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.