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Modulational instability and wave amplification in finite water depth

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posted on 2024-07-09, 15:56 authored by L. Fernandez, M. Onorato, J. Monbaliu, Alessandro Toffoli
The modulational instability of a uniform wave train to side band perturbations is one of the most plausible mechanisms for the generation of rogue waves in deep water. In a condition of finite water depth, however, the interaction with the sea floor generates a wave-induced current that subtracts energy from the wave field and consequently attenuates the instability mechanism. As a result, a plane wave remains stable under the influence of collinear side bands for relative depths kh <= 1.36 (where k is the wavenumber of the plane wave and h is the water depth), but it can still destabilise due to oblique perturbations. Using direct numerical simulations of the Euler equations, it is here demonstrated that oblique side bands are capable of triggering modulational instability and eventually leading to the formation of rogue waves also for kh <= 1.36. Results, nonetheless, indicate that modulational instability cannot sustain a substantial wave growth for kh < 0.8.

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ISSN

1684-9981

Journal title

Natural Hazards and Earth System Sciences

Volume

14

Issue

3

Pagination

6 pp

Publisher

Copernicus

Copyright statement

Copyright © 2014 The authors.

Language

eng

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