Graduate School in Nonlinear Science
MIDIT OFD CATS
Modelling, Nonlinear Dynamics Optics and Fluid Dynamics Chaos and Turbulence Studies
and Irreversible Thermodynamics Risø National Laboratory Niels Bohr Institute and
Technical University of Denmark Building 128 Department of Chemistry
Building 321 P.O. Box 49 University of Copenhagen
DK-2800 Lyngby DK-4000 Roskilde DK-2100 Copenhagen Ø
Denmark Denmark Denmark
HOMOCLINIC CHAOS INCREASES THE LIKELIHOOD OF ROGUE WAVE FORMATION
by Annalisa Calini
Department of Mathematics,
College of Charleston
Charleston SC, USA
MIDIT-seminar 507
Thursday, May 30, 2002, 16.00 h
at IMM, Bldg. 305, Room 130, DTU
Abstract:
In this work with C. Schober (ODU), we numerically investigate dispersive
perturbations of the nonlinear Schroedinger (NLS) equation, which model
waves in deep water. We observe that a chaotic regime greatly increases
the likelihood of rogue wave formation.
These large amplitude waves are well modeled by higher order homoclinic
solutions of the NLS equation for which the spatial excitations have
coalesced to produce a wave of maximal amplitude.
A Melnikov analysis of the conditions for the onset of chaos identifies
the observed maximal amplitude homoclinic solutions as the persistent
hyperbolic structures throughout the perturbed dynamics.