TY - JOUR

T1 - Nonlinear surface waves interacting with a linear shear current

AU - Choi, Wooyoung

N1 - Funding Information:
The author gratefully acknowledges support from the US Office of Naval Research through Grant N00014-05-1-0537. The author is grateful to Chin H. Wu for useful discussions.
Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.

PY - 2009/9

Y1 - 2009/9

N2 - 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.

AB - 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.

KW - Benjamin-Feir instability

KW - Linear shear current

KW - Nonlinear surface waves

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U2 - 10.1016/j.matcom.2009.06.021

DO - 10.1016/j.matcom.2009.06.021

M3 - Article

AN - SCOPUS:70349185094

VL - 80

SP - 29

EP - 36

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

SN - 0378-4754

IS - 1

ER -