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):


== Komar and Miller ==
{{Equation|<math>
Komar and Miller (1975):
\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}
  \begin{cases}  
</math>|2}}
0.19 (d_{50})^{0.1} \log{_{10} \big( \frac{4h}{d_{90}} \big) }, & \text{for } 0.1 \le d_{50} \le 0.5 mm \\  
 
8.5 (d_{50})^{0.6} \log{_{10} \big( \frac{4h}{d_{90}} \big) }, & \text{for } 0.5 \le d_{50} \le 2.0 mm
The critical shear stress for incipient motion is given by
  \end{cases}
 
</math>|11}}
{{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>|12}}
</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.



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