Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model
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Sapsis_Quantification and.pdf
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2.37 MB
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a14ccf459106d1f0613e3d85167ed807
Author(s)
Cousins, William
Sapsis, Themistoklis P.
Date Issued
May 2014
Journal
Physica D: Nonlinear Phenomena
Publisher
Elsevier
Citation
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.
Version
Original manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/j.physd.2014.04.012
