Nonlinear Evolution of a Steep, Focusing Wave Group in Deep Water Simulated with OceanWave3D

• Published in: Journal of Offshore Mechanics and Arctic Engineering
• Main Authors: Barratt, Dylan, Bingham, Harry B., Adcock, Thomas A. A.
• Format: Article in Journal/Newspaper
• Language: English
• Published: 2020
• Subjects: Nonlinear wave mechanics; Directional energy transfers; wing waves; OCEANWAVE3D; /dk/atira/pure/sustainabledevelopmentgoals/affordable_and_clean_energy; name=SDG 7 - Affordable and Clean Energy; Arctic
• Online Access: https://orbit.dtu.dk/en/publications/34d52f43-4ecb-4b13-8ce7-2ff6b010f98c; https://doi.org/10.1115/1.4044989; https://backend.orbit.dtu.dk/ws/files/193384775/Barratt_et_al_2019_final.pdf

Steep, focusing waves can experience fast and local nonlinear evolution of the spectrum due to wave-wave interactions resulting in energy transfer to both higher and lower wavenumber components. The shape and kinematics of a steep wave may, thus, differ substantially from the predictions of linear theory. We have investigated the role of nonlinear interactions on group shape for a steep, narrow-banded, directionally-spread wave group focusing in deep water using the fully-nonlinear potential flow solver, OceanWave3D. Exact second-order correction of the initial conditions has been implemented together with a novel third-order approximate correction based on a Stokes-type formulation for surface elevation combined with a scaling argument for the third-order velocity potential. Four-phase separation reveals that the third-order scheme provides a good estimate for the third-order superharmonics. A quantitative assessment of numerical error has also been performed for the spatial and temporal discretization, including energy conservation, a reversibility check and validation against previous simulations performed with a higher-order spectral (HOS) code. The initially narrowbanded amplitude spectrum exhibits the formation of sidelobes at angles of approximately ± 35deg to the spectral peak during the simulated extreme wave event, occurring in approximately 10 wave periods, with a preferential energy transfer to highwavenumber components. The directional energy transfer is attributed to resonant third-order interactions with a discussion of the engineering implications.