Journal article
Shoaling of sixth-order stokes waves on a current
Jonsson and Arneborg (Jonsson, I.G., Arneborg, L., 1995. Energy properties and shoaling of higher-order Stokes waves on a current. Ocean Engng 22, 819-857.) combined energy flux and set-down to make shoaling predictions for fourth-order Stokes waves with and without a net volume flux. With basis in their expressions, sixth-order expressions are derived and combined to make shoaling predictions correct to sixth order with an arbitrary net volume flux.
The new sixth-order results are compared with the fourth-order results and the practically exact results obtained by Sobey and Bando (Sobey R.J., Bando K., 1991. Variations on higher-order shoaling. J. Waterway, Port, Coastal Ocean Engng ASCE 117, 348-368) with a Fourier 18 model. The effects of introducing sixth-order theory rather than the fourth-order theory in shoaling calculations are in general found to be small.
As expected the deviations increase with increasing wave-steepness, decreasing depth and opposing currents. Also as expected, the results obtained with the sixth-order expressions improve the results obtained with the fourth-order expressions when compared to the results of Sobey and Bando. As novelties, some considerations regarding the consistency of odd- and even-order shoaling calculations, and the magnitude of the bottom slope, are presented.
Furthermore a comparison between the wave-induced current and the total current is given. © 2000 Published by Elsevier Science Ltd.
Language: | English |
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Year: | 2001 |
Pages: | 667-687 |
ISSN: | 18735258 and 00298018 |
Types: | Journal article |
DOI: | 10.1016/S0029-8018(00)00017-2 |
ORCIDs: | Bredmose, Henrik |