Analytic solutions of longitudinal and cross waves in the wave flume with an exponential symmetric shoal

Xie Rong; Xiong Yan; Tong Chaofeng; Wang Gang

doi:10.12284/hyxb2023081

Volume 45 Issue 6

Jun. 2023

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Xie Rong，Xiong Yan，Tong Chaofeng, et al. Analytic solutions of longitudinal and cross waves in the wave flume with an exponential symmetric shoal[J]. Haiyang Xuebao，2023, 45(6)：44–51 doi: 10.12284/hyxb2023081

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Analytic solutions of longitudinal and cross waves in the wave flume with an exponential symmetric shoal

doi: 10.12284/hyxb2023081

Xie Rong^{1, 2
,},
Xiong Yan^{1, 2
,
,},
Tong Chaofeng^{1, 2},
Wang Gang^{1, 2}

1.
Key Laboratory of Coastal Disaster and Defence, Ministry of Education, Hohai University, Nanjing 210098, China
2.
College of Harbour, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China

Received Date: 2022-11-11
Rev Recd Date: 2023-01-12

Available Online: 2023-05-16

Publish Date: 2023-06-30

Abstract

Abstract

The flume experiment is commonly used to investigate the wave propagation deformation and the stability of the breakwater armor block, with the wave elements changing along the longitudinal direction of the flume while remaining unchanged in the cross direction perpendicular to the flume. However, when the wavelength has a certain relationship with the flume width, visible cross fluctuations may occur. In this paper, the analytical expressions of longitudinal wave along the flume direction and cross wave perpendicular to the flume direction on an exponential symmetric shoal are derived respectively based on the linear long wave equation. The longitudinal waves on symmetric exponential topography in the flume can be expressed as the first and second kinds of first order Bessel function, and the complete solution can be obtained by combining with the conditions of free surface and velocity continuity. Cross waves with even symmetric and odd symmetric modes in the flume with an exponential symmetric shoal can be expressed as the first kind of ν order Bessel function. The even symmetric (n, m) mode has n nodal lines along the direction of the flume and 2m nodal lines perpendicular to the direction of the flume; odd symmetric (n, m) mode has n nodal lines along the direction of the flume and 2m−1 nodal lines in the cross direction.
- cross waves,
- analytical theory,
- wave flume,
- exponential terrain

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References(20)

References

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