Impact of sea-bed trench on the deflection of a floating ice sheet due to a moving load

The steady-state response of an ice sheet floating above a trench-shaped sea-bed and subjected to a concentrated load moving at a constant speed is investigated. The fluid domain is divided into three virtual regions corresponding to the geometry of the sea-bed, and the required matching conditions between these regions are provided. To ensure the structural continuity of the ice sheet, conditions on deflection, slope, shear force, and bending moment are imposed at the virtual boundaries on the upper surface, together with appropriate matching conditions at the instantaneous position of the moving load. The dispersion relation of flexural-gravity waves is used to study phase speed and group speed in shallow and deep water regimes, providing insight into their dispersive properties. The ice deflection is described in a piecewise analytical form across various regions by solving the governing equations using standard ordinary differential equation techniques in a moving coordinate framework. The steady-state deflection profile of the ice sheet is then obtained, highlighting the combined influence of the sea-bed geometry, trench depth, and load speed on wave propagation. The results further demonstrate that increasing trench depth leads to a reduction in ice sheet deflection by weakening the ice-water interaction, whereas higher load speeds intensify wave generation and amplify the dynamic response of the ice sheet, particularly within the critical speed range.