Sediment Transport

Lund-CIRP Transport Equations

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

${\frac {q_{b}}{\sqrt {(s-1)gd^{3}}}}=a_{c}{\sqrt {\theta _{c}}}\theta _{cw}\exp {{\biggl (}-b_{c}{\frac {\theta _{cr}}{\theta _{cw}}}}{\biggr )}$

(1)

Suspended load

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

${\frac {q_{s}}{\sqrt {(s-1)gd^{3}}}}=Uc_{R}{\frac {\epsilon }{w_{s}}}{\biggl [}1-\exp {{\biggl (}-{\frac {w_{s}d}{\epsilon }}}{\biggr )}{\biggr ]}$

(2)

The reference sediment concentration is obtained from

$c_{R}=A_{cR}\exp {{\biggl (}-4.5{\frac {\theta _{cr}}{\theta _{cw}}}}{\biggr )}$

(3)

where the coefficient $A_{cR}$ is given by

$A_{cR}=3.5x10^{3}\exp {{\bigl (}-0.3d_{*}}{\bigr )}$

(4)

with $d_{*}=d{\sqrt {(s-1)g\nu ^{-2}}}$ being the dimensionless grain size and $\nu$ the kinematic viscosity of water.

The sediment mixing coefficient is calculated as

$\epsilon =h{\biggl (}{\frac {k_{b}^{3}D_{b}+k_{c}^{3}D_{c}+k_{w}^{3}D_{w}}{\rho }}{\biggr )}^{1/3}$

(5)

Soulsby-van Rijn Transport Formula

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle C_{*} = \frac{A_{sb}+A_{ss}}{ h} \biggl[ \frac{ U^2 + 0.018 \frac{U_{rms}^2}{C_d} \biggr]^{2.4} }

(6)

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Symbol	Description	Units
$q_{bc}$	Bed load transport rate	m3/s
$s$	Relative density	m
$\theta _{c}$	Shields parameter due to currents	-
$\theta _{cw}$	Shields parameter due to waves and currents	-
$\theta _{cw}$	Critical shields parameter	-
$a_{c}$	Empirical coefficient	-
$b_{c}$	Empirical coefficient	-