Three-Dimensional Creeping Flow—Systematic Derivation of the Shallow Flow Approximations

  • Kolumban HutterEmail author
  • Yongqi Wang
Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM)


This chapter is devoted to the approximate determination of the velocity field in a shallow layer of ice or granular soil, treated as a non-Newtonian material flowing under the action of its own weight and assuming its velocity to be so small that Stokes flow can be assumed. Two limiting cases can be analyzed: (i) The deforming material flows on a steep slope (which is the case for creeping landslides or snow deposits on mountain topographies with inclination angles that are large). (ii) In the second case the inclination angles are small. Situation (ii) is apt to ice flow in large ice sheets such as Greenland and Antarctica, important in climate scenarios in a warming atmosphere. The two situations require different approximations. Perturbation schemes are derived in terms of a shallowness parameter in the two situations; applications are discussed under real world conditions. Applications focus on thermo-mechanical coupled plane ice sheet flows and to the Greenland ice sheet response to present day climate driving. In shallow, but still slow gravity driven free surface flows the acceleration terms in Newton’s law are no longer negligible.


Viscous material spreading Thermo-mechanical coupling Stokes approximation Free surface shallow creeping flows Inclined and horizontal gravity driven creep flow. 


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.c/o Versuchsanstalt für Wasserbau, Hydrologie und GlaziologieETH ZürichZürichSwitzerland
  2. 2.Department of Mechanical EngineeringTechnische Universität DarmstadtDarmstadtGermany

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