TY - JOUR
T1 - On finite amplitude solitary waves - A review and new experimental data
AU - Wang, Yufei
AU - Liu, Philip L.F.
N1 - Funding Information:
Philip L.-F. Liu would like to acknowledge the support from the National University of Singapore, Cornell University, and the Ministry of Education in Singapore through a research Grant (No. MOE2018-T2-2-040). This research was also supported in part by the Yushan Program, Ministry of Education in Taiwan. Yufei Wang would like to thank the Ministry of Education in Singapore for a Ph.D. Scholarship. The authors would also like to thank Stephan Grilli for providing the computer program to calculate Tanaka’s solutions. Insightful discussions with Harry Yeh and Pablo Higuera during the early stage of the work are also appreciated. They also thank Ignacio Barranco and In Mei Sou for their generous help in the experiments.
Publisher Copyright:
© 2022 Author(s).
PY - 2022/10/1
Y1 - 2022/10/1
N2 - The existing analytical solutions for finite amplitude solitary waves, including the perturbation solutions, based on either the nonlinearity parameter, α = H / h, or the dispersion parameter, ϵ = k 2 h 2, 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, α ≤ 0.2, all theories and numerical results agree very well with the experimental data. However, when α ≥ 0.3 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.
AB - The existing analytical solutions for finite amplitude solitary waves, including the perturbation solutions, based on either the nonlinearity parameter, α = H / h, or the dispersion parameter, ϵ = k 2 h 2, 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, α ≤ 0.2, all theories and numerical results agree very well with the experimental data. However, when α ≥ 0.3 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.
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U2 - 10.1063/5.0109902
DO - 10.1063/5.0109902
M3 - Review article
AN - SCOPUS:85141038717
SN - 1070-6631
VL - 34
JO - Physics of Fluids
JF - Physics of Fluids
IS - 10
M1 - 101304
ER -