Wave group focusing in the ocean: estimations using crest velocities and a Gaussian linear model
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Wave group focusing in the ocean: estimations using crest velocities and a Gaussian linear model Paul Platzer1,2,3,4 · Jean‑François Filipot1 · Philippe Naveau2,4 · Pierre Tandeo3 · Pascal Yiou2,4 Received: 13 May 2020 / Accepted: 29 August 2020 © Springer Nature B.V. 2020
Abstract Wave group focusing gives rise to the formation of large gravity waves at the surface of the ocean, some of which are called rogue waves and represent a natural hazard for ships and offshore platforms. For safety purposes, it is crucial to predict when and where these large waves will appear and how large they will be. This work focuses on crest velocities, a quantity that is relatively easy to extract from sea surface elevation fields. It is shown that there is a direct link between crest velocity gradient and wave group linear dispersive focusing. Studying analytically the focusing of one-dimensional Gaussian wave packets under linear evolution makes it possible to derive estimates of quantities at focus, based only on crest velocity measurements. In this way, the focusing time, focusing size and focusing amplitude (relative to instantaneous amplitude) of an isolated Gaussian wave packet can be estimated. Our work is also applicable to second-order non-linear waves. Limitations due to higher-order non-linear effects are studied in numerical simulations of the non-linear Schrödinger equation. Keywords Ocean wave · Rogue wave · Wave group · Wave packet · Crest velocity · Focusing · Schrödinger equation
1 Introduction Human and material losses caused by large amplitude ocean surface waves are significant, as reported by Kharif and Pelinovsky (2003). The term “rogue wave” refers to waves with a crest-to-trough wave height larger than 2Hs , where Hs is the significant wave height and
* Paul Platzer paul.platzer@ite‑fem.org 1
France Énergies Marines, 525 Avenue Alexis de Rochon, 29280 Plouzané, France
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Laboratoire des Sciences du Climat et de l’Environnement, UMR8212 CEA‑CNRS‑UVSQ, IPSL, U Paris-Saclay, l’Orme des Merisiers, 91191 Gif‑sur‑Yvette Cedex, France
3
Lab‑STICC, UMR CNRS 6285, IMT Atlantique, F‑29238 Plouzané, France
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ESTIMR ‑ Extrèmes : Statistiques,Impacts et Régionalisation, LSCE - Laboratoire des Sciences du Climat et de l’Environnement, Gif‑sur‑Yvette, France
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Natural Hazards
is defined as four times the standard deviation of the sea surface elevation (Dysthe et al. 2008). The threshold of 2Hs is arbitrary, and in the following, “rogue wave” might simply refer to waves with a large height compared to local statistics. Many rogue waves have been measured in the ocean, including the famous 26-m-high Draupner wave (Haver 2004). Even in moderate sea states, the occurrence of rogue waves can be problematic for operations (e.g. cable layout from a ship) or for transferring staff from a ship to an offshore platform or wind turbine. The harmful potential of rogue waves is a natural motivation for the forecast of their position, amplitude and spatial width over time, based on real-time measu
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