The role of blocking dynamics and current on wave scattering due to finite floating elastic plate

Abstract

The role of wave blocking on flexural gravity wave motion with oblique incidence and current is discussed. The oblique wave incidence due to a finite floating elastic plate is investigated using the eigenfunction expansion method. The role of different wave propagating modes on reflection coefficient is discussed. The reflection and transmission coefficients, the surface elevation, and plate deflection in the presence of current are derived. The effects of flexural rigidity and the uniform current speed on reflection and transmission coefficients are analyzed. The resonating nature of reflection coefficient for some fixed values of plate length is observed. Significant effects of different combinations of wave propagating modes of plate covered regions and open water regions on the reflection and transmission coefficients are observed. The wave energy propagation from reflection coefficient decreases whenever the Froude number increases. It has been found that the amplitude of the plate deflection increases as the value of the Froude number increases. The amplitude and wavelength of the reflection coefficient are higher for the combination of the first propagating mode of the plate covered region and the second propagating mode of the open water region. Moreover, it is found that zero reflection and full transmission occurs periodically. Co-propagating waves are found to transmit more energy while counter-propagating waves reflect more energy. Higher values of flexural rigidity result in reduced wave energy transmission.