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Nonlinear surface waves interacting with a linear shear current

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  • Choi, Wooyoung

Abstract

To describe the evolution of fully nonlinear surface gravity waves in a linear shear current, a closed system of exact evolution equations for the free surface elevation and the free surface velocity potential is derived using a conformal mapping technique. Traveling wave solutions of the system are obtained numerically and it is found that the maximum wave amplitude for a positive shear current is much smaller than that in the absence of any shear while the opposite is true for a negative shear current. The new evolution equations are also solved numerically using a pseudo-spectral method to study the Benjamin–Feir instability of a modulated wave train in both positive and negative shear currents. With a fixed wave slope, compared with the irrotational case, the envelope of the modulated wave train grows faster in a positive shear current and slower in a negative shear current.

Suggested Citation

  • Choi, Wooyoung, 2009. "Nonlinear surface waves interacting with a linear shear current," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(1), pages 29-36.
    • Handle: RePEc:eee:matcom:v:80:y:2009:i:1:p:29-36
    DOI: 10.1016/j.matcom.2009.06.021
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    Cited by:

    1. M. V. Flamarion & E. Kochurin & R. Ribeiro-Jr, 2023. "Fully Nonlinear Evolution of Free-Surface Waves with Constant Vorticity under Horizontal Electric Fields," Mathematics, MDPI, vol. 11(21), pages 1-13, October.
    2. Julien Touboul & Christian Kharif, 2016. "Effect of vorticity on the generation of rogue waves due to dispersive focusing," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 84(2), pages 585-598, November.

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