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Rogue waves and large deviations in deep sea

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Dematteis, Giovanni, Grafke, Tobias and Vanden-Eijnden, Eric (2018) Rogue waves and large deviations in deep sea. Proceedings of the National Academy of Sciences of the United States of America, 115 (5). pp. 855-860. doi:10.1073/pnas.1710670115

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Official URL: https://doi.org/10.1073/pnas.1710670115

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Abstract

Quantifying the departure from Gaussianity of the wave-height distribution in the seas and thereby estimating the likelihood of appearance of rogue waves is a long-standing problem with important practical implications for boats and naval structures. Here, a procedure is introduced to identify ocean states that are precursors to rogue waves, which could permit their early detection. Our findings indicate that rogue waves obey a large deviation principle—i.e., they are dominated by single realizations—which our method calculates by solving an optimization problem. The method generalizes to estimate the probability of extreme events in other deterministic dynamical systems with random initial data and/or parameters, by using prior information about the nature of their statistics.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Rogue waves , Rogue waves--Mathematical models, Laplace transformation, Instantons, Wave equation, Monte Carlo method
Journal or Publication Title: Proceedings of the National Academy of Sciences of the United States of America
Publisher: National Academy of Sciences
ISSN: 0027-8424
Official Date: January 2018
Dates:
DateEvent
January 2018Published
11 December 2017Accepted
Volume: 115
Number: 5
Page Range: pp. 855-860
DOI: 10.1073/pnas.1710670115
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
DMR-1420073National Science Foundationhttp://dx.doi.org/10.13039/100000001
DMS-1522767National Science Foundationhttp://dx.doi.org/10.13039/100000001
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