[Modélisation de l'écoulement des glaciers : comparaison entre l'approximation de la couche mince et les équations de Stokes complètes.]
De nombreuses approches, plus ou moins complexes, sont envisageables pour modéliser l'écoulement des glaciers et des calottes polaires. Parmi ces méthodes, l'approximation de la couche mince (Shallow Ice Approximation, SIA) semble être la plus utilisée, notamment pour sa grande simplicité. La SIA, essentiellement utilisée pour modéliser l'écoulement des calottes polaires, repose sur le faible rapport d'aspect ζ caractéristique de ces objets glaciaires. Pour des objets plus petits, comme les glaciers Alpins, la question de l'applicabilité de la SIA se pose puisque sa validé diminue lorsque ζ augmente. Avec comme objectif de définir le domaine de validité de cette méthode, les résultats de la SIA sont comparés à ceux obtenus en résolvant complètement les équations de Stokes à l'aide d'un code aux éléments finis. A partir de tests bidimensionnels, on montre que la solution donnée par la SIA est plus détériorée lorsque la pente du socle augmente que lorsque l'accumulation augmente, même si une augmentation de l'accumulation conduit à une augmentation de ζ. Par conséquent, lorsque la pente du socle devient importante, c'est elle qui doit être considérée, et non plus le rapport d'aspect, indiquant que la pente est donc le plus sévère des critères de validité de la SIA pour les applications glaciaires. Des simulations tridimensionnelles montrent que la non prise en compte des contraintes de cisaillement longitudinal dans la SIA contribue significativement à la différence avec la solution complète de Stokes.
Several different approaches of various complexities have been used in glacier and ice sheet modelling studies. Amongst them, owing to its simplicity, the Shallow Ice Approximation appears to be the most widely adopted method. This approach, essentially used for ice sheets, owes its success to the shallow aspect of the modelled ice mass embodied in an aspect ratio ζ. When considering smaller ice bodies like alpine-type glaciers, the question arises as to whether the SIA is still valid, given that the method is all the more accurate as ζ is small. In order to test the domain of applicability of the method, results of a SIA finite difference model are compared to those of a finite element model in which the flow equations are fully considered. From a set of two-dimensional flow tests, it is shown that the accuracy of the method is much more deteriorated with increasing bedrock slopes than it is with increasing accumulation rates, even if higher accumulations lead to thicker glaciers with a larger ζ. This leads to the conclusion that when slopes become pronounced, it is a bedrock-related aspect ratio that becomes of relevance such that the bedrock slope should be the most important parameter to consider for assessing the validity of the SIA Method. A 3-dimensional simulation shows that longitudinal shear stresses explain a large part of the misfit between SIA and full-Stokes approaches.
Mot clés : Modélisation de l'écoulement des glaciers, Approximation de la couche mince de glace, Solution de Stokes
Emmanuel Le Meur 1 ; Olivier Gagliardini 1 ; Thomas Zwinger 2 ; Juha Ruokolainen 2
@article{CRPHYS_2004__5_7_709_0,
author = {Emmanuel Le Meur and Olivier Gagliardini and Thomas Zwinger and Juha Ruokolainen},
title = {Glacier flow modelling: a comparison of the {Shallow} {Ice} {Approximation} and the {full-Stokes} solution},
journal = {Comptes Rendus. Physique},
pages = {709--722},
publisher = {Elsevier},
volume = {5},
number = {7},
year = {2004},
doi = {10.1016/j.crhy.2004.10.001},
language = {en},
}
TY - JOUR AU - Emmanuel Le Meur AU - Olivier Gagliardini AU - Thomas Zwinger AU - Juha Ruokolainen TI - Glacier flow modelling: a comparison of the Shallow Ice Approximation and the full-Stokes solution JO - Comptes Rendus. Physique PY - 2004 SP - 709 EP - 722 VL - 5 IS - 7 PB - Elsevier DO - 10.1016/j.crhy.2004.10.001 LA - en ID - CRPHYS_2004__5_7_709_0 ER -
%0 Journal Article %A Emmanuel Le Meur %A Olivier Gagliardini %A Thomas Zwinger %A Juha Ruokolainen %T Glacier flow modelling: a comparison of the Shallow Ice Approximation and the full-Stokes solution %J Comptes Rendus. Physique %D 2004 %P 709-722 %V 5 %N 7 %I Elsevier %R 10.1016/j.crhy.2004.10.001 %G en %F CRPHYS_2004__5_7_709_0
Emmanuel Le Meur; Olivier Gagliardini; Thomas Zwinger; Juha Ruokolainen. Glacier flow modelling: a comparison of the Shallow Ice Approximation and the full-Stokes solution. Comptes Rendus. Physique, Volume 5 (2004) no. 7, pp. 709-722. doi : 10.1016/j.crhy.2004.10.001. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2004.10.001/
[1] Theoretical Glaciology: Material Science of Ice and the Mechanics of Glaciers and Ice Sheets, Reidel, Dordrecht, The Netherlands, 1983 (510 pp)
[2] A two-dimensional shallow ice flow model of glacier de Saint Sorlin, France, J. Glaciology, Volume 49 (2003) no. 167, pp. 527-538
[3] On estimating length fluctuations of glaciers caused by changes in climatic forcing, J. Geophys. Res., Volume 109 (2004) no. F1, p. F01007 | DOI
[4] http://www.csc.fi//elmer (URL)
[5] IPCC: Climate Change 2001, Contribution of working group I to the Third Assessement Report of the Intergovernmental Panel of Climate Change, Cambridge University Press
[6] Meteorological controls on glacier mass balance: empirical relations suggested by measurements on glacier de Sarennes, France, J. Glaciology, Volume 43 (1997) no. 143, pp. 131-137
[7] A continuum-mechanical formulation for shallow polythermal ice sheets, Philos. Trans. Roy. Soc. London A, Volume 355 (1997), pp. 921-974
[8] The creep of polycrystalline ice, Proc. Roy. Soc. London, Ser. A, Volume 228 (1955) no. 1175, pp. 519-538
[9] Asymptotic theories of large-scale motion, temperature, and moisture distribution in land-based polythermal ice sheets: a critical review and new developments, Appl. Mech. Rev., Volume 54 (2001) no. 3, pp. 215-256
[10] Thermo-mechanical balance of ice sheet flows, J. Geophys. Astrophys. Fluid Dyn., Volume 29 (1984), pp. 237-266
[11] The Antarctic ice sheet and environmental changes: a three-dimensional modelling study, Ber Polarforsh, vol. 99, Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany, 1992, p. 241
[12] Virtual bubbles and the Galerkin least squares method, Comput. Methods Appl. Mech. Engrg., Volume 105 (1993), pp. 125-141
[13] Stabilized finite element methods: I. Application to the advective-diffusive model, Comput. Methods Appl. Mech. Engrg., Volume 95 (1992), pp. 253-276
[14] Stabilized finite element methods: II. The incompressible Navier–Stokes equations, Comput. Methods Appl. Mech. Engrg., Volume 99 (1992), pp. 209-233
[15] The Physics of Glaciers, Elsevier, Oxford, 1994 (480 p)
[16] Dynamic behaviour analysis of glacier de Saint Sorlin, France, from 40 years of observations, 1957–97, J. Glaciology, Volume 46 (2000) no. 154, pp. 499-506
[17] Stress-gradient coupling in glacier flow: I. Longitudinal averaging of the influence of ice thickness and surface slope, J. Glaciology, Volume 32 (1986) no. 211, pp. 267-284
[18] Qualitative dynamics of marine ice sheets (W.R. Peltier, ed.), Ice in the Climate System, NATO ASI Ser. I: Global Environmental Change, vol. 12, Springer-Verlag, Berlin, 1993, pp. 67-99
[19] Stability of ice rises and uncoupled marine ice sheets, Ann. Glaciology, Volume 23 (1996), pp. 105-115
[20] Transmission of basal variability to a glacier surface, J. Geophys. Res. Ser. B, Volume 108 (2003) no. 5 (9-1–9-19)
[21] Cemagref, Atlas des glaciers à risques, inventaire et suivi, Publication Cemagref, 1999
Cité par Sources :
Commentaires - Politique