CMS-Flow:Incipient Motion

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):

${\mathrm{\Theta }}_{cr}=\frac{0.3}{1+1.2d_{*}}+0.055[1-exp(-0.02d_{*})]$

(1)

in which the dimensionless grain size (d_*) is defined

$d_{*}=d{\left[\frac{(s-1)g}{v^2}\right]}^{1/3}$

(2)

The critical shear stress for incipient motion is given by

$\frac{{\tau }_{cr}}{g({\rho }_s-\rho )d}={\mathrm{\Theta }}_{cr}$

(3)

The critical depth-averaged velocity for currents alone (U_crc) is calculated using the formula proposed by van Rijn (1984 c):

$U_{crc}=\{\begin{array}{rl}& 0.19d_{50}^{0.1}lo{g}_{10}\left(\frac{4h}{d_{90}}\right),for0.1\le d_{50}\le 0.5mm\\ & 8.5d_{50}^{0.6}lo{g}_{10}\left(\frac{4h}{d_{90}}\right),for0.5\le d_{50}\le 2.0mm\end{array}$

(4)

where d₅₀ and d₉₀ are the sediment grain size in meters of 50^th and 90^th 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):

$U_{crw}=\{\begin{array}{ll}0.24[(s-1)g{]}^{0.66}(d_{50}{)}^{0.33}{T}_p^{0.33},& \text{for }0.1\le d_{50}\le 0.5mm\\ 0.95[(s-1)g{]}^{0.57}(d_{50}{)}^{0.43}{T}_p^{0.14},& \text{for }0.5\le d_{50}\le 2.0mm\end{array}$

(5)

where T_p is the peak wave period.

References

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