A Solitary Wave Propagates through a Gap into a Channel with an Upward Step

Abstract

Abstract-The theme of this article is to apply a three-dimensional fully-nonlinear hydrodynamic model to simulate a solitary wave passing through a gap into a canal of expanded cross-section with a raised channel bottom. When a solitary wave impacts on an infinitely long breakwater with a gap width L 1 , part of the wave energy is reflected by the breakwater and part is transmitted through the gap. Here the domain with incident and reflected waves is called Region I and that with transmitted waves in a channel of width L 2 (L 2 >=L 1 ) is Region II. As the bottom of Region II has an upward step, the wave is transitioned to propagate from a deep water region (normalized depth=1) into a shallow water region (depth=D). The transmitted waves are subject to be diffracted and reflected by the confined boundaries. These diffraction and reflection effects are governed by D and L 2 . For L 2 =L 1 , it is similar to the case for a solitary wave climbing upon a step to generate soliton fission phenomenon. The results show that the condition of D>0 can enhance the nonlinearity of waves while L 2 >L 1 allows the transmitted waves to expand with reduced wave height. It is noticed that part of the transmitted outward-propagating waves are reflected back from the wall boundaries to interact with longitudinal traveling waves forming a wave front oscillating transversely with nonuniform wave height across the channel.Index Terms-Solitary wave, fully-nonlinear wave, three-dimensional wave, diffraction, tsunami.