Numerical Simulations of Water Waves' Modulational Instability Under the Action of Wind and Dissipation

Touboul, Julien; Kharif, Christian

doi:10.5772/48595

Cited by 1 publication

(1 citation statement)

References 35 publications

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“…On one hand, the HOS model did not account for higher order nonlinear terms representing wave-current interactions. On the other hand, it fails to preserve the Hamiltonian structure of the prognostic equations [66], of which the insufficiency is reported for modeling long-time wave propagation [67]. Although it can be improved by employing another version of the HOS suggested by West, et al [68], further investigations are required.…”

Section: Discussionmentioning

confidence: 99%

A fully nonlinear numerical method for modeling wave–current interactions

Wang

Yan

2018

Journal of Computational Physics

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The presence of current in the ocean can significantly modify the characteristics of ocean waves, and it is considered as an important factor responsible for the occurrence of extreme waves, e.g., rogue waves, which are well known as great threats to ocean engineering practices. The magnitude and direction of ocean current normally vary spatially and ocean waves can become very large and steep. Accurate and efficient phase-revolved numerical methods of fully nonlinear wave-current interactions on a large scale in three dimensions (3D) are required to understand their properties, but the existing phase-revolved methods are all based on the assumption of linear or weakly nonlinear interactions. This paper will address the issues and present a fully nonlinear numerical method to model the 3D interactions between waves and varying current on a large scale using a phase-revolved formulation. A new set of equations describing the threedimensional, fully nonlinear interactions between waves and horizontally shearing current is proposed. They are derived by making no assumption on wave steepness or the order of wave-current interaction. The resulting new equations correctly describe the free surface boundary conditions by representing the fully nonlinear wave-current interactions, removing the limitation to the small wave steepness of the existing formulations in literature.On this basis, the recently developed Enhanced Spectral Boundary Integral (short as ESBI) method is further enhanced to be able to model the wave-current interactions using the new equations, by developing the appropriate procedure for dealing with the extra terms related to nonlinear wave-current interactions.The new equations are used as the prognostic equations for updating the free surface in time domain, and a fast converging iterative technique is employed to solve them. The robustness of the newly developed method is demonstrated through comparing with experimental data available in literature and good agreements are observed in the several different cases, including the 3D fully interaction between ocean waves and horizontally varying current. A comparison with a Higher Order Spectrum (HOS) method based on weak-nonlinear formulation of wave-current interaction is also made to confirm larger error does appear if the wave steepness is large. The method presented in the paper can be employed to simulate the real evolution of ocean waves on current in a phase-revolved way to give deep insights to the dynamics of wavecurrent interactions, which may not be done correctly by the existing methods so far.

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Section: Discussionmentioning

confidence: 99%