with the boundary condition at the structure being tan αb = dy/dx, and the boundary condition at *x *= 4 being

can be utilized to estimate planform shapes on the updrift side of coastal structures where bypassing does not

take place.

(9) The dimensionalized solution for these conditions is given by Pelnard-Considre (1956) to be

2

1

exp &

, for *t *< *t*f

(III-2-28)

&

2 ε*t*

2 ε*t*

2 ε*t*

π

where *t*f is the time at which the structure fills to its capacity via this solution and where *erfc*( ) is the

complementary error function defined as *erfc*( ) = 1 - *erf*( ) where *erf*( ) is the error function and

2

π m0

()

2

erf ( ) '

Both *erfc *( ) and *erf *( ) are tabulated in various mathematical handbooks. Figures III-2-32 and III-2-33

provide graphs of *erfc *( ) and *erf *( ).

(10) The time required for the structure to fill to capacity *t *= *t*f can be found from the previous solution

with ordinate *x *= 0; i.e.,

III-2-60

Longshore Sediment Transport

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