Charles Darwin's Geophysical Reports as Models of the Theory of Catastrophic Waves

Abstract

As it is the 200th anniversary of Darwin’s birth, 2009 has also been marked as 170 years since the publication of his book Journal of Researches, commonly referred to as The Voyage of the Beagle. During the voyage Darwin landed at Valdivia and Concepcion, Chile, just before, during and after a great earthquake which demolished hundreds of buildings, killing and injuring many people. It was a giant natural catastrophe. He saw the land rise before his eyes. Land was waved, lifted, and cracked, volcanoes awoke and giant ocean waves attacked the coast. There are two main goals of this book. The first is emphasising the priority of Darwin in the description and the analysis of the results of the severe earthquakes (Chapter I). Extracts from Darwin’s Diary and Narrative 2, ‘Journal of Researches’ and ‘The autobiography of Charles Darwin’ are presented. In the extracts Darwin described a few days of his work. Perhaps, those days were among the most important days of his life. We group the material of the extracts so that a reader can trace the evolution of Darwin’s thoughts. The key observations and ideas of Darwin, presented in the material, are shortly formulated. Then these ideas are analysed and compared with modern experimental and theoretical data. Taking into account Darwin’s key ideas we construct the mathematical models of natural catastrophic phenomena. Chapters II and III are devoted to catastrophic ocean waves. The Lagrangian description is used. Highly-nonlinear wave equations, which describe the evolution of the waves propagating over a variable depth, are derived. Attention is focused on the transresonant evolution of periodic ocean waves and tsunami. It was found that the height of the catastrophic waves changes from two to four of the height of the significant waves. The theory of uplift, loosening and rupture of weakly-cohesive geomaterials, gassy soils, and magma under sharp decompression within tension-seismic waves is developed in Chapter IV. The last Chapter is devoted to Nonlinear Science problems, in particular, to the transresonant evolution of initially smooth wave motion into vortex motion and turbulence. This evolution can take place in many layered systems: ground, ocean, air, and plasma. The generation of elastica (mushroom)-like waves, surface drops and jets, vortices and turbulence is simulated by the same highly-nonlinear wave equation. The results were used so that to describe the vortex generation in the Bose-Einstein condensate and plasma of early Universe.