Generation and evolution of oblique solitary waves in supercritical flows |
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| Affiliation: | 1. Mathematisches Institut A, Universität Stuttgart, Germany;1. School of Biomedical and Pharmaceutical Sciences, Guangdong University of Technology, Guangzhou, 510006, PR China;2. School of Chemical Engineering and Light Industry, Guangdong University of Technology, Guangzhou, 510006, PR China;3. School of Materials and Energy, Guangdong University of Technology, Guangzhou, 510006, PR China;1. Escola Superior de Enfermagem do Porto, Portugal;2. Emergency Department, Royal London Hospital, Barts Health NHS Trust, UK;1. Department of Civil & Mineral Engineering, University of Toronto, 35 St. George Street, Toronto, Ontario M5S 1A4, Canada;2. Percy Edward Hart Professor in Civil & Mineral Engineering, University of Toronto, 35 St. George Street, Toronto, Ontario M5S 1A4, Canada;1. State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;2. Centre for Marine Geotechnical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;3. Griffith School of Engineering, Griffith University Gold Coast Campus, Queensland QLD 4222, Australia |
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| Abstract: | It is considered that a thin strut sits in a supercritical shallow water flow sheet over a homogeneous or very mildly varying topography. This stationary 3-D problem can be reduced from a Boussinesq-type equation into a KdV equation with a forcing term due to uneven topography, in which the transverse coordinate Y plays a same role as the time in original KdV equation. As the first example a multi-soliton wave pattern is shown by means of N-soliton solution. The second example deals with the generation of solitary wave-train by a wedge-shaped strut on an even bottom. Whitham's average method is applied to show that the shock wave jump at the wedge vertex develops to a cnoidal wave train and eventually to a solitary wavetrain. The third example is the evolution of a single oblique soliton over a periodically varying topography. The adiabatic perturbation result due to Karpman & Maslov (1978) is applied. Two coupled ordinary differential equations with periodic disturbance are obtained for the soliton amplitude and phase. Numerical solutions of these equations show chaotic patterns of this perturbed soliton. |
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