Iterative analytical solution for wave reflection by a multi-chamber partially perforated caisson breakwater
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Iterative analytical solution for wave reflection by a multichamber partially perforated caisson breakwater Yang Zhao1, Yong Liu1*, Huajun Li1 1 Institute of Coastal and Ocean Engineering, Ocean University of China, Qingdao 266100, China
Received 28 May 2019; accepted 8 August 2019 © Chinese Society for Oceanography and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract
This study examines wave reflection by a multi-chamber partially perforated caisson breakwater based on potential theory. A quadratic pressure drop boundary condition at perforated walls is adopted, which can well consider the effect of wave height on the wave dissipation by perforated walls. The matched eigenfunction expansions with iterative calculations are applied to develop an analytical solution for the present problem. The convergences of both the iterative calculations and the series solution itself are confirmed to be satisfactory. The calculation results of the present analytical solution are in excellent agreement with the numerical results of a multi-domain boundary element solution. Also, the predictions by the present solution are in reasonable agreement with experimental data in literature. Major factors that affect the reflection coefficient of the perforated caisson breakwater are examined by calculation examples. The analysis results show that the multi-chamber perforated caisson breakwater has a better wave energy dissipation function (lower reflection coefficient) than the single-chamber type over a broad range of wave frequency and may perform better if the perforated walls have larger porosities. When the porosities of the perforated walls decrease along the incident wave direction, the perforated caisson breakwater can achieve a lower reflection coefficient. The present analytical solution is simple and reliable, and it can be used as an efficient tool for analyzing the hydrodynamic performance of perforated breakwaters in preliminary engineering design. Key words: partially perforated caisson, multi-chamber, reflection coefficient, quadratic pressure drop, matched eigenfunction expansions, iterative calculation Citation: Zhao Yang, Liu Yong, Li Huajun. 2020. Iterative analytical solution for wave reflection by a multi-chamber partially perforated caisson breakwater. Acta Oceanologica Sinica, 39(7): 115–126, doi: 10.1007/s13131-020-1622-0
1 Introduction A perforated caisson breakwater with a wave absorbing chamber (Jarlan, 1961) has been often used to dissipate wave energy and reduce the reflection coefficient and wave force of the structure. In order to dissipate more wave energy, multi-chamber perforated caisson breakwaters have been applied in practical engineering (Franco, 1994; Franco et al., 1998; Bergmann and Oumeraci, 2000; Liu et al., 2012). In addition, a partially perforated caisson breakwater (the water depth inside the wave chamber is reduced) with better stability against sliding and overturning has been used instead of a fully perforated caisson breakwater (Liu et al., 2008a, 2009; Huang et a
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