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WFU Physics and Mathematics Colloquium

TITLE: The Formation of Rogue Waves in Nonlinear Schroedinger Models

SPEAKER: Professor Annalisa Calini,

Department of Mathematics
College of Charleston, Charleston, SC

TIME: Wednesday October 9, 2013 at 4:00 PM

PLACE: Room 101 Olin Physical Laboratory


Refreshments will be served at 3:30 PM in the Olin Lounge. All interested persons are cordially invited to attend.

ABSTRACT

Rogue or freak waves are giant waves that can appear without warning on the ocean surface in a variety of physical settings. Rogue waves have been observed in both shallow and deep water, with or without strong currents, more frequently than ordinary wave statistics would suggest.

The modeling of rogue wave generation in deep water is based on the classical Benjamin-Feir instability and nonlinear focusing, and is well described by the cubic focusing nonlinear Schroedinger (NLS) equation. After introducing the model, I will describe the family of spatially periodic breathers (homoclinic orbits of unstable NLS Stokes waves), and which amongst them can be regarded as good candidates for physical rogue waves in the light of two criteria: stability under perturbation of initial data, and persistence under perturbations of the NLS model. A linear stability analysis selects breathers of maximal dimension, and persistence under (a particular) perturbation indicates that maximal breathers all whose spatial modes are coalesced are the robust ones. These results suggest that more realistic sea states may be analyzed in terms of proximity to NLS homoclinic data, and may also have practical implications for experimentalists, as they seek to generate robust and reproducible rogue waves in a laboratory setting.

This talk is based on ongoing work with Connie Schober of the University of Central Florida.

Reference:

"Dynamical criteria for rogue waves in nonlinear Schroedinger models", Calini and C. M. Schober, 2012 Nonlinearity 25, R99



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