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Modeling of ocean wave periodical impact to across the crevasse-ridden ice shelf: focus on the comparison of two models
  • Yuri Konovalov
Yuri Konovalov
ORCID: orcid.org/0000-0002-8469-9706

Corresponding Author:yu-v-k@yandex.ru

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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.