layer and Plasmons as the Synchronizators
14.6 Testing of thought Experiments
14.7 Main thought Experiment
14.8 Resonant Dynamics of Particle-Wave, Vacuum, and Universe
Chapter 15 Resonant Models of Origin of Particles from Scalar Fields
15.1 Basic Equation and Relations
15.2 A Landscape of the Scalar Potential
15.3 Effects of Interaction of Dynamic and Stationary Parts of Scalar Field: Eruption and Tunneling
15.4 Description of Quantum Perturbations
15.4.1 Modeling of Quantum Actions: Theory
15.4.2 Modeling of Quantum Actions: Calculations
15.5 Oscillations of Scalar Field and the Bose–Einstein Condensate
15.6 Modelling of the Origin of the Particles
15.7 Remarks and Conclusion to Part IV
References
Conclusion to Volume I
Index
Volume 02
Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Acknowledgments
Author
Part I Basic Models, Equations, and Ideas
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 Materials
2.1.1 Phenomenological Approach
2.1.2 Microstructural Approach
2.2 Models of Interacting Voids (Bubbles, Pores)
2.3 Pore 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 Extreme Waves
3.2 Modeling of Gassy Media
3.2.1 State Equation for Condensed Matter–Gas Mixture
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 Chapters 1–3
References
Part II Extreme Waves and Structural Elements
Chapter 4 Extreme Effects and Waves in Impact Loaded Hydrodeformable Systems
4.1 Introduction
4.2 Underwater Explosions and Extreme Waves of the Cavitation: Experiments
4.3 Experimental Studies of Formation and Propagation of the Cavitation Waves
4.3.1 Elastic Plate–Underwater Wave Interaction
4.3.2 Elastoplastic Plate–Underwater Wave Interaction
4.4 Extreme Underwater Wave and Plate Interaction
4.4.1 Effects of Deformability
4.4.2 Effects of Cavitation on the Plate Surface
4.4.3 Effects of Cavitation in the Liquid Volume on the Plate–Liquid Interaction
4.4.4 Effects of Plasticity
4.5 Modeling of Extreme Wave Cavitation and Cool Boiling in Tanks
4.5.1 Impact Loading of a Tank
4.5.2 Impact Loading of Liquid in a Tank
Chapter 5 Shells and Cavitation (Cool Boiling) Waves
5.1 Interaction of a Cylindrical Shell with Underwater Shock Wave in Liquid
5.2 Extreme Waves in Cylindrical Elastic Container
5.2.1 Effects of Cavitation and Cool Boiling on the Interaction of Shells
5.2.2 Features of Bubble Dynamics and Their Effect on Shells
5.3 Extreme Wave Phenomena in the Hydro-Gas-Elastic System
5.4 Effects of Boiling of Liquids Within Rarefaction Waves on the Transient Deformation of Hydroelastic Systems
5.5 A Method of Solving Transient Three-Dimensional Problems of Hydroelasticity for Cavitating and Boiling Liquids
5.5.1 Governing Equations
5.5.2 Numerical Method
5.5.3 Results and Discussion
Chapter 6 Interaction of Extreme Underwater Waves with Structures
6.1 Fracture and Cavitation Waves in Thin-Plate/Underwater Explosion System
6.2 Fracture and Cavitation Waves in Plate/Underwater Explosion System
6.3 Generation of Cavitation Waves after Tank Bottom Buckling
6.4 Transient Interaction of a Stiffened Spherical Dome with Underwater Shock Waves
6.4.1 The Problem and Method of Solution
6.4.2 Numeric Method of Problem Solution
6.4.3 Results of Calculations
6.5 Extreme Amplicafition of Waves at Vicinity of the Stiffening Rib
References
Part III: Counterintuitive Behavior of Structural Elements after Impact Loads
Chapter 7 Experimental Data
7.1 Introduction and Method of Impact Loading
7.2 CIB of Circular Plates: Results and Discussion
7.3 CIB of Rectangular Plates and Shallow Caps
7.3.1 Discussion of CIB of Shallow Caps
7.3.2 Cap/Permeable Membrane System
7.3.3 CIB of Panels
Chapter 8 CIB of Plates and Shallow Shells: Theory and Calculations
8.1 Distinctive Features of CIB of Plates and Shallow Shells
8.1.1 Investigation Techniques
8.1.2 Results and Discussion: Plates, Spherical Caps, and Cylindrical Panels
8.2 Influences of Atmosphere and Cavitation on CIB
8.2.1 Theoretical Models
8.2.2 Calculation Details
8.2.3 Results and Discussion
References
Part IV: Extreme Waves Excited by Impact of Heat, radiation, or Mass
Chapter 9 Forming and Amplifying of Heat Waves
9.1 Linear Analysis – Influence of Hyperbolicity
9.2 Forming and Amplifying Nonlinear Heat Waves
9.3 Strong Nonlinearity of Thermodynamic Function as a Cause of Formation of Cooling Shock Wave
Conclusions
Chapter 10 Extreme Waves Excited by Radiation Impact
10.1 Impulsive Deformation and Destruction of Bodies at Temperatures below the Melting Point
10.1.1 Thermoelastic Waves Excited by Long-Wave Radiation
10.1.2 Thermoelastic Waves Excited by Short-Wave Radiation
10.1.3 Stress and Fracture Waves in Metals During Rapid Bulk Heating
10.1.4 Optimization of the Outer Laser-Induced Spalling
10.2 Effects of Melting of Material under Impulse Loading
10.2.1 Mathematical Model of Fracture under Thermal Force Loading
10.2.2 Algorithm and Results
10.3 Modeling of Fracture, Melting, Vaporization, and Phase Transition
10.3.1 Calculations: Effects of Temperature
10.3.2 Calculations: Effects of Vaporization
10.3.3 Calculations: Effect of Vaporization on Spalling
10.4 Two-Dimensional Fracture and Evaporation
10.5 Fracture of Solid by Radiation Pulses as a Method of Ensuring Safety in Space
10.5.1 Introduction
10.5.2 Mathematical Formulation of the Problem
10.5.3 Calculation Results and Comparison with Experiments
10.5.4 Special Features of Fracture by Spalling
10.5.5 Efficiency of Laser Fracture
10.5.6 Discussion and Conclusion
Conclusion
Reference
Chapter 11 Melting Waves in Front of a Massive Perforator
11.1 Experimental Investigation
11.2 Numerical Modeling
11.3 Results of the Calculation and Discussion
References
Index