Elastohydrodynamic response of an ice sheet to forced sub-surface uplift

Abstract T he objective of this study is to investigate the dynamic response of an ice sheet under transient subsurface uplift. The ice sheet is modeled as an infinite thin plate undergoing small deflections that is pushed vertically upwards by a rigid flat-ended cylinder ; the water underneath the ice sheet is modeled using incompressible potential flow theory. Ultimately, the deflection of the ice sheet is expressed in terms of an integral of the unknown indentation force. For a given motion of the cylinder, the corresponding indentation force must be determined by solving a Volterra integral equation of the first kind. After some numerical experimentation, it proved advantageous to transform the governing equation into an integro-difierential equation. Once the indentation force is obtained, the other physical quantities of interest — the temporal and spatial distributions of the displacement, moment, shear, the buoyant force, the inertial force of the water underneath the ice sheet and the inertial force of the ice sheet — can be evaluated numerically. The results reveal that the inclusion of the hydrodynamic reaction is of major importance.