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Natural Hazards and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 14, issue 3 | Copyright

Special issue: Extreme seas and ship operations

Nat. Hazards Earth Syst. Sci., 14, 705-711, 2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 27 Mar 2014

Research article | 27 Mar 2014

Modulational instability and wave amplification in finite water depth

L. Fernandez1, M. Onorato2,3, J. Monbaliu1, and A. Toffoli4 L. Fernandez et al.
  • 1Department of Civil Engineering, KU Leuven, Kasteelpark Arenberg 40 box 2448, 3001 Heverlee, Belgium
  • 2Dipartimento di Fisica, Universita' di Torino, Via P. Giuria, Turin, 10125, Italy
  • 3INFN, Sezione di Torino, Via Pietro Giuria 1, 10125 Turin, Italy
  • 4Centre for Ocean Engineering Science and Technology, Swinburne University of Technology, P.O. Box 218, Hawthorn, VIC., 3122, Australia

Abstract. 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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