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A short comment on the effect of a shear layer on nonlinear water waves |
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| Authors: | CANG Jie CHENG Jun & GRIMSHAW Roger School of Naval Architecture Ocean Civil Engineering Shanghai Jiao Tong University Shanghai China |
| Institution: | CANG Jie1,CHENG Jun2 & GRIMSHAW Roger3 1School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China,2Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200072,3Department of Mathematical Sciences,Loughborough University,Loughborough LE11 3TU,UK |
| Abstract: | In this paper we study nonlinear periodic deep water waves propagating on a background shear current,which decays exponentially with depth.We extend the study of Cheng,Cang and Liao(2009) by introducing a second parameter which measures the depth of the shear current.A high-order convergent analytical series solution is obtained by the homotopy analysis method(HAM).A detailed analysis of the impact of the depth parameter is given.We find that increasing this parameter so that the shear current is thinner re... |
| Keywords: | nonlinear water waves wave-current interaction homotopy analysis method |
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