Ocean Surface Gravity Wave Excitation of Flexural-Gravity and Longitudinal Waves in Ice Shelves

Ice shelf stability and strength play an important role in understanding and predicting sea-level rise. Ice shelves restrain ice sheets; as ice shelves collapse, ice streams accelerate, allowing ice to flow directly into the ocean (Pritchard et al., 2012). Melting and thinning weakens ice shelves, arguably making them susceptible to catastrophic break-ups in response to some external perturbation. The break-up of Larsen B in 2002 and Wilkins in 2008 may have been triggered by storm-driven ocean swells (Bromirski et. al, 2010; Massom et. al, 2018). These observations have prompted research to examine how incident ocean waves convert to flexural-gravity and longitudinal waves in the ice shelves and to quantify the tensile stresses carried by those waves. While most models of the wave response of ice shelves have focused exclusively on the flexural response, data from the Ross Ice Shelf shows longitudinal waves of comparable or even larger amplitude. Our objective is to model the full-wave response of ice shelves, including ocean compressibility, ice elasticity, and gravity. Our model is a 2D vertical cross-section of the ice shelf and sub-shelf ocean cavity. The ice and ocean obey the elastic and acoustic wave equations, respectively, and gravity is added using an extension of the fully coupled method introduced by Lotto & Dunham (2015). This allows us to capture all wave modes, in contrast to models based on the shallow water and/or plate approximations that are restricted to the fundamental modes of the system. The ice shelf is forced by an incident surface gravity wave in the open water. We vary ice thickness, ocean depth, and the period of the incident ocean wave and quantify the relative excitation of flexural and longitudinal waves. We anticipate this work to extend the existing understanding of reflection/transmission coefficients of surface gravity waves incident on ice shelves that have largely been conducted using a plate model for the ice shelf and shallow water model for the ocean. This 2D model could be extended to 3D or used to justify depth-integrated models that could be solved in 2D map view to capture the geometric complexity of real ice shelves.