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 L1, 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 L2 (L2>=L1) 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 >L1 allows the transmitted waves to expand with reduced wave height. It is noticed that part of the transmitted outward-propagating waves are r eflected 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.
C. H. Chang is with the Department of Information Management, Ling-Tung University, Taichung, Taiwan (e-mail: changbox@ teamail.ltu.edu.tw).
K. H. Wang is with the Department of Civil and Environmental Engineering, University of Houston, Houston, TX, USA (e-mail: KHWang@uh.edu).
Cite:Chih-Hua Chang and Keh-Han Wang, "A Solitary Wave Propagates through a Gap into a Channel with an Upward Step," International Journal of Environmental Science and Development vol. 5, no. 5, pp. 467-472, 2014.