Oblique wave-current with a semi-infinite compressed ice sheet integrated with a rigid vertical barrier and wave blocking

This paper develops a mathematical model to investigate the coupling between oblique waves and currents interacting with a half-infinite, floating ice sheet subjected to compressional forces in proximity to a vertical, solid impermeable wall, utilising linear hydrodynamic theory. The floating ice sheet is modelled based on the thin elastic plate theory. The rigid, non-porous vertical barrier can either vibrate harmonically with a uniform lateral motion, inducing flexural gravity waves in the presence of a flowing current, or remain stationary, effectively analogous to the behaviour of a vertically oriented, harmonically oscillating wavemaker plane. The constant parameters in the Fourier series representation of the potential fields are derived from relationships that describe the higher-order mode-coupling condition. The convergence of the solution is demonstrated, and the current result is verified against existing literature. A comprehensive analysis investigates how the ice sheet's angle of attack, the velocity of the surrounding water, compressive forces, and its dimensions affect its behaviour. Further, the wave blocking in the presence of compressive force against an opposing current is analysed via group and phase velocities from the dispersion relation. These outcomes include the resulting strain and displacement of the ice, the amplitude of the waves reflected, and the magnitude of the horizontal force exerted on a vertical, unyielding barrier.