Abstract
We provide a mechanistic explanation for observed metrics for drumlins, which represent their sizes and shapes. Our explanation is based on a concept of drumlin growth occurring through a process of instability, whereby small amplitude wave forms first grow as ice slides over a bed of deformable sediments, followed by a coarsening process, in which the wavelength as well as the relief of the drumlins continues to grow. The observations then provide inferences about the growth process itself.
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Clark, C.D., Hughes, A.L.C., Greenwood, S.L., Spagnolo, M., Ng, F.S.L.: Size and shape characteristics of drumlins, derived from a large sample, and associated scaling laws. Quat. Sci. Revs. 28, 677–692 (2009)
Chapwanya, M., Clark, C.D., Fowler, A.C.: Numerical computations of a theoretical model of ribbed moraine formation. Earth Surf. Process. Landf. 36, 1105–1112 (2011)
Dunlop, P., Clark, C.D., Hindmarsh, R.C.A.: Bed ribbing instability explanation: testing a numerical model of ribbed moraine formation arising from coupled flow of ice and subglacial sediment. J. Geophys. Res. 113, F03005 (2008). doi:10.1029/2007JF000954
Gardiner, C.: Stochastic methods: a handbook for the natural and social sciences, 4th edn. Springer, Berlin (2009)
Goodwin, I.D.: The nature and origin of a jökulhlaup near Casey Station. Antarct. J. Glaciol. 34, 95–101 (1988)
Hillier, J.K., Smith, M.J., Clark, C.D., Stokes, C.R., Spagnolo, M.: Subglacial bedforms reveal an exponential size-frequency distribution. Geomorphology 190, 82–91 (2013)
King, E.C., Hindmarsh, R.C.A., Stokes, C.R.: Formation of mega-scale glacial lineations observed beneath a West Antarctic ice stream. Nat. Geosci. 2, 585–588 (2009)
Kolmogorov, A.N.: Über das logarithmisch normale Verteilungsgesetz der Dimensionen der Teilchen bei Zerstückelung. Dokl. Akad. Nauk. SSSR 31, 99–101. Translated as “The logarithmically normal law of distribution of dimensions of particles when broken into small parts”, NASA technical translation NASA TT F-12,287, NASA, Washington, DC, June 1969 (1941)
Kondolf, G.M., Adhikari, A.: Weibull vs. lognormal distribution for fluvial gravels. J. Sediment. Res. 70, 456–460 (2000)
Limpert, E., Stahel, W.A., Abbt, M.: Log-normal distributions across the sciences: keys and clues. Bioscience 51, 341–352 (2001)
Smith, A.M., Murray, T., Nicholls, K.W., Makinson, K., Adalgeirsdttir, G., Behar, A.E., Vaughan, D.G.: Rapid erosion, drumlin formation, and changing hydrology beneath an Antarctic ice stream. Geology 35, 127–130 (2007)
Spagnolo, M., Clark, C.D., Hughes, A.L.C.: Drumlin relief. Geomorphology 153–154, 179–191 (2012)
Van Kampen, N., G., : Stochastic processes in physics and chemistry, 3rd edn. North-Holland, Amsterdam (2007)
Wingham, D.J., Siegert, M.J., Shepherd, A., Muir, A.S.: Rapid discharge connects Antarctic subglacial lakes. Nature 440, 1033–1037 (2006)
Acknowledgments
A. C. F. acknowledges the support of the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie) funded by the Science Foundation Ireland grant 12/1A/1683, and we acknowledge the support of NERC grant NE/D013070/1, Testing the instability theory of subglacial bedform production. Thanks also to Bruce Malamud for useful discussions.
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Fowler, A.C., Spagnolo, M., Clark, C.D. et al. On the size and shape of drumlins. Int J Geomath 4, 155–165 (2013). https://doi.org/10.1007/s13137-013-0050-0
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DOI: https://doi.org/10.1007/s13137-013-0050-0