TY - JOUR
T1 - Wave-wave interactions on a sloping bottom
AU - Chen, Yang Yih
AU - Yang, Bin Da
N1 - Funding Information:
The authors acknowledge the support from National Science Council Taiwan , under the Grants NSC99-2221-E-110-087-MY3 and NSC102-2911-I-006-302 . We are especially grateful to Prof. Guan-Yu Chen for polishing the manuscript that helped in improving the presentation of this paper.
Publisher Copyright:
© 2014 Elsevier B.V.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - This study derived an analytic solution for two progressive waves propagating on a sloping bottom. The solution of flow field in explicit form is obtained as a three-parameter function of rendering the two wave ordering parameter ε1,ε2 and the bottom slope perturbed to the third order. The results can be simplified to a single propagating wave on sloping beach and wave-wave interaction in uniform depth. The wave number and angular frequency are related to water depth, bottom slope, and wave steepness and are also affected by another propagating wave, the increasing wave steepness or wave length of which will enhance the influence of the dispersion relation. The solutions include the wave-wave interaction, wave shoaling, nonlinearity, and the effect of bottom slope. Those are observed by means of the discussion of the free-surface displacement. The resonance caused by wave-wave interaction will occur in a specified water depth and the ratio of two wave numbers, leading to the singularity of free-surface displacement.
AB - This study derived an analytic solution for two progressive waves propagating on a sloping bottom. The solution of flow field in explicit form is obtained as a three-parameter function of rendering the two wave ordering parameter ε1,ε2 and the bottom slope perturbed to the third order. The results can be simplified to a single propagating wave on sloping beach and wave-wave interaction in uniform depth. The wave number and angular frequency are related to water depth, bottom slope, and wave steepness and are also affected by another propagating wave, the increasing wave steepness or wave length of which will enhance the influence of the dispersion relation. The solutions include the wave-wave interaction, wave shoaling, nonlinearity, and the effect of bottom slope. Those are observed by means of the discussion of the free-surface displacement. The resonance caused by wave-wave interaction will occur in a specified water depth and the ratio of two wave numbers, leading to the singularity of free-surface displacement.
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U2 - 10.1016/j.coastaleng.2014.10.001
DO - 10.1016/j.coastaleng.2014.10.001
M3 - Article
AN - SCOPUS:84908642295
VL - 95
SP - 84
EP - 93
JO - Coastal Engineering
JF - Coastal Engineering
SN - 0378-3839
ER -