Study on the applicability of a simplified formula of the transmission coefficient of floating breakwater with a rectangular cross-section

Wave attenuation performance of floating breakwater (FB) is an important parameter in its engineering application. The objective of the article is to evaluate the applicability of a simplified formula for estimating the transmission coefficient of the floating breakwater. The simplified formula for the FB with a rectangular cross-section is derived using potential flow theory. The theoretical analytical solution, which is based on a matched eigenfunction expansion method, serves as a useful benchmark against which to verify the accuracy of the simplified formula. The results indicate that the ratio of breakwater width to water depth exerts a substantial influence on the accuracy of the Drimer transmission coefficient simplified formula. When the ratio exceeds or equals 3, the accuracy of the simplified formula closely aligns with that of the analytical solution. Conversely, a significant velocity discrepancy in the beneath area of the FB emerges between the analytical and simplified solutions, leading to a reduction in the accuracy and applicability of the simplified formula. The simplified formula can be modified by defining an equivalent water depth, in which case it agrees well with the analytical solution for a stationary FB. The deviation is slightly larger under only a small number of conditions, with a maximum deviation of 0.11. Nonetheless, the modified simplified formula is not entirely applicable to a moving FB. This article has provided the L / d range of applicability of the modified simplified transmission coefficient formula that meets the required accuracy for the moving state, which can be used to guide the calculation of the transmission coefficient for more complex FB configurations. • Identify that the direct cause of the accuracy deviation Drimer’s formula is the unreasonable simplification method of the velocity potential under the breakwater. • Modify the Drimer's formula, and the precision of the calculated transmission coefficient of the breakwater can be controlled around 0.1. • The research results provide a reliable theoretical analysis formula for the configuration design of marine engineering floating breakwaters and pile-supported breakwaters.