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

current and waves is defined as the integration of the

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

employed in these regions with empirical expressions

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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