Wave reflection by a submerged cycloidal breakwater using the Modified Mild-Slope Equation

In this work, formulas for the reflection and transmission coefficients of one-dimensional linear water waves propagating on a submerged structure with a cycloidal cross section are obtained. In the specialized literature, the previous coefficients have been obtained mainly for the limit of linear long water waves, which is a strong restriction for their application. To avoid this restriction, we obtain an approximate analytical solution, based on a Taylor polynomial, to the Modified Mild-Slope Equation, which models the interactions of a wide range of water waves, from short waves to long waves. The dimensionless governing equation is a function of a kinematical parameter and a geometrical parameter. It is found that for a value of 0.35 of the geometrical parameter, the reflection coefficient tends increase significantly. The results show that as the magnitude of the kinematical parameter increases, the reflection coefficient exhibits oscillatory behaviour and increases in magnitude. In addition, for some discrete values of this parameter, the zero-reflection phenomenon occurs. To validate the present approximate analytical solution, we present a comparison against two analytical solutions obtained with the aid of linear long wave theory, in which it is found that three solutions behave properly.