Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model
The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime th...
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| Format: | Article |
| Language: | en_US |
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Elsevier
2016
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| Online Access: | http://hdl.handle.net/1721.1/103870 https://orcid.org/0000-0003-0302-0691 https://orcid.org/0000-0001-7552-9062 |
| _version_ | 1826201178713620480 |
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| author | Cousins, William Sapsis, Themistoklis P. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Cousins, William Sapsis, Themistoklis P. |
| author_sort | Cousins, William |
| collection | MIT |
| description | The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. |
| first_indexed | 2024-09-23T11:47:27Z |
| format | Article |
| id | mit-1721.1/103870 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:47:27Z |
| publishDate | 2016 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/1038702022-09-27T21:56:43Z Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model Cousins, William Sapsis, Themistoklis P. Massachusetts Institute of Technology. Department of Mechanical Engineering Cousins, William Sapsis, Themistoklis P. The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. Massachusetts Institute of Technology (Naval Engineering Education Center (NEEC), Grant 3002883706) 2016-08-08T20:52:56Z 2016-08-08T20:52:56Z 2014-05 2014-04 Article http://purl.org/eprint/type/JournalArticle 01672789 http://hdl.handle.net/1721.1/103870 Cousins, Will, and Themistoklis P. Sapsis. “Quantification and Prediction of Extreme Events in a One-Dimensional Nonlinear Dispersive Wave Model.” Physica D: Nonlinear Phenomena 280–281 (July 2014): 48–58. https://orcid.org/0000-0003-0302-0691 https://orcid.org/0000-0001-7552-9062 en_US http://dx.doi.org/10.1016/j.physd.2014.04.012 Physica D: Nonlinear Phenomena Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier arXiv |
| spellingShingle | Cousins, William Sapsis, Themistoklis P. Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model |
| title | Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model |
| title_full | Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model |
| title_fullStr | Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model |
| title_full_unstemmed | Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model |
| title_short | Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model |
| title_sort | quantification and prediction of extreme events in a one dimensional nonlinear dispersive wave model |
| url | http://hdl.handle.net/1721.1/103870 https://orcid.org/0000-0003-0302-0691 https://orcid.org/0000-0001-7552-9062 |
| work_keys_str_mv | AT cousinswilliam quantificationandpredictionofextremeeventsinaonedimensionalnonlineardispersivewavemodel AT sapsisthemistoklisp quantificationandpredictionofextremeeventsinaonedimensionalnonlineardispersivewavemodel |