Time-domain analysis of an ice shelf in a bounded domain

A time-domain model of an ice shelf interacting with ocean water in a finite domain is developed, which combines Kirchhoff–Love plate theory with the shallow-water wave equations. In particular, the domain is divided into an open-water region and a region in which the ocean is covered by an ice shelf. Boundary conditions, together with continuity conditions at the ice–water interface, lead to a nonlinear matrix eigenvalue problem, which is solved numerically to obtain the natural modes and frequencies of the system. These form the basis for reconstructing the transient response to wave forcing using a spectral method. Simulations show how wave packets excite multiple modes and generate interference patterns through boundary reflections. Since the method solves the initial value problem in a geometry containing both an open-ocean region and an ice-shelf-covered region, it provides a foundation for simulating sequential break-up of ice shelves due to wave-induced mechanical stresses, and contributes to broader efforts to model ice shelf disintegration under ocean forcing.