COASTAL ENGINEERING 2004

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response in shoreline orientation to the incident waves, and the shoreline lies

almost parallel to the wave crests at all times (Fig. 2). The parameter ζ becomes

small if the amplitude of the transport rate *Q*o is large, the length of the enclosed

beach *B *small, or the frequency ω of the wave angle variation small. For large ζ

there is a distinct phase difference between the shoreline response and αo (Fig.

3) and the oscillation in the shoreline position is less than for smaller ζ* *For very

large ζ, there will be no effect on the shoreline except close to the boundaries.

The complete solution also has a transient part. However, this part decays

exponentially with time and is not included in (11).

As indicated by the previous case, situations with higher values on the

( ∂2 y / *dx*2 ) near the groin. Thus, with the shoreline orientation closest to the

groin corresponding to *Q *= 0 as well as a zero wave-generated longshore

current, a larger curvature indicates that the shoreline orientation a bit further

away from the groin corresponds to a larger transport rate (and longshore current

velocity) that, if directed towards the groin, is anticipated to generate an offshore

rip-related transport. This also follows from Eq. (6) where *Q *is seen to be

proportional to ∂*y*/∂*x*, leading to ∂*Q*/∂*x *~ ∂2y/∂*x*2. In mathematical terms this

boundary condition at the groin location is formulated as,

π/2

π

ξ=1

Figure 2. Shoreline evolution in enclosed groin compartment at steady-state conditions when

breaking-wave angle varies sinusoidally with time for ζ = 1. (Modified from Larson *et al*. 1997).

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