Comparison of two versions of the MNLS with the full water wave equation

Conference item

Versions of the non-linear Schrödinger equation are frequently used for modelling the non-linear propagation of water waves. In this paper, we compare two models against the results of fully non-linear numerical simulations. We consider uni-directional versions of the non-linear Schrödinger equation of Dysthe et al. with the hybrid model of Trulsen et al. The model of Trulsen et al. is shown to have clear advantages in all situations considered including modelling wave crest statistics for highly non-linear cases. However, for very broad bandwidths this model does start to break down, presumably due to the inherent limitation of the envelope representation of water waves. This in turn leads to a small, non-physical, leakage of energy in nonlinear simulations, although, this leakage is much smaller than for the version with 5th order linear dispersion relationship.

Authors: Tang, T; Li, Y; Bingham, HB; Adcock, TA

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Society of Mechanical Engineers
• Host title: Proceedings of the ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering
• Chapter number: Volume 6B: Ocean Engineering
• Publication date: 2020-12-18
• Acceptance date: 2020-04-23
• Event title: 39th International Conference on Ocean, Offshore and Arctic Engineering
• Event location: Online
• Event website: https://event.asme.org/OMAE-2020
• Event start date: 2020-08-03
• Event end date: 2020-08-07
• DOI: 10.1115/OMAE2020-18919
• ISBN: 978-0-7918-8438-6
• Language: English
• Keywords: modeling; FFR; statistics as topic; computer simulation; waves; leakage; water waves; engineering simulation; Schrödinger equation