Nonlinear surface waves interacting with a linear shear current

Wooyoung Choi

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 80, issue 1, 29-36

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.

Keywords: Nonlinear surface waves; Linear shear current; Benjamin-Feir instability (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:80:y:2009:i:1:p:29-36

DOI: 10.1016/j.matcom.2009.06.021

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