CMS-Flow:Variable D50

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The standard sediment transport model in CMS is a single-size sediment transport model. This means that only one grain size can be simulated (one transport equation). In many cases the bed material is dominated by a single sediment size with patches of other sediment sizes or materials (e.g. shell hash), which do not contribute significantly to morphology change at specific regions, but do modify the sediment transport through hiding and exposure. In CMS, the spatially variable D50 dataset is used in calculating a hiding and exposure correction to the critical bed shear stress. By assuming that the spatial distribution of the bed material composition is constant in time, the hiding and exposure can be included in a single-sized sediment transport model (Sanchez and Wu 2011). CMS V4.0 has the option to simulate multiple-sized (noncohesive) sediment transport in which the D50 dataset can be used to construct an initial bed grain size distribution at every cell and bed layer. For more information on using the multiple-sized sediment transport option in CMS click here.

Hiding and Exposure Correction

The correction function for the critical shields parameter is defined as

   \theta_{ck} = \xi_k \theta_{c50} (1)

where  \xi_k is the dimensionless hiding and exposure function, \theta_{c50} is the critical Shields parameter of the median sediment grain size d_{50} and \theta_{ck} is the critical Shields parameter for the transport grain size d_{k}. In CMS a formula similar to that of Parker et al. (1982) and others is used given by

   \xi_k = (d_k/d_{50})^{-m} (2)

where m is an empirical hiding and exposure coefficient. The transport grain size is the grain size which is transported and solved in by the advection diffussion equation. The sediment fall velocity is calculated with the transport grain while the skin friction and critical bed shear stress are calculated with d_{50}.


  • Parker, G., Klingeman, P.C., and McLean, D.G. (1982). "Bed load and size distribution in paved gravel-bed streams", Journal of the Hydraulic Division, 108(4), 544-571.
  • Sánchez, A., and Wu, W. (2011). "A Non-equilibrium Sediment Transport Model for Coastal Inlet Applications", Journal of Coastal Research, [In Press] PDF

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