96
A. Bayram et al. / Coastal Engineering 44 (2001) 7999
integrating along the vertical from the reference height
mobility number. The dimensionless parameters are
to the water surface, the total suspended sediment load
written, respectively,
is determined as,
n 1 0:2432lndgr
!
9:66
33h
1:34
m
qs;B 1:83qb;B
I2
I1ln
dgr
r
Cd;gr exp 2:86lndgr 0:4343lndgrŠ2
where I1 and I2 are the Einstein integrals (e.g., Van
8:128
Rijn, 1993). The total load is computed as the sum of
0:23
bed load and suspended load ( qt,B = qb,B + qs,B).
A pffiffiffiffiffiffi 0:14
dgr
A.2. Engelund and Hansen (1967) formula
where,
1=3
Engelund and Hansen (1967) developed a formula
gs 1
dgr d35
to compute the bed load transport under a current.
v2
This formula was later used to compute the total load
and also modified to take into account wave stirring.
and m is the kinematic viscosity. The sediment mobi-
Applied to calculate the longshore sediment transport,
lity number is defined as,
n
the formula yields:
V
n
V
Cd
!2
V
1 u0 2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
FC
2
0:05Csb;c 1
n
Cdgn=2 s 1d35
2
V
V
qt;EH
s 12d50q2g5=2
in which:
10h
Cd 18 log
This formula is also composed of a stirring term and a
d35
transporting term, much in accordance with Watanabe
(1992). The same coefficient value ( = 0.05) apply for
The modified equation by Van De Graaff and Van
both monochromatic and random waves in the orig-
Overeem (1979) to take into account waves is written,
& 0 'n
inal formula.
1
Vwc
Cd;gr
qt;AWM V
d35
Am
1p
V;wc
A.3. Ackers and White (1973) formula
&
'n
9m
8
> V 0 V;wc Cn
>
>
> wc
=
<
Similarly to Engelund and Hansen (1967), the
d
0
Vwc
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A
formula proposed by Ackers and White (1973) ini-
>
>Cd gn=2 s 1d35
>
>
;
:
tially predicted the total load transport under a current,
but was later enhanced by Van De Graaff and Van
Overeem (1979) to describe the effects of waves. The
where,
original Ackers White formula may be written,
!1=2
1 u0 2
V 1
n
V;wc
n
2
V
1
V
Cd;gr
FC Am
qt;AW V
d35
m
1p
V
A
and:
!1=2
1 0 u0 2
0
V 1
where p is the porosity of the sediment, d35 the
n
Vwc
2
V
particle diameter exceeded by 65% of the weight,
In the above formulation, n0 is based on d35 and n
V * the shear velocity due to the current, n, m, Cd,gr,
and A dimensionless parameters, and FC a sediment
on the bed roughness r.
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