CMS-Flow:Transport Formula

From CIRPwiki
Revision as of 16:53, 25 January 2011 by Deleted (talk | contribs) (→‎van Rijn)
Jump to navigation Jump to search

Lund-CIRP

Camenen and Larson (2005, 2007, and 2008) developed a general sediment transport formula for bed and suspended load under combined waves and currents.

Bed load

The current-related bed load transport with wave stirring is given by

  (1)

Suspended load

The current-related suspended load transport with wave stirring is given by

  (2)

The reference sediment concentration is obtained from

  (3)

where the coefficient is given by

  (4)

with being the dimensionless grain size and the kinematic viscosity of water.

The sediment mixing coefficient is calculated as

  (5)

van Rijn

  (6)
  (7)


  (7)

Watanabe

The equilibrium total load sediment transport rate of Watanabe (1987) is given by

  (6)

where is the maximum shear stress, is the critical shear stress of incipient motion, and is an empirical coefficient typically ranging from 0.1 to 2.

The critical shear stress is determined using

  (6)

In the case of currents only the bed shear stress is determined as where is the current friction factor. The friction factor is calculated as where is the Nikuradse equivalent sand roughness obtained from .

If waves are present, the maximum bed shear stress is calculated based on Soulsby (1997)

  (6)

where is the mean shear stress by waves and current over a wave cycle, math> \tau_w </math> is the mean wave bed shear stress, and is the angle between the waves and the current. The mean wave and current bed shear stress is

  (6)

The wave bed shear stress is given by where is the wave friction factor, and is the wave orbital velocity amplitude based on the significant wave height.

The wave friction factor is calculated as (Nielsen 1992) where

where is the relative roughness defined as and is semi-orbital excursion .

Soulsby-van Rijn

The equilibrium sediment concentration is calculated as (Soulsby 1997)

  (7)

Symbol Description Units
Bed load transport rate m3/s
Relative density -
Shields parameter due to currents -
Shields parameter due to waves and currents -
Critical shields parameter -
Empirical coefficient -
Empirical coefficient -
Current magnitude m/s

References

  • Camenen, B., and Larson, M. (2005). "A bed load sediment transport formula for the nearshore," Estuarine, Coastal and Shelf Science, 63, 249-260.
  • Camenen, B., and Larson, M. (2007). "A unified sediment transport formulation for coastal inlet applications", ERDC/CHL-TR-06-7, US Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, Vicksburg, MS.
  • Camenen, B., and Larson, M., (2008). "A General Formula for Non-Cohesive Suspended Sediment Transport," Journal of Coastal Research, 24(3), 615-627.
  • Soulsby, D.H. (1997). "Dynamics of marine sands. A manual for practical applications," Thomas Telford Publications, London, England, 249 p.
  • van Rijn, L. C. (1984a). "Sediment transport. Part I: Bed load transport", Journal of Hydraulic Engineering, 110(10), 1431–1456.
  • van Rijn, L. C. (1984b). "Sediment transport. Part II: Suspended loadtransport", Journal of Hydraulic Engineering, 110(11), 1613–1641.
  • van Rijn, L.C., (2007a). "Unified View of Sediment Transport by Currents and Waves. I: Initiation of Motion, Bed Roughness, and Bed-load Transport", Journal of Hydraulic Engineering, 133(6), 649-667.
  • van Rijn, L.C., (2007b). "Unified View of Sediment Transport by Currents and Waves. II: Suspended Transport", Journal of Hydraulic Engineering, 133(6), 668-689.
  • Watanabe, A. (1987). "3-dimensional numerical model of beach evolution," Proceedings Coastal Sediments '87, ASCE, 802-817.

Documentation Portal