Numerical Experiments on Extreme Waves Through Oblique–Soliton Interactions

Choi, J.; Bokhove, O.; Kalogirou, A.; Kelmanson, M. A.

Abstract

Extreme water-wave motion is investigated analytically and numerically by considering two-soliton and three-soliton interactions on a horizontal plane. We successfully determine numerically that soliton solutions of the unidirectional Kadomtsev–Petviashvili equation (KPE), with equal far-field individual amplitudes, survive reasonably well in the bidirectional and higher-order Benney–Luke equations (BLE). A well-known exact two-soliton solution of the KPE on the infinite horizontal plane is used to seed the BLE at an initial time, and we confirm that the KPE-fourfold amplification approximately persists. More interestingly, a known three-soliton solution of the KPE is analysed further to assess its eight- or ninefold amplification, the latter of which exists in only a special and difficult-to-attain limit. This solution leads to an extreme splash at one point in space and time. Subsequently, we seed the BLE with this three-soliton solution at a suitable initial time to establish the maximum amplification: it is approximately 7.8 for a KPE amplification of 8.4. Herein, the computational domain and solutions are truncated approximately to a fully periodic or half-periodic channel geometry of sufficient size, essentially leading to cnoidal-wave solutions. Moreover, special geometric (finite-element) variational integrators in space and time have been used in order to eradicate artificial numerical damping of, in particular, wave amplitude.

Citation

Choi, J., Bokhove, O., Kalogirou, A., & Kelmanson, M. A. (2022). Numerical Experiments on Extreme Waves Through Oblique–Soliton Interactions. Water Waves, 4(2), 139–179. https://doi.org/10.1007/s42286-022-00059-3

• Journal Article Type: Article
• Acceptance Date: Apr 14, 2022
• Online Publication Date: Jun 2, 2022
• Publication Date: Jul 1, 2022
• Deposit Date: May 23, 2022
• Publicly Available Date: Dec 3, 2022
• Journal: Water Waves
• Print ISSN: 2523-367X
• Electronic ISSN: 2523-3688
• Publisher: Springer Nature
• Peer Reviewed: Peer Reviewed
• Volume: 4
• Issue: 2
• Pages: 139–179
• DOI: https://doi.org/10.1007/s42286-022-00059-3
• Keywords: Applied Mathematics; Computational Mathematics; Modeling and Simulation; Analysis
• Public URL: https://nottingham-repository.worktribe.com/output/8218146
• Publisher URL: https://link.springer.com/article/10.1007/s42286-022-00059-3
• Additional Information: Received: 18 February 2022; Accepted: 14 April 2022; First Online: 2 June 2022; : ; : The authors declare that they have no conflict of interest.