Abstract
Hydroelastic oscillations of ice shelves, induced by the action of ocean waves, produce deflection and stresses that could potentially lead to calving events. Due to the large horizontal span of several Antarctic ice shelves, like the Ross, Ronne or Larsen C, hydroelastic models for the ice shelf/ice shelf cavity configuration based on long wave approximations can be very effective. Such a model, based on the linearised Shallow Water Equations and the Kirchhoff–Love bending theory for slender plates is considered. For ice shelf modal analysis, in the framework of the specific model, a nonconforming hydroelastic finite element is developed. The new hydroelastic triangle is based on coupling Specht’s plate element with a linear triangle for the velocity potential approximation. It enables explicit computation of the hydroelastic coupling matrix and optimal convergence rates for the eigenpairs. The element efficiency is verified against a semi-analytical solution and the theoretically predicted convergence rates are validated for solutions with sufficient regularity. The SHEEL element (Specht HydroElastic ELement) can be used for cases of variable bathymetry and mild variations of the ice shelf thickness. The same element can be employed for time domain hydroelastic analysis with very slight modifications. A model of the Larsen C ice shelf is considered as a case study.
Highlights
Other phenomena observed in Antarctic regions, like persistent atmospheric waves monitored over the McMurdo station at the vicinity of Ross ice shelf (Chen et al, 2016), might be related to the resonant hydroelastic oscillations of ice shelves as well (Godin and Zabotin, 2016)
The aim of the present study is to introduce a hydroelastic finite element scheme for the coupled problem of a slender plate interacting with long waves
The governing equations are coupled and expressed in terms of the ice shelf deflection and the velocity potential of the water basin defined by the sub ice shelf cavity
Summary
Hydroelastic flexure of ice shelves, caused by the impact of ocean waves, is a challenging wave-solid interaction problem related to the integrity of Antarctic ice shelves, formation of ridges and the potential occurrence of calving events (Massom et al, 2018; Bromirski et al, 2017, 2010; Brunt et al, 2011; Squire et al, 1994; MacAyeal et al, 2006; Bromirski and Stephen, 2012; Banwell et al, 2017; Lescarmontier et al, 2012). Pulses with larger wavelengths propagate further inside the ice shelf/sub ice shelf cavity region and are less influenced by the buffering effect of the Marginal Ice Zone (MIZ) (Zhang et al, 2015; Montiel and Squire, 2017; Squire and Williams, 2008; Meylan et al, 2018) For these reasons, hydroelastic analysis due to the impact of long waves (ranging from tidal waves to long period swells) is important for ice shelf integrity assessment. Studies in two horizontal dimensions include the analytical results in Godin and Zabotin (2016) and a 3D finite element model in COMSOL, regarding the hydroelastic response of the Ross ice shelf, presented recently by Sergienko (2017). The paper concludes with some remarks on the effectiveness of the newly derived hydroelastic finite element and suggestions for future developments regarding its applicability in the analysis of ice shelf vibrations
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
