Rogue waves, dissipation, and downshifting
Abstract
We investigate the effects of dissipation on the development of rogue waves and downshifting by adding nonlinear and linear damping terms to the onedimensional 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 wellpredicted by proximity to homoclinic data, as measured by the spectral splitting distance δ. The cut off distance δ 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.
 Publication:

Physica D Nonlinear Phenomena
 Pub Date:
 June 2011
 DOI:
 10.1016/j.physd.2011.03.002
 Bibcode:
 2011PhyD..240.1041I