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Propagation of fractal tsunami solitary waves

机译：Propagation of fractal tsunami solitary waves

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In this paper, tsunami dynamics and solitary waves are constructed in fractal dimensions based on the concept of product-like fractal measure introduced recently by Li and Ostoja-Starzewski in their formulation of anisotropic continuum media. The tsunami waves are comparable to some extent to varying-speed wave equations which are used in several studies including the spreading of shallow-water wave in certain continuous depth variations, tsunami and Rayleigh waves. Nonlinear effects were studied and the associated solitary wave in fractal dimension has been derived. It was observed that the shape of the solitary wave is affected by the fractal dimension and is analogous to an asymmetric wave train. Besides, its period is long and differs from the famous Korteweg-De Vries soliton. Such a deformation in the wave profile results in a steep wave front configuration which is observed during large tsunamis such as the 2011 Tohoku tsunami and the 2004 Indian Ocean tsunami. Our analysis shows also that short tsunamis wave could drastically enhance the maximum flow velocities, a result which is in agreement with several analytical and experimental studies.

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