Here we consider a simple weakly nonlinear model that describes the interaction of two-wave systems in deep water with two different directions of propagation. Under the hypothesis that both sea systems are narrow banded, we derive from the Zakharov equation two coupled nonlinear Schro¨dinger equations. Given a single unstable plane wave, here we show that the introduction of a second plane wave, propagating in a different direction, can result in an increase of the instability growth rates and enlargement of the instability region. We discuss these results in the context of the formation of rogue waves.
Modulational instability in crossing sea states: a possible mechanism for the formation of freak waves
ONORATO, Miguel;OSBORNE, Alfred Richard;SERIO, Marina
2006-01-01
Abstract
Here we consider a simple weakly nonlinear model that describes the interaction of two-wave systems in deep water with two different directions of propagation. Under the hypothesis that both sea systems are narrow banded, we derive from the Zakharov equation two coupled nonlinear Schro¨dinger equations. Given a single unstable plane wave, here we show that the introduction of a second plane wave, propagating in a different direction, can result in an increase of the instability growth rates and enlargement of the instability region. We discuss these results in the context of the formation of rogue waves.File in questo prodotto:
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