Strong solutions for the Alber equation and stability of unidirectional wave spectra
© American Institute of Mathematical Sciences. The Alber equation is a moment equation for the nonlinear Schrodinger equation, formally used in ocean engineering to investigate the stability of stationary and homogeneous sea states in terms of their power spectra. In this work we present the first w...
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ftmit:oai:dspace.mit.edu:1721.1/133414 2023-10-29T02:38:26+01:00 Strong solutions for the Alber equation and stability of unidirectional wave spectra G Athanassoulis, Agissilaos A Athanassoulis, Gerassimos Ptashnyk, Mariya Sapsis, Themistoklis Massachusetts Institute of Technology. Department of Mechanical Engineering 2020-08-04T17:51:42Z application/pdf https://hdl.handle.net/1721.1/133414 en eng American Institute of Mathematical Sciences (AIMS) 10.3934/KRM.2020024 Kinetic & Related Models https://hdl.handle.net/1721.1/133414 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Institute of Mathematical Sciences Article http://purl.org/eprint/type/JournalArticle 2020 ftmit 2023-10-02T18:05:01Z © American Institute of Mathematical Sciences. The Alber equation is a moment equation for the nonlinear Schrodinger equation, formally used in ocean engineering to investigate the stability of stationary and homogeneous sea states in terms of their power spectra. In this work we present the first well-posedness theory for the Alber equation with the help of an appropriate equivalent reformulation. Moreover, we show linear Landau damping in the sense that, under a stability condition on the homogeneous background, any inhomogeneities disperse and decay in time. The proof exploits novel L2 space-time estimates to control the inhomogeneity and our result applies to any regular initial data (without a mean-zero restriction). Finally, the sufficient condition for stability is resolved, and the physical implications for ocean waves are discussed. Using a standard reference dataset (the \North Atlantic Scatter Diagram") it is found that the vast majority of sea states are stable, but modulationally unstable sea states do appear, with likelihood O(1/1000); these would be the prime breeding ground for rogue waves. Article in Journal/Newspaper North Atlantic DSpace@MIT (Massachusetts Institute of Technology) |
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description |
© American Institute of Mathematical Sciences. The Alber equation is a moment equation for the nonlinear Schrodinger equation, formally used in ocean engineering to investigate the stability of stationary and homogeneous sea states in terms of their power spectra. In this work we present the first well-posedness theory for the Alber equation with the help of an appropriate equivalent reformulation. Moreover, we show linear Landau damping in the sense that, under a stability condition on the homogeneous background, any inhomogeneities disperse and decay in time. The proof exploits novel L2 space-time estimates to control the inhomogeneity and our result applies to any regular initial data (without a mean-zero restriction). Finally, the sufficient condition for stability is resolved, and the physical implications for ocean waves are discussed. Using a standard reference dataset (the \North Atlantic Scatter Diagram") it is found that the vast majority of sea states are stable, but modulationally unstable sea states do appear, with likelihood O(1/1000); these would be the prime breeding ground for rogue waves. |
author2 |
Massachusetts Institute of Technology. Department of Mechanical Engineering |
format |
Article in Journal/Newspaper |
author |
G Athanassoulis, Agissilaos A Athanassoulis, Gerassimos Ptashnyk, Mariya Sapsis, Themistoklis |
spellingShingle |
G Athanassoulis, Agissilaos A Athanassoulis, Gerassimos Ptashnyk, Mariya Sapsis, Themistoklis Strong solutions for the Alber equation and stability of unidirectional wave spectra |
author_facet |
G Athanassoulis, Agissilaos A Athanassoulis, Gerassimos Ptashnyk, Mariya Sapsis, Themistoklis |
author_sort |
G Athanassoulis, Agissilaos |
title |
Strong solutions for the Alber equation and stability of unidirectional wave spectra |
title_short |
Strong solutions for the Alber equation and stability of unidirectional wave spectra |
title_full |
Strong solutions for the Alber equation and stability of unidirectional wave spectra |
title_fullStr |
Strong solutions for the Alber equation and stability of unidirectional wave spectra |
title_full_unstemmed |
Strong solutions for the Alber equation and stability of unidirectional wave spectra |
title_sort |
strong solutions for the alber equation and stability of unidirectional wave spectra |
publisher |
American Institute of Mathematical Sciences (AIMS) |
publishDate |
2020 |
url |
https://hdl.handle.net/1721.1/133414 |
genre |
North Atlantic |
genre_facet |
North Atlantic |
op_source |
American Institute of Mathematical Sciences |
op_relation |
10.3934/KRM.2020024 Kinetic & Related Models https://hdl.handle.net/1721.1/133414 |
op_rights |
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. |
_version_ |
1781064465329946624 |