98
A. Bayram et al. / Coastal Engineering 44 (2001) 7999
turbulence, and b is a coefficient quantifying the
in which Hs is the significant wave height. The depth-
integrated suspended load transport in the presence of
influence of the centrifugal forces on suspended
particles.
product of velocity (v) and concentration (c) from the
Van Rijn (1984) calculated the concentration dis-
edge of the bed-load layer (z = a) to the water surface,
tribution c in three separate layers, namely:
yielding:
from the reference level a to the end of a near-
Z h
bed mixing layer (of thickness ds)
qs;VR
vcdz
from the top of the ds-layer to half the water
a
depth (h/2)
from (h/2) to h
Integrating after substituting in the longshore cur-
rent can be shown to give,
Z
Different exponential or power functions are
1 h v c
qs;VR caVh
dz caVhF
h a V ca
depending on the mixing characteristics in each layer.
where c is the concentration distribution, V the mean
A.6. Watanabe (1992) formula
longshore current, and,
Z 0:5
0
V a Z
hz Z
The formula proposed by Watanabe (1992) for the
F
lnz=z0dz=h
total load was developed to calculate the longshore
jV h a
z
a=h
sediment transport rate as combined bed and sus-
!
Z
1
pended load according to,
0
e4Z z=h0:5 lnz=z0dz=h
!
0:5
sb;wc sb;crV
qt;W A
qg
d50 T 1:5
ca 0:015
a D0:3
where A is an empirical coefficient (about 0.5 for
monochromatic waves and 2.0 for random waves) and
sb,cr is the critical bed shear stress for incipient motion
Z0 Z w
(determined from the Shield curve for oscillatory
flow). This formula is composed of one part repre-
senting stirring of the sediment (the shear stress term)
w
and another term describing the transport (the long-
Z
bjV
shore current speed).
0:8 0:4
References
w
ca
W 2:5
V
c0
Ackers, P., White, W.R., 1973. Sediment transport: new approach
and analysis. Journals of Hydraulics Division 99 (1), 2041
2060.
w 2
Bailard, J.A., 1984. A simplified model for longshore sediment
b12
transport. Proceedings of the 19th Coastal Engineering Confer-
V
ence, pp. 1454 1470.
Bailard, J.A., Inman, D.L., 1981. An energetics bedload model for
in which Z is a suspension parameter reflecting the
plane sloping beach: local transport. Journal of Geophysical
ratio of the downward gravity forces and upward fluid
Research 86 (C3), 2035 2043.
forces acting on a suspended sediment particle in a
Bagnold, R.A., 1966. An approach to the sediment transport prob-
current, w is an overall correction factor representing
lem from general physics. Geological Survey Professional Pa-
damping and reduction in particle fall speed due to
pers 422-1, Washington, USA.
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