Affiliation:
1. Department of Civil and Environmental Engineering, National University of Singapore, Singapore 117576, Singapore
2. School of Civil and Environmental Engineering, Cornell University, Ithaca, New York 14850, USA
3. Institute of Hydrological and Oceanic Sciences, National Central University, Taoyuan City, 32001 Taiwan
4. Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan City 70101, Taiwan
Abstract
The existing analytical solutions for finite amplitude solitary waves, including the perturbation solutions, based on either the nonlinearity parameter, [Formula: see text], or the dispersion parameter, [Formula: see text], and the closed form solutions, are reviewed. The convergence characteristics of the perturbation solutions are discussed, showing that the perturbation solutions for the velocity field diverge for large wave amplitude. The relationships between three existing closed form solutions are discussed. The analytical solutions are then compared with exact numerical solutions. The agreement is generally good for the free surface profiles, but not for the velocity field. One of the closed form solutions [Clamond, D. and Fructus, D., “Accurate simple approximation for the solitary wave,” C. R. Mec. 331, 727 (2003)] is in almost perfect agreement with the exact numerical solutions for both the free surface profiles and the velocity fields. New laboratory experiments, measuring both free surface profile and velocity field over a wide range of α values (up to 0.6) are then presented. High speed particle image velocimetry is used to measure the velocity field in the entire water column. Detailed comparisons among the experimental data, analytical theories, and numerical solutions show that for relatively small amplitude solitary waves, say, [Formula: see text], all theories and numerical results agree very well with the experimental data. However, when [Formula: see text] only [Clamond, D. and Fructus, D., “Accurate simple approximation for the solitary wave,” C. R. Mec. 331, 727 (2003)]'s solution and the numerical agree with the experimental data.
Funder
Ministry of Education - Singapore
Subject
Condensed Matter Physics,Fluid Flow and Transfer Processes,Mechanics of Materials,Computational Mechanics,Mechanical Engineering
Cited by
3 articles.
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