Title

Rogue Waves, Dissipation, And Downshifting

Keywords

Downshifting; Dysthe equation; Freak waves; Nonlinear damping; Nonlinear Schrdinger equation; Rogue waves

Abstract

We investigate the effects of dissipation on the development of rogue waves and downshifting by adding nonlinear and linear damping terms to the one-dimensional Dysthe equation. Significantly, rogue waves do not develop after the downshifting becomes permanent. Thus in our experiments permanent downshifting serves as an indicator that damping is sufficient to prevent the further development of rogue waves. Using the inverse spectral theory of the NLS equation, simulations of the damped Dysthe equation for sea states characterized by JONSWAP spectrum consistently show that rogue wave events are well-predicted by proximity to homoclinic data, as measured by the spectral splitting distance δ. The cut off distance δcutoff decreases as the strength of the damping increases, indicating that for stronger damping the JONSWAP initial data must be closer to homoclinic data for rogue waves to occur. © 2011 Elsevier B.V. All rights reserved.

Publication Date

6-1-2011

Publication Title

Physica D: Nonlinear Phenomena

Volume

240

Issue

12

Number of Pages

1041-1054

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.physd.2011.03.002

Socpus ID

79958209046 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/79958209046

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