Atmosphere Ocean Science Colloquium

Quantification and Prediction of Rare Events in Nonlinear Waves

Speaker: Themistoklis Sapsis

Location: Warren Weaver Hall 1302

Date: Wednesday, October 8, 2014, 3:30 p.m.


The scope of this work is the quantification and prediction of rare events characterized by extreme intensity, in nonlinear dispersive models that simulate water waves. In particular we are interested for the understanding and the short-term prediction of rogue waves in the ocean and to this end, we consider 1-dimensional nonlinear dispersive models and in particular the Majda-McLaughlin-Tabak MMT model and the Modified Nonlinear Schrodinger (MNLS) model, which have regimes with extreme localized events. 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 wave numbers by means of the Gabor transform. A stochastic 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 Gabor coefficients) where a critical energy can trigger the formation of an extreme event. The unstable character of these critical localized modes is analyzed directly through the system equation by formulating a reduced order model over an appropriate space of functions. These unstable modes are randomly triggered through the dispersive "heat bath'' of random waves that propagate in the nonlinear medium. Using these properties we formulate low-dimensional functional of these Gabor coefficients that allow for the prediction of extreme events well before the strongly nonlinear interactions begin to occur. The prediction window is further enhanced by the combination of the developed scheme with traditional filtering schemes with traditional filtering schemes.