Modeling of extreme waves in technology and nature. (2020)

• Record Type: Book
• Further Information: Note: Shamil U. Galiev.
• Authors: Galiev, Shamilʹ Usmanovich
• Contents: 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 References 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; 9.3
• Edition: 1st
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2020
• Extent: 1 online resource, illustrations (black and white, and colour)
• Subjects: 531.1133; Waves; Rogue waves; Waves -- Mathematical models; Rogue waves -- Mathematical models
• Languages: English
• ISBNs: 9781351059374; 9781351059381; 9781351059367; 9781351059398
• Related ISBNs: 9781138479517
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