On the Fifth-Order Stokes Solution for Steady Water Waves |
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| Authors: | ZHAO Hong-jun SONG Zhi-yao LI Ling KONG Jun WANG Le-qiang and YANG Jie |
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| Institution: | Key Laboratory of Coastal Disasters and Defence, Ministry of Education; College of Harbor,
Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China;Key Lab of Virtual Geographic Environment under Ministry of Education, Nanjing Normal University,
Nanjing 210023, China;School of Engineering, The University of Queensland, Brisbane St Lucia, QLD 4072, Australia;Key Laboratory of Coastal Disasters and Defence, Ministry of Education; College of Harbor,
Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China;Xiamen Branch of CCCC Third Harbor Consultants Co. Ltd., Xiamen 361005, China;Key Laboratory of Coastal Disasters and Defence, Ministry of Education; College of Harbor,
Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China |
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| Abstract: | This paper presents a universal fifth-order Stokes solution for steady water waves on the basis of potential theory. It uses a global perturbation parameter, considers a depth uniform current, and thus admits the flexibilities on the definition of the perturbation parameter and on the determination of the wave celerity. The universal solution can be extended to that of Chappelear (1961), confirming the correctness for the universal theory. Furthermore, a particular fifth-order solution is obtained where the wave steepness is used as the perturbation parameter. The applicable range of this solution in shallow depth is analyzed. Comparisons with the Fourier approximated results and with the experimental measurements show that the solution is fairly suited to waves with the Ursell number not exceeding 46.7. |
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| Keywords: | steady water waves universal Stokes solution fifth-order global perturbation parameter uniform current wave steepness |
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