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Earth System Dynamics An interactive open-access journal of the European Geosciences Union

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doi:10.5194/esdd-6-1605-2015
© Author(s) 2015. This work is distributed
under the Creative Commons Attribution 3.0 License.
Review article
07 Sep 2015
Review status
This discussion paper has been under review for the journal Earth System Dynamics (ESD). The revised manuscript was not accepted.
The eigenvalue problem for ice-shelf vibrations: comparison of a full 3-D model with the thin plate approximation
Y. V. Konovalov Department of Mathematics, National Research Nuclear University MEPhI, Kashirskoe Shosse, 31, 115409, Moscow, Russia
Abstract. Ice-shelf forced vibration modelling is performed using a full 3-D finite-difference elastic model, which also takes into account sub-ice seawater flow. The ocean flow in the cavity is described by the wave equation; therefore, ice-shelf flexures result from hydrostatic pressure perturbations in sub-ice seawater layer. Numerical experiments have been carried out for idealized rectangular and trapezoidal ice-shelf geometries. The ice-plate vibrations are modelled for harmonic ingoing pressure perturbations and for high-frequency spectra of the ocean swells. The spectra show distinct resonance peaks, which demonstrate the ability to model a resonant-like motion in the suitable conditions of forcing. The spectra and ice-shelf deformations obtained by the developed full 3-D model are compared with the spectra and the deformations modelled by the thin-plate Holdsworth and Glynn model (1978). The main resonance peaks and ice-shelf deformations in the corresponding modes, derived by the full 3-D model, are in agreement with the peaks and deformations obtained by the Holdsworth and Glynn model. The relative deviation between the eigenvalues (periodicities) in the two compared models is about 10 %. In addition, the full model allows observation of 3-D effects, for instance, the vertical distribution of the stress components in the plate. In particular, the full model reveals an increase in shear stress, which is neglected in the thin-plate approximation, from the terminus towards the grounding zone with a maximum at the grounding line in the case of the considered high-frequency forcing. Thus, the high-frequency forcing can reinforce the tidal impact on the ice-shelf grounding zone causing an ice fracture therein.

Citation: Konovalov, Y. V.: The eigenvalue problem for ice-shelf vibrations: comparison of a full 3-D model with the thin plate approximation, Earth Syst. Dynam. Discuss., 6, 1605-1633, doi:10.5194/esdd-6-1605-2015, 2015.
Y. V. Konovalov
Y. V. Konovalov

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