Rogue waves, dissipation, and downshifting

    Authors

    A. Islas;C. M. Schober

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    Physica D

    Keywords

    Rogue waves; Freak waves; Downshifting; Nonlinear damping; Nonlinear; Schrodinger equation; Dysthe equation; NONLINEAR SCHRODINGER-EQUATION; DEEP-WATER WAVES; SURFACE GRAVITY-WAVES; FREQUENCY DOWNSHIFT; MODULATIONAL INSTABILITY; FREAK WAVES; EVOLUTION; WIND; MECHANISM; DYNAMICS; Mathematics, Applied; Physics, Multidisciplinary; Physics, Mathematical

    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 delta. The cut off distance delta(cutoff) 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. (C) 2011 Elsevier B.V. All rights reserved.

    Journal Title

    Physica D-Nonlinear Phenomena

    Volume

    240

    Issue/Number

    12

    Publication Date

    1-1-2011

    Document Type

    Article

    Language

    English

    First Page

    1041

    Last Page

    1054

    WOS Identifier

    WOS:000292807600007

    ISSN

    0167-2789

    Share

    COinS