Propagation and Evolution of Transient Water Waves
This chapter deals with some aspects of the initial-boundary-value problems of the initiation, generation and propagation of tsunami waves. The generation of tsunami waves by bottom movements is considered. We formulate an appropriate initial-boundary-val
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Propagation and Evolution of Transient Water Waves
6.1
Generation of Tsunami Waves by Underwater Earthquakes
The generation and propagation of tsunami waves have long been a subject of extensive studies. The main theoretical and applied aspects of this problem are well described in Refs. [37, 51, 58, 90]. The stages of tsunami wave evolution are well known: generation, propagation, transformation and run-up on the coast. Nevertheless, predicting the tsunami wave run-up on the coast within an acceptable time still remains to be a crucial task that should allow the timely evacuation of the regions under the risk and mitigation of the destructive effect of tsunamis. The indeterminacy of the problem of the tsunami wave generation is mainly attributed to the mechanism of underwater earthquakes that represent the major source of tsunami waves. The corresponding initial-boundary-value problem also remains to be nondetermined, in view of the unknown exact initial moment of tsunami generation [68]. Another problematic issue is the indeterminacy in the tsunami wave initiation in each particular case. Some underwater earthquakes of the similar power do generate the tsunami waves and some do not. A typical example is the tsunami that took place in Southeast Asia (December 2004, 9.3 magnitude) [31], whereas the recurring earthquakes (March 2005, 6.3 magnitude) did not result in the generation of any tsunami wave. In this regard, special attention must be given to some characteristic examples. One should recall the tsunami event that took place on the coast of Kamchatka in 1737, when 70 m waves were running up on the coastline. They followed one another at intervals of 10 min. Other big tsunami events include those in Kamchatka (1952), Chile (1960, 9 magnitude), Mexico City (1985, 8.5 magnitude) and Hokkaido island (1993, 7.5 magnitude, 30 m). Smaller tsunami waves of up to 2 m were even observed in the Black and Azov seas (1959, Kerch Strait). Modelling the tsunami waves generated by the landslide of Mt. Mayuyama in 1792 showed that such a landslide could generate 20 m high tsunami waves [2]. Three large tsunami © Springer Nature Singapore Pte Ltd. 2018 I.T. Selezov et al., Wave Propagation and Diffraction, Foundations of Engineering Mechanics, DOI 10.1007/978-981-10-4923-1_6
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6 Propagation and Evolution of Transient Water Waves
waves (10 m elevation above the sea level) were observed in a lagoon in Papua New Guinea in 1998. They were generated by an underwater earthquake caused by earthquake shocks. After the destructive tsunami in South-East Asia in December 2004 and January 2005, there was an earthquake in the Crimea near Sudak. These events could probably be connected, the latter being the result of the solitary wave propagation in accordance with the new model of wave-type earthquake proposed in Ref. [85]. This model is based on the concept of the hydrodynamic flow of geomass along the tectonic ray tube, and the evolution of the damaged medium is described by the kinetic equation for the damage coefficient λ
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