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

$\frac{q_b}{\sqrt{(s-1)g{d}^3}}=a_c\sqrt{{\theta }_c}{\theta }_{cw}\exp (-b_c\frac{{\theta }_{cr}}{{\theta }_{cw}})$

(1)

Suspended load

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

$\frac{q_s}{\sqrt{(s-1)g{d}^3}}=U{c}_R\frac{ϵ}{w_s}[1-\exp (-\frac{w_{s}d}{ϵ})]$

(2)

The reference sediment concentration is obtained from

$c_R=A_{cR}\exp (-4.5\frac{{\theta }_{cr}}{{\theta }_{cw}})$

(3)

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

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

(4)

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

The sediment mixing coefficient is calculated as

$ϵ=\left(\frac{k_b^3{D}_b+k_c^3{D}_c+k_w^3{D}_w}{\rho }\right)$

(5)

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	-