2626

COASTAL ENGINEERING 2004

**0.15**

**0.10**

**0.05**

**0.00**

**Phase**

**-0.05**

**0**

π/2

**-0.10**

π

**3**π/2

ξ=6

**-0.15**

**0.0**

**0.2**

**0.4**

**0.6**

**0.8**

**1.0**

**Alongshore Distance (x/B)**

Figure 3. Shoreline evolution in enclosed groin compartment at steady-state conditions when

breaking-wave angle varies sinusoidally with time for ζ = 6.

∂*Q*

∂2 y

= -*R*

= 2*RQ*o 2

(13)

*Qoff*

∂*x*

∂*x*

*x*=0

*x*=0

where *R *is a dimensional coefficient [m]. If the wave crests make a constant

angle -αo with the *x*-axis, giving rise to a longshore transport in the negative *x*-

direction, the solution describing the accumulation on the updrift side becomes,

⎡ ε *t * - *x*2

*x * ε*t*

ε *t *⎞⎤

⎛ x

⎛ x ⎞

+

(

) ⎜

⎢2

⎟⎥

*y*(*x*, *t*) = -α0

*R R*2 erfc

4ε*t *- *R *+ *x *erfc

⎟ + *Re*

+

⎜

*e*

⎜ 2 ε*t*

*R *⎟⎥

⎢ π

⎝ 2 ε*t *⎠

⎝

⎠⎦

⎣

(14)

A non-dimensional plot of this shoreline evolution is shown in Figure 4

where the solution for *R *= 0.5 (saying that half of the transport rate approaching

the groin is redirected into the rip) is shown and compared to the case *R *= 0, i.e.

no offshore rip transport. Based on Eq. (13), the offshore transport *Q*off next to

the groin becomes:

∂2 y

⎡ 1

2

*e*- *x */ 4ε*t *+

= -2*RQ*oα0 ⎢

*Qoff *= 2*RQ*o

∂*x*2

⎣ πε *t*

*x*=0

⎤

2

⎛* x*

⎞

ε*t*

⎛ *x * ε*t *⎞

-⎜

+

⎛* x*

ε*t *⎞

⎟

⎥

⎜ *R*+ 2 ⎟

1

1

⎜ 2 ε*t*

⎟

*R*

*e*⎝ * R *⎠

*e* ⎝

⎠

+

+

⎟-

erfc ⎜

(15)

⎥

⎜ 2 ε*t*

*R* ⎟

πε *t*

*R*

⎝

⎠

⎥

⎦