Modeling of ocean wave periodical impact to across the crevasse-ridden
ice shelf: focus on the comparison of two models
Abstract
The propagation of high-frequency elastic-flexural waves through an ice
shelf was modeled by a full 3-D elastic models. These models based on
the momentum equations that were written as the well-known differential
equations (model#1) and as the integro-differential equations
(model#2). The integro-differential form implies the vertical
integration of the momentum equations from the ice surface to the
current vertical coordinate z like, for instance, in the Blatter-Pattyn
ice flow model (e.g., Pattyn, 2000). The sea water flow under the ice
shelf is described by the wave equation (Holdsworth and Glynn, 1978).
The numerical solutions were obtained by a finite-difference method.
Numerical experiments were undertaken for a crevasse-ridden ice shelf
(Freed-Brown et al., 2012) with different spatial periodicities of the
crevasses. In this research the modeled positions of the band gaps in
the dispersion spectra are investigated from the point of view of
agreement of these positions with the Bragg’s law. The performed
numerical experiments showed the different response to the periodical
ocean wave impact in the considered models in the context of appearance
of the band gaps in the dispersion spectra. The distinction is in the
threshold value of the crevasses depth, at which the band gaps that
should appear accordingly the Bragg’s law, in fact, arise in the
dispersion spectra obtained by the models (Fig.1). In particular, the
model#2 based on the depth-integrated momentum equations provides the
smaller threshold value, which depends on the spatial periodicity of the
crevasses. References Freed-Brown, J., Amundson, J., MacAyeal, D., &
Zhang, W. Blocking a wave: Frequency band gaps in ice shelves with
periodic crevasses. Annals of Glaciology, 53(60), 85-89.
doi:10.3189/2012AoG60A120, 2012. Holdsworth, G., & Glynn, J.: Iceberg
calving from floating glaciers by a vibrating mechanism. Nature, 274,
464-466, 1978 Konovalov, Y.V.: Ice-shelf vibrations modeled by a full
3-D elastic model. Annals of Glaciology, 60(79) 68-74, doi:
10.1017/aog.2019.9, 2019. Konovalov, Y.V.: Abatement of Ocean-Wave
Impact by Crevasses in an Ice Shelf. J. Mar. Sci. Eng. 9, 46. doi:
10.3390/jmse9010046, 2021. Pattyn F.: Ice-sheet modeling at different
spatial resolutions: focus on the grounding zone, Annals of Glaciology,
31, 211-216, 2000.