CMS-Flow:Incipient Motion: Difference between revisions
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=Incipient Motion= | |||
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): | |||
= | {{Equation|<math> | ||
\Theta_{cr} = \frac{0.3}{1 + 1.2d_*} + 0.055 \left[1 - exp(-0.02d_*) \right] | |||
</math>|1}} | |||
in which the dimensionless grain size (d<sub>*</sub>) is defined | |||
{{Equation|<math> | {{Equation|<math> | ||
U_{crc} = | d_* = d \left[\frac{(s-1)g}{v^2} \right]^{1/3} | ||
</math>|2}} | |||
0.19 | |||
The critical shear stress for incipient motion is given by | |||
</math>| | {{Equation|<math>\frac{\tau_{cr}}{g(\rho_s - \rho)d} = \Theta_{cr}</math>|3}} | ||
The critical depth-averaged velocity for currents alone (U<sub>crc</sub>) is calculated using the formula proposed by van Rijn (1984 c): | |||
{{Equation|<math>U_{crc} = | |||
\left\{ | |||
\begin{align} | |||
&0.19 \ d_{50}^{0.1}log_{10}\left(\frac{4h}{d_{90}} \right), \quad\quad for \ 0.1 \leq d_{50} \leq 0.5 \ mm \\ | |||
&8.5 \ d_{50}^{0.6}log_{10}\left(\frac{4h}{d_{90}} \right), \quad\quad for \ 0.5 \leq d_{50} \leq 2.0 \ mm | |||
\end{align} | |||
\right. | |||
</math>|4}} | |||
where d<sub>50</sub> and d<sub>90</sub> are the sediment grain size in meters of 50<sup>th</sup> and 90<sup>th</sup> 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): | |||
{{Equation|<math> | {{Equation|<math> | ||
U_{crw} = | U_{crw} = | ||
\begin{cases} | \begin{cases} | ||
0.24 [(s-1)g]^{0.66} (d_{50})^{0.33} T_p^{0.33} , & \text{for } 0.1 \le d_{50} \le 0.5 mm \\ | 0.24 [(s-1)g]^{0.66} (d_{50})^{0.33} T_p^{0.33} , & \text{for } 0.1 \le d_{50} \le 0.5 \ mm \\ | ||
0.95 [(s-1)g]^{0.57} (d_{50})^{0.43} T_p^{0.14}, & \text{for } 0.5 \le d_{50} \le 2.0 mm | 0.95 [(s-1)g]^{0.57} (d_{50})^{0.43} T_p^{0.14}, & \text{for } 0.5 \le d_{50} \le 2.0 \ mm | ||
\end{cases} | \end{cases} | ||
</math>| | </math>|5}} | ||
where T<sub>p</sub> is the peak wave period. | |||
= References = | = References = | ||
*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. | |||
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Latest revision as of 15:41, 15 January 2015
Incipient Motion
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):
| (1) |
in which the dimensionless grain size (d*) is defined
| (2) |
The critical shear stress for incipient motion is given by
| (3) |
The critical depth-averaged velocity for currents alone (Ucrc) is calculated using the formula proposed by van Rijn (1984 c):
| (4) |
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):
| (5) |
where Tp is the peak wave period.
References
- 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.