Flexural-gravity wave scattering due to a crack in a floating ice sheet in the perspective of wave blocking in a three-layer fluid

Abstract

Flexural-gravity wave blocking is demonstrated in a three-layer fluid having a floating ice-covered surface in the water of finite depth. The study reveals that wave blocking occurs for higher values of compressive force in either of the modes, which depends on the density ratio and the wave frequency. Two (three) roots of the dispersion relation coalesce at the blocking (saddle) frequencies. Further, within the blocking frequencies, the dispersion relation possesses five propagating wave modes, of which three are affiliated with the layer where blocking occurs, whilst the other two modes are connected with the wave motion propagating in the respective layers. Dead water analogue is established due to the propagation of internal waves along the interface when the thickness of an individual layer is either thin or the density of two consecutive layers is close to each other. Subsequently, the role of blocking dynamics on the flexural-gravity wave scattering by a linear crack in an ice sheet floating in a three-layer fluid is studied. The canonical energy balance relation is generalized to account for multiple propagating wave modes. The velocity potentials are expanded in terms of a scattering matrix to account for the multiple incidents and scattered wave modes within the blocking frequencies. The study depicts the occurrence of removable/jump discontinuities in the scattering coefficients, both at the points where blocking/mode conversion takes place. Irregularities in the ice sheet's deflection and interface elevations are due to the superposition of multiple propagating wave modes within the blocking frequencies.