Darwin, Geodynamics and Extreme Waves

<p><p><p>Preface <p>Prologue: a few notes about Charles Darwin, his research and the contents of the book </p><p>1. Introduction </p></p><p>Prologue: a few notes about Charles Darwin, his research and the contents of the book </p><p>1. Introduction </p><p><p>Prologue: a few notes about Charles Darwin, his research and the contents of the book </p><p>1. Introduction </p><p>1.1. Extreme vertical dynamics of the land surface during earthquakes </p><p>1.2. Features of destruction of weakly-cohesive materials by extreme vertical dynamics </p><p>1.3. Instability of the land surface and a connection of seismic and volcanic phenomena </p><p>2. Extracts from Darwin’s publications, and his basic geophysical ideas </p><p>2.1. Extracts from Darwin’s Journal of Researches </p><p>2.1.1. The great shock </p><p>2.1.2. The great waves </p><p>2.1.3. Paroxysmal vertical movement and volcanoes </p><p>2.2. Extracts from Darwin's Autobiographies </p><p>2.3. Darwin on earthquakes, land elevation, volcanic eruptions </p><p>and catastrophic ocean waves </p><p>2.3.1. The 1835 Chilean earthquake as a part of one great phenomenon </p><p>2.3.2. The Earth as a global seismic system </p><p>2.3.3. The earthquake-induced elevation of the land </p><p>2.3.4. The topographical effect </p><p>2.3.5. Darwin’s triggering mechanism of volcano eruptions </p><p>2.3.6. Tsunami, huge oceanic waves and resonant amplification of seismic waves in sediment layers </p><p><br>3. Darwin’s reports on catastrophic natural phenomena and modern science: topographic effect and local circumstances </p><p>3.1. Ground elevation and the strongly-nonlinear topographic effect </p><p>3.1.1. Some physical mechanisms for ground subsidence and lift </p><p>3.1.2. Loosening of sediments due to vibrations </p><p>3.1.3. Loosening of surface layers due to strongly-nonlinear wave phenomena </p><p>3.1.4. Topographical effect: extreme dynamics of Tarzana hill </p><p>3.1.5. Topographical effects: uplift and fissure of the top of a ridge </p><p>3.1.6. Topographical effect: uplift and fissure of island surfaces </p><p>3.2. Darwin’s ideas about an intimate connection between volcanic and elevatory forces </p><p>3.2.1. Earthquake-induced ground elevation as a triggering mechanism for large-scale volcanic eruptions 114 </p><p>3.2.2. Surface waves in the crater and short-time volcanic eruptions </p><p>3.2.3. Short-time eruptions from craters </p><p>3.2.4. Discussion of earthquake-induced volcanic eruptions </p><p>3.3. Amplification of the earthquake convulsion. Effects of the geology and relief </p><p>3.4. Darwin on avalanches as a cause of tsunamis </p><p>3.5. Darwin on transient cavitation within volcanic bombs </p><p>3.6. Darwin on his theories of a mountain formation </p><p>3.7 Dynamic instability and … a vorticose movement … within the surface layers </p><p><p><br>4. Darwin’s reports on catastrophic natural phenomena and modern science: seaquake-induced waves, atomization and cavitation </p><p>4.1. Darwin’s description of tsunamis generated by coastal earthquakes </p><p>4.1.1. Effect of the coast bottom on the generation of a catastrophic tsunami </p><p>4.1.2. Effect of the coast bottom on the ocean ebb and the steep front of a tsunami </p><p>4.1.3. Effects of the bottom friction </p><p>4.2. Seaquakes, transient cavitation, internal and surface waves </p><p>4.2.1. Seaquakes and cavitation </p><p>4.2.2. Seaquakes and internal waves </p><p>4.2.3. Strongly-nonlinear resonant waves and surface atomization: experiments </p><p>4.2.4. Strongly-nonlinear resonant waves and elastica forms </p><p>4.2.5. Strongly-nonlinear resonant waves, drops, bubbles and craters: calculations </p><p>4.3. Evolution of vertically-induced waves on liquid surface: from jets to breakers and vibration solitons </p><p>4.4. Solitons and oscillons </p><p>4.5. Evolution of vertically-induced granular waves: from jets to breakers and vibration solitons </p><p><br>5. Extreme wave/ship interaction </p><p>5.1. Extreme (catastrophic) ocean waves </p><p>5.2. Reasons for catastrophic ocean wave generation </p><p>5.2.1. Underwater topographies and topographic resonance </p><p>5.2.2. Discussion of some ocean resonances </p><p>5.3 Results of modelling of catastrophic ocean waves </p><p>5.3.1. Long waves </p><p>5.3.2. Short waves </p><p>5.4. The generation of catastrophic ocean waves </p><p>5.4.1. Lagrangian description of extreme ocean waves and a depth-average model </p><p>5.4.2. Quadratic and cubic -nonlinear equations for gravity waves in deep ocean </p><p>5.4.3. Solitary ocean waves </p><p>5.4.4. Catastrophic amplification of harmonic ocean waves </p><p>5.4.5. Nonlinear dispersive relation and extreme waves </p><p>5.5. Surface-breaking waves, underwater explosions and hull cavitation </p><p>5.5.1. Effects of the breaking </p><p>5.5.2. Underwater explosions and hull cavitation: descriptions </p><p>5.5.3. Underwater explosions and hull cavitation: experiments </p><p>5. 6. Experimental studies of hull cavitation </p><p>5.6.1. Elastic plate/underwater wave interaction </p><p>5. 6.2. Elastoplastic plate/underwater wave interaction </p><p>5.7. Results of modelling of wave/plate interaction </p><p>5.7.1. Effects of deformability </p><p>5.7.2 Effects of cavitation </p><p>5.7.3. Effects of plasticity </p><p><br>Chapter 6. Modelling of extreme waves in natural resonators: from gravity waves to the origin of the Universe </p><p>6.1 Governing relations describing extreme seismic waves in certain natural resonators </p><p>6.1.1. One-dimensional highly nonlinear wave equation and the nonlinear generalization of d’Alembert’s solution </p><p>6.1.2. The equations of continuity and state for different waves and materials </p><p>6.1.3. Experimental modelling of seismic waves in natural resonators </p><p>6.2. Resonant surface gravity waves </p><p>6.3. Resonant waves in closed, gas-filled tubes as a model of vertical earthquake-induced body waves </p><p>6.4. Extreme waves in semi-open resonators: ocean, sediment layers and volcano conduits </p><p>6.5. Resonant coastal waves </p><p>6.6. The experiments of Sir Geoffrey Taylor </p><p>6.7. The introduction and versions of the nonlinear Klein-Gordon equation (NKGE) </p><p>6.8. A landscape of the scalar potential </p><p>6.9. The tunnelling of the energy bubble through the potential wall </p><p>6. 9. 1. Instant quantum action </p><p>6. 9. 2. Finite time quantum action </p><p>6.9.3. Transresonant tunnelling </p><p>6.9.4. The fragmentation of multidimensional space-time during the tunnelling </p><p>6.10. The origin of the particles of energy and matter </p><p>6.10.1. Boundary conditions &amp;Phi; = 0 at x&lt;sub&gt;i&lt;/sub&gt; = 0;L<p>6.10.2. Boundary conditions at &amp;delta;&amp;Phi;/&amp;delta;x&lt;sub&gt;i&lt;/sub&gt; = 0 at x&lt;sub&gt;i&lt;/sub&gt; = 0;L </p></p><p>6.10.2. Boundary conditions at &amp;delta;&amp;Phi;/&amp;delta;x&lt;sub&gt;i&lt;/sub&gt; = 0 at x&lt;sub&gt;i&lt;/sub&gt; = 0;L </p><p>6.11. Supporting experimental results: gravity waves </p><p>6.12. The origin of the Universe </p><p>6. 13. The evolution of the Universe after the tunnelling </p><p>6. 14. Resume of the sections 6.7-6.13 </p><p>6. 15. Discussion and comments <br></p><p>7. Final comments on Charles Darwin's geophysical observations </p><p>7.1. Darwin’s discoveries and the instability of Nature </p><p>7.2. Catastrophic earthquakes and tsunamis of recent years </p><p>7.3. Closing remarks </p><p>