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| Titel |
Rogue waves and downshifting in the presence of damping |
| VerfasserIn |
A. Islas, C. M. Schober |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1561-8633
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| Digitales Dokument |
URL |
| Erschienen |
In: Natural Hazards and Earth System Science ; 11, no. 2 ; Nr. 11, no. 2 (2011-02-09), S.383-399 |
| Datensatznummer |
250009154
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| Publikation (Nr.) |
 copernicus.org/nhess-11-383-2011.pdf |
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| Zusammenfassung |
| Recently Gramstad and Trulsen derived a new higher order nonlinear
Schrödinger (HONLS) equation which is Hamiltonian (Gramstad and Trulsen, 2011). We
investigate the effects of dissipation on the development of rogue waves and
downshifting by adding an additonal nonlinear damping term and a uniform
linear damping term to this new HONLS equation. We find irreversible
downshifting occurs when the nonlinear damping is the dominant damping
effect. In particular, when only nonlinear damping is present, permanent
downshifting occurs for all values of the nonlinear damping parameter
β. 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. We examine the generation of rogue waves in the presence of
damping for sea states characterized by JONSWAP spectrum. Using the inverse
spectral theory of the NLS equation, simulations of the NLS and damped HONLS
equations using JONSWAP initial data consistently show that rogue wave events
are well predicted by proximity to homoclinic data, as measured by the
spectral splitting distance δ. We define δcutoff by
requiring that 95% of the rogue waves occur for δ < δcutoff.
We find that 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. As a result
when damping is present the proximity to homoclinic data and instabilities is
more crucial for the development of rogue waves. |
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