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COASTAL ENGINEERING 2004

holding *Q*n fixed. In this study it will also be shown that, for the same ratio

The history and basic assumptions of one-line theory, with the line taken to

represent the shoreline, are discussed extensively by Hanson and Kraus (1989).

In the one-line model, longshore sand transport is assumed to occur uniformly

over the beach profile down to a certain critical depth D called the depth of

closure. By considering a control volume of sand and formulating a mass

balance during an infinitesimal interval of time, while neglecting the cross-shore

transport, the following differential equation is obtained,

∂*Q*

∂*y*

+*D*

=0

(1)

∂*x*

∂*t*

where *Q *= longshore sediment (sand) transport rate, *x *= space coordinate along

the axis parallel to the trend of the shoreline, *y *= the shoreline position, and *t *=

time. Line discharges of sediment representing cross-shore transport can be

added to Eq. (1) (Kraus and Harikai, 1983; Hanson and Kraus, 1989), but this

capability is not exploited here.

Eq. (1) states that the longshore variation in the sand transport rate is

balanced by changes in the shoreline position. In order to solve Eq. (1), it is

necessary to specify an expression for the longshore sand transport rate. A

general expression for this rate in agreement with several predictive

formulations is,

(2)

where *Q*o = amplitude of longshore sand transport rate, and αb = angle between

breaking wave crests and shoreline. This angle may be expressed as,

⎛ ∂*y *⎞

αb = αo - arctan ⎜ ⎟

(3)

⎝ ∂*x *⎠

in which αo = angle of breaking wave crests relative to an axis set parallel to the

trend of the shoreline, and ∂*y*/∂*x *= local shoreline orientation

A wide range of expressions exists for the amplitude of the longshore sand

transport rate, mainly based on empirical results. For example, the SPM (1984)

gives the following equation,

ρ 2

(4)

(ρs - ρ )(1 - λ )

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