Analytical determination of the reflection coefficient by the evanescent modes model during the wave–current–horizontal plate interaction

Our work presents an analytical study of the determination of the reflection coefficient during the interaction between the regular wave current and a horizontal plate. This study was done using the linearized potential flow theory with the evanescent modes model, while searching for complex solutions to the dispersion equation that are neither real pure nor imaginary pure. To validate the established model, it has been confronted with the experimental results of V. Rey and J. Touboul, in a first phase, and then compared to those of the numerical study by H.-X. Lin et al. Then, this model was used to study the effect of current on the reflection coefficient.