Closed-form solutions for wave reflection and transmission by vertical slotted barrier

In this paper, we introduce the closed-form solution developed by Kim in 1998 for calculating the reflection and transmission coefficients of a vertical slotted barrier, which is not well known because it is presented in his thesis. It is then compared with other closed-form solutions developed by different authors. It is shown that all the solutions give a wrong result for long waves, i.e., large reflection and small transmission. It is also shown that the inertia term is important for intermediate-depth and deep water waves so that the solution including the inertial effect gives better prediction than those neglecting the inertial effect. The accuracy of the existing closed-form solutions is not satisfactory, even though they have been developed based on fundamental fluid mechanics principles. We propose a hybrid solution several parameters of which are based on empirical formulas. The hybrid solution better predicts the reflection and transmission coefficients than the existing solutions. Moreover, it gives a correct result, i.e., small reflection and large transmission, for long waves.