A transit through the trapping and blocking of flexural-gravity wave: Impact of two-dimensional current and in-plane compression

The combined effect of two-dimensional ocean current and compression on flexural-gravity waves trapping and blocking is investigated under the oblique incidence of the propagating mode on the floating ice sheet. The submerged horizontal cylinder has been considered to analyze the existence of trapped modes. The multipole expansion method has been used by modifying the multipoles to match the upper surface condition, including current magnitudes along the x- and y-directions. This method gives rise to a coupled system of equations having singular coefficients, which makes the problem more challenging. The occurrence of the trapped waves depends on the nature of the current, the angle of the incident wave, and the compressive force acting on the ice sheet. It has been observed that there exists a critical range of compressive force in which trapped modes show their existence, even when both the components of the current are acting in the positive direction. When the trapped mode frequency approaches the blocking frequency, a jump in the trapped wavenumber occurs due to the existence of multiple propagating modes at blocking frequency. Thus, the occurrence of frequency band of wave blocking results in a quantitative measure of trapped wave frequency under the assumption of a single propagating mode. Such a frequency band of wave blocking is shown under different choices of current type. A modified theory based on multipole expansion method that could cater to the multiple propagating modes will be required in future to obtain trapped modes within the frequency band of wave blocking.