Nonlinear surface waves interacting with a linear shear current

Document Type

Article

Publication Date

9-1-2009

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. © 2009 IMACS.

Identifier

70349185094 (Scopus)

Publication Title

Mathematics and Computers in Simulation

External Full Text Location

https://doi.org/10.1016/j.matcom.2009.06.021

ISSN

03784754

First Page

29

Last Page

36

Issue

1

Volume

80

Grant

N00014-05-1-0537

Fund Ref

Office of Naval Research

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