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

• Published in: Volume 7B: Ocean Engineering
• Main Authors: Barratt, Dylan, Bingham, Harry B., Adcock, Thomas A. A.
• Format: Other Non-Article Part of Journal/Newspaper
• Language: English
• Published: American Society of Mechanical Engineers 2019
• Subjects: Nonlinear wave mechanics; Directional energy transfers; wing waves; OCEANWAVE3D; /dk/atira/pure/sustainabledevelopmentgoals/affordable_and_clean_energy; SDG 7 - Affordable and Clean Energy; Arctic
• Online Access: https://orbit.dtu.dk/en/publications/6ca1a8b5-719a-47a0-af70-b5d1609b2bdc; https://doi.org/10.1115/OMAE2019-95299

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 narrow-banded amplitude spectrum exhibits the formation of sidelobes at angles of approximately ±35° to the spectral peak during the simulated extreme wave event, occurring in approximately 10 wave periods, with a preferential energy transfer to high-wavenumber components. The directional energy transfer is attributed to resonant third-order interactions with a discussion of the engineering implications.