Scattering of flexural-gravity waves due to a crack in a floating ice sheet in a two-layer fluid in the context of blocking dynamics

The influence of wave blocking on the scattering of a flexural-gravity wave by a linear crack in a thin ice cover resting over a two-layer ocean having a rigid flat seafloor is investigated. The wave dispersion curve reveals the existence of multiple propagating wave modes within the blocking frequencies, either in the surface or interface mode. The Sommerfeld radiation condition depends on multiple propagating wave modes within the blocking frequency and contributes to wave energy propagation. The solution process involves the appropriate transition of wave modes within the blocking frequencies, which is obtained with the help of the dispersion curve. The reflection and transmission coefficients are generalized in the case of multiple propagating wave modes, and the associated energy balance relation is derived using Green's integral theorem. The scattering matrix is generated to describe all the possible transmitted and incident wave modes. The role of lateral compressive force and the density ratio on the scattering process, ice deflection, and interface elevation are shown graphically. This study reveals the occurrence of removable and jump discontinuities in the reflection and transmission coefficients at the saddle point as well as blocking frequencies and at the frequency for which incident wave mode changes. Irregular plate deflection and interface elevation patterns are found due to the superposition of multiple propagating wave modes within the primary and secondary blocking frequencies.