In the case of the Lund-CIRP (Camenen and Larson 2005, 2007, 2008) and Watanabe (1987) formulas, the incipient motion is based on the critical Shields parameter and estimated using the formula proposed by Soulsby (1997):
in which the dimensionless grain size (d*) is defined
The critical shear stress for incipient motion is given by
The critical depth-averaged velocity for currents alone (Ucrc) is calculated using the formula proposed by van Rijn (1984 c):
where d50 and d90 are the sediment grain size in meters of 50th and 90th percentiles, respectively. The above criteria are used in the van Rijn (2007 a,b) and Soulsby-van Rijn (Soulsby 1997) transport formulas.
The critical bottom orbital velocity magnitude for waves alone is calculated using the formulation of Komar and Miller (1975):
where Tp is the peak wave period.
- Camenen, B., and M. Larson. 2005. A general formula for non-cohesive bed-load sediment transport. Estuarine, Coastal and Shelf Science (63)2:49–260.
- Camenen, B., and M. Larson. 2007. A unified sediment transport formulation for coastal inlet application. ERDC/CHL CR-07-1. Vicksburg, MS: US Army Engineer Research and Development Center.
- Camenen, B., and M. Larson. 2008. A general formula for noncohesive suspended sediment transport. Journal of Coastal Research 24 (3):615–627.
- Komar, P. D., and M. C. Miller. 1975. On the comparison between the threshold of sediment motion under waves and unidirectional currents with a discussion of the practical evaluation of the threshold. Journal of Sedimentary Petrology (45):362–367.
- Soulsby, R. L. 1997. Dynamics of marine sands. London, England: Thomas Telford Publications.
- van Rijn, L. C. 1984c. Sediment transport, Part III: Bed forms and alluvial roughness. Journal of Hydraulic Engineering, ASCE 110(12):1733–1754.
- Watanabe, A. 1987. 3-dimensional numerical model of beach evolution. In Proceedings, Coastal Sediments ’87, 802–817. New Orleans, LA.