Rogue waves, dissipation, and downshifting
Abbreviated Journal Title
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
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.
Physica D-Nonlinear Phenomena
"Rogue waves, dissipation, and downshifting" (2011). Faculty Bibliography 2010s. 1421.