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

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© 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 is a preprint. It 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.,, 2015.
Y. V. Konovalov
Y. V. Konovalov


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