Abstract
The glacial trough is a common glacier erosion landscape, which plays an important role in the study of glacier erosion processes. In a sharp contrast with the developing river, which is generally meandering, the developing glacial trough is usually wide and straight. Is the straightness of the glacial trough just the special phenomenon of some areas or a universal feature? What controls the straightness of the glacial trough? Until now, these issues have not been studied yet. In this paper, we conduct systematic numerical models of the glacier erosion and simulate the erosion evolution process of the glacial trough. Numerical simulations show that: (1) while the meandering glacier is eroding deeper to form the U-shaped cross section, the glacier is eroding laterally. The erosion rate of the ice-facing slope is bigger than that of the back-slope. (2) The smaller (bigger) the slope is, the smaller (bigger) the glacier erosion intensity is. (3) The smaller (bigger) the ice discharge is, the smaller (bigger) the glacier erosion intensity is. In the glacier erosion process, the erosion rate of the ice-facing slope is always greater than that of the back-slope. Therefore, the glacial trough always develops into more straight form. This paper comes to the conclusion that the shape evolution of the glacial trough is controlled mainly by the erosion mechanism of the glacier. Thereby, the glacial trough prefers straight geometry.
Similar content being viewed by others
References
Aniya M, Welch R. 1981. Morphological analyses of glacial valleys and estimates of sediment thickness on the valley floor: Victoria Valley system, Antarctica. Antarct Rec, 71: 76–95
Bathe K J. 1982. Finite Element Procedures in Engineering Analysis. Englewood Cliffs: Prentice-Hall. 728
Benn D, Evans D J. 2010. Glaciers and Glaciation. 2nd ed. NewYork: Routledge. 802
Benzi M, Golub G H, Liesen J. 2005. Numerical solution of saddle point problems. Acta Numer, 14: 1–137
Budd W F, Keage P L, Blundy N A. 1979. Empirical studies of ice sliding. J Glaciol, 23: 157–170
Burden R L, Faires J D. 2011. Numerical Analysis. 9th ed. Boston: Brooks/Cole. 893
Cuffey K M, Paterson W S B. 2010. The Physics of Glaciers. 4th ed. Builington: Butterworth-Heinemann. 693
Cuvelier C, Segal A, Van Steenhoven A A. 1986. Finite Element Methods and Navier-Stokes Equations. Dordrecht: D. Reidel Publishing Company. 483
Dabrowski M, Krotkiewski M, Schmid D. 2008. MILAMIN: MATLAB-based finite element method solver for large problems. Geochem Geophys Geosyst, 9: 1–24tiFinite Element Method. United States: John Wiley & Sons. 600
Donea J, Huerta A. 2003. Finite Element Methods for Flow Problems. New York: John Wiley & Sons. 358
Drewry D. 1986. Glacial Geologic Processes. London: Edward Arnold Baltimore. 276
Fowler A. 2011. Mathematical Geoscience. London: Springer. 902
Frank H N. 1987. Basal hydrology of a surge-type glacier: Observations and theory relating to Variegated Glacier. Ph.D Thesis. Seattle: University of Washington. 227
Gagliardini O, Cohen D, Råback P, et al. 2007. Finite-element modeling of subglacial cavities and related friction law. J Geophys Res-Earth Surface. 112: F02027
Glowinski R. 2003. Finite element methods for incompressible viscous flow. In: Ciarlet P G, Lions J L, eds. Handbook of Numerical Analysis. Amsterdam: Elsevier. 9. 3–1176
Graf W L. 1970. The geomorphology of the glacial valley cross-section. Arct Antarct Alp Res, 2: 303–312
Gunzburger M D. 1989. Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice, and Algorithms. Boston: Academic Press. 269
Hallet B. 1979. A theoretical model of glacial abrasion. J Glaciol, 23: 39–50
Harbor J M. 1992. Numerical modeling of the development of U-shaped valleys by glacial erosion. Geol Soc Am Bull, 104: 1364–1375
Hughes T J. 2000. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. NewYork: Dover Publications. 876
Hughes T J, Liu W K, Brooks A. 1979. Finite element analysis of incompressible viscous flows by the penalty function formulation. J Comput Phys, 30: 1–60
Ismail-Zadeh A, Tackley P. 2010. Computational Methods for Geodynamics. Cambridge: Cambridge University Press. 347
Jiang H J, Li C G, Zhang Y F, et al. 2013. Meander characteristics of the Jialing River’s old channels. Earth Sci, 38: 417–422
Karato S I. 2008. Deformation of Earth Materials: An Introduction to the Rheology of Solid Earth. Cambridge: Cambridge University Press. 484
Li Z H, Di Leo J F, Ribe N M. 2014. Subduction-induced mantle flow, finite strain and seismic anisotropy: Numerical modeling. J Geophys Res Solid Earth, 119: 5052–5076
Li Z H, Liu M Q, Gerya T. 2015. Material transportation and fluid-melt activity in the subduction channel: numerical modeling. Sci China Earth Sci, 58: 1251–1268
Li Y K, Liu G N. 2000. The cross-section variatioin of glacial valley and its reflection to the glaciation. Acta Geogr Sin, 55: 235–242
Li Y K, Liu G N, Cui Z J. 1999. The morphological character and paleo-climate indication of the cross section of glacial valleys. J Basic Sci Eng, 7: 163–170
Liu G N. 1989. Research on glacial erosional landforms: Case study of Luojishan Mt. Western Sichuan. J Glaciol Geocryol, 11: 249–260
Lliboutry L. 1968. General theory of subglacial cavitation and sliding of temperate glaciers. J Glaciol, 7: 21–58
Lliboutry L. 1979. Local friction laws for glaciers: A critical review and new openings. J Glaciol, 23: 67–95
Lutgens F K, Tarbuck E J. 2012. Essentials of Geology. 11th ed. Englewood Cliffs: Prentice Hall. 554
MacGregor K R, Anderson R S, Anderson S P, et al. 2000. Numerical simulations of glacial-valley longitudinal profile evolution. Geology, 28: 1031–1034
McGee W J. 1883. Glacial canons. J Geol, 2: 365–382
Raymond C F. 1971. Flow in a transverse section of Athabasca Glacier, Alberta, Canada. J Glaciol, 10: 55–84
Reddy J. 1982. On penalty function methods in the finite element analysis of flow problems. Int J Numer Methods Fluids, 2: 151–171
Schmalholz S M, Schmid D W, Fletcher R C. 2008. Evolution of pinch-and-swell structures in a power-law layer. J Struct Geol, 30: 649–663
Seddik H, Greve R, Sugiyama S, et al. 2009. Numerical simulation of the evolution of glacial valley cross sections. arXiv. 0901.1177. 1–14
Shewchuk J R. 2002. Delaunay refinement algorithms for triangular mesh generation. Comput Geom, 22: 21–74
Sugden D E. 1974. Landscapes of glacial erosion in Greenland and their relationship to ice, topographic and bedrock conditions. Prog Geomorphol, 7: 177–195
Sugden D E, John B S. 1976. Glaciers and Landscape. London: Edward Arnold. 376
Svensson H. 1959. Is the cross-section of a glacial valley a parabola? J Glaciol, 3: 362–363
Swift D A, Persano C, Stuart F M, et al. 2008. A reassessment of the role of ice sheet glaciation in the long-term evolution of the East Greenland fjord region. Geomorphology, 97: 109–125
Thieulot C. 2011. FANTOM: Two- and three-dimensional numerical modelling of creeping flows for the solution of geological problems. Phys Earth Planet Inter, 188: 47–68
Weertman J. 1964. The theory of glacier sliding. J Glaciol, 5: 287–303
Yu W C. 2006. Preliminary study on forming condition of lower Jingjiang meandering channels of middle Yangtze River. J Yangtze River Sci Res Inst, 23: 9–13
Zhang B, Ai N S, Huang Z W, et al. 2007. Meanders of the Jialing River in China: Morphology and formation. Chin Sci Bull, 53: 267–281
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yang, S., Shi, Y. Three-dimensional numerical simulation of glacial trough forming process. Sci. China Earth Sci. 58, 1656–1668 (2015). https://doi.org/10.1007/s11430-015-5120-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11430-015-5120-8