Prograding and Retrograding Hypo- and Hyper-Pycnal Deltaic Formations into Quiescent Ambients

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


Sediment transport from mountainous rivers into a quiescent ambient with simultaneous formation of deltas is reviewed. The focus is restricted to flow in vertical cross-sections with no changes perpendicular to the plane of the flow. The bed load transport in the river is derived for quasi-steady situations using sediment mass balance and the Mohr-Terzaghi shear stress-pressure relation with the angle of internal friction, \(\varphi \), as the essential frictional parameter. The emerging model is a diffusion equation for the upper surface of the moving sediment layer and corresponding boundary conditions. Its diffusivity is expressible in terms of the hydraulic discharge, the densities of the sediment and the turbid water, the angle of internal friction and a parameter characterizing the bed-parallel sediment velocity in terms of the average velocity in the turbid layer. When this river flow enters quiescent water, two different classes of deltas can be formed. When the entering water is either neutrally buoyant or lighter than the ambient water, the sudden reduction in tractive force along the bed generates a conspicuous avalanching flow to depth. This leads to steep-sloped foreset deposits with delta fronts inclined by the angle of internal friction. Such so-called Gilbert-type deltas are governed by a jump requirement of the sediment flux across the shore line and the geometry of the receiving basin. When the inflowing discharge is denser than the receiving ambient water, it will dive down as a turbulent under-current. The basal sediment transport in this subaqueous density current is analogous to the subaerial case and again described by a diffusion equation with similarly determined diffusivity. The combined dual subaerial-subaqueous sedimenting process is mathematically very similar to a (generalized) Stefan problem, e.g. the freezing of an ice cover on a lake. We present (mostly analytical) solutions for (1) bedrock-alluvial transitions, (2) overtopping failure of a dam, (3) topset-foreset diffusion processes for hypo- and hyper-pycnal deltas. Laboratory experiments demonstrate the adequacy of the models.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Kolumban Hutter
    • 1
    Email author
  • Yongqi Wang
    • 2
  • Irina P. Chubarenko
    • 3
  1. 1.c/o Laboratory of Hydraulics, Hydrology and Glaciology at ETHZürichSwitzerland
  2. 2.Chair of Fluid Dynamics, Department of Mechanical EngineeringTU DarmstadtDarmstadtGermany
  3. 3.P.P. Shirshov Institute of OceanologyRussian Academy of SciencesKaliningradRussia

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