Abstract
The kinematic and dynamic of steep two-dimensional focusing wave trains on a shearing flow in deep water are investigated analytically and numerically. In the absence of waves, the vorticity due to the vertical gradient of the horizontal current velocity is assumed constant. A linear kinematic model based on the spatio-temporal evolution of the frequency is derived, predicting the focusing distance and time of a chirped wave packet in the presence of constant vorticity. Furthermore, a linear model, based on a Fourier integral, is used to describe the evolution of the free surface on shearing current. To compute the fully nonlinear evolution of the wave group in the presence of vorticity, a new numerical model, based on a BIEM approach, is developed. On the basis of these different approaches, the role of constant vorticity on rogue wave occurrence is analysed. Two main results are obtained: (1) the linear behaviour expected in the presence of constant vorticity is significantly different from what is commonly expected in the presence of constant current and (2) the nonlinear effects are found to be of significant influence in the case at hand.
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Acknowledgments
This work is the continuation of a long collaboration initiated jointly with Pr. Efim Pelinovsky. The authors are also thankful to the editors for organizing such an issue. The authors would like to thank the French DGA, who supported this work through the ANR Grant ANR-13-ASTR-0007.
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Touboul, J., Kharif, C. Effect of vorticity on the generation of rogue waves due to dispersive focusing. Nat Hazards 84 (Suppl 2), 585–598 (2016). https://doi.org/10.1007/s11069-016-2419-5
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DOI: https://doi.org/10.1007/s11069-016-2419-5