A new method for fast calculation of steady periodic water waves

Zhang Yang

doi:10.12284/hyxb2024109

Volume 46 Issue 10

Oct. 2024

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Zhang Yang. A new method for fast calculation of steady periodic water waves[J]. Haiyang Xuebao，2024, 46(10)：88–97 doi: 10.12284/hyxb2024109

Citation:

Zhang Yang. A new method for fast calculation of steady periodic water waves[J]. Haiyang Xuebao，2024, 46(10)：88–97 doi: 10.12284/hyxb2024109

Citation:

Zhang Yang. A new method for fast calculation of steady periodic water waves[J]. Haiyang Xuebao，2024, 46(10)：88–97 doi: 10.12284/hyxb2024109

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A new method for fast calculation of steady periodic water waves

doi: 10.12284/hyxb2024109

Zhang Yang

School of Civil Engineering and Architecture, Xiamen University of Technology, Xiamen 361024, China

Received Date: 2024-05-05
Accepted Date: 2024-09-27
Rev Recd Date: 2024-09-20

Available Online: 2024-09-29

Publish Date: 2024-10-30

Abstract

Abstract

A method for the fast calculation of steadily progressing periodic waves by using parameterized expressions is presented. The free surface elevation of steady periodic water waves is approximated by ABR triangular series, and the nonlinear parameter in ABR series is obtained by a numerical calculation of the free surface boundary conditions. The advantage of using ABR series is that it is simple in form and contains only one parameter, so it is convenient to study the relationship between this parameter and wave parameters, and then estimate the wave free surface elevation. For conditions of different wave theories applying (Stokes wave theory and cnoidal wave theory), the results calculated by the new method are compared with the analytical solutions of Stokes wave theory, cnoidal wave theory, and the numerical solutions given by the Fourier method. In addition, the expressions of the nonlinear parameter in the ABR series determined by the wave steepness (in deep water) or the Ursell number (in non-deep water) are given in order to efficiently predict free surface elevations. Finally, the method of calculating time averaged sand transport rates related to wave nonlinearity by using free surface elevation is given for practical engineering applications.
- Steady periodic water wave,
- Fast calculation,
- Ursell number

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References(20)

References

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