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Sediment Transport in Alluvial Systems

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

Abstract

Sediment transport arises in alluvial lake-river systems in two different forms: (i) as bed load, comprising the moving detritus of the river bed and of the shallow, often only near-shore regions, and (ii) the suspended sediment load of the finer fractions. In river hydraulics the latter are often neglected; so, the bed load transport is treated without back-coupling with the wash-load. This is justified on decadal time scales. In the deeper parts of lakes wind-induced shearing in the benthic boundary layer hardly mobilizes the bed material, which stays immobile for most time and may be set in motion only interruptedly. However, the particle laden fluid transports the suspended material, which is advected and may on longer time scales settle in deposition-prone regions. In general, the deposition to and erosion from the basal surface occur concurrently. This environmental interplay is studied in this article. The slurry—a mixture of the bearer fluid and particles of various sizes—is treated as a mixture of class I, in which mass, momentum and energy balances for the mixture as a whole are formulated to describe the geophysical fluid mechanical setting, whilst the suspended solid particles move through the bearer medium by diffusion. The governing equations of this problem are formulated, at first for a compressible, better non-density preserving, mixture. They thus embrace barotropic and baroclinic processes. These equations, generally known as Navier–Stokes–Fourier–Fick (NSFF) fluids, are subjected to turbulent filter operations and complemented by zeroth and first order closure schemes . Moreover, simplified versions, e.g. the (generalized) Boussinesq, shallow water and hydrostatic pressure assumptions are systematically derived and the corresponding equations presented in both conservative and non-conservative forms. Beyond the usual constitutive postulates of NSFF-fluids and turbulent closure schemes the non-buoyant suspended particles give rise to settling velocities; these depend on the particle size, expressed by a nominal particle diameter. A review of the recent hydraulic literature of terminal settling velocities is given. It shows that the settling velocity depends on the particle diameter and on the particle Reynolds number. A separate section is devoted to the kinematic and dynamic boundary conditions on material and non-material singular surfaces as preparation for the mathematical-physical description of the sediment transport model, which follows from an analysis of jump transition conditions at the bed. The simplest description of bed load transport does not use the concept of the motion of a thin layer of sediments. It treats it as a singular surface, which is equipped with surface grains of various grain size diameters. Such a simplified theoretical level is also used in this chapter; it implies that solid mass exchange, as erosion and deposition of different particle size fractions, is the only physical quantity relevant in the description of the sediment transport. It entails formulation of surface mass balances of an infinitely thin detritus layer for the sediment and surface momentum balance of the mixture. The deposition rate of the various grain fractions, expressed as grain classes, follows from a parameterization of the free fall velocity of isolated particles in still water, but is in general coupled with the local flow and then follows from the solution of the hydrodynamic equations and the processes at the basal surface. The erosion rate is governed by two statements, (a) a fracture criterion determining the threshold value of a stress tensor invariant at the basal surface, which separates existence and absence regimes of erosion, and (b) determination of the amount of erosion beyond the threshold value of the mentioned stress invariant.

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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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