L. Erikson et al. / Coastal Engineering 52 (2005) 285302
287
results with and without the collision mechanism are
presented in Section 5.
superimposing run-up parabolas using the ballistic
model without friction. Mase and Iwagaki (1984)
ran a series of tests in the laboratory with random
waves and found that the ratio of the number of
3. Model formulation
individual run-up waves to that of incident waves
3.1. Model basis
decreased as the beach slope decreased. Based on
additional laboratory experiments, Mase (1989)
The model is based on the hypothesis that swash
developed an empirical formula to predict the
motion is largely driven by bores that collapse at the
maximum run-up on a range of slopes while
shoreline and then propagate up the beach face (Ho et
accounting for swash interaction between random
al., 1963; Shen and Meyer, 1963; Hibberd and
waves. Baldock and Holmes (1999) presented
Peregrine, 1979). By considering a fluid element at
experimental data and found excellent agreement
the leading edge of a collapsed bore (swash lens), a
between predicted values and measured swash
force balance can be derived (Kirkgoz, 1981; Hughes,
motion for regular waves, wave groups, and random
1995; Puleo and Holland, 2001):
waves on a steep (1:10) impermeable beach in a
laboratory setting. Although the experiment was
2
conducted on a fairly steep beach face, they
d2xs
f
dxs
gsinbF
1
reported considerable interaction between subse-
dt2
2dh
dt
quent bores in the swash zone, for the cases where
bi-chromatic wave groups of varying height were
where the coordinate system has x positive onshore
run. The interaction often caused the smallest bores
(along the foreshore) and z positive upwards, t=time,
at the beginning of the group to run up further than
xs=shoreline position of the swash front relative to
the subsequent larger bores.
the initial shoreline position (Fig. 1), g=acceleration
It appears that the collision mechanism of swash
due to gravity, b=beach slope angle, f=friction
interaction has not previously been explicitly
factor, and yh=height of the leading fluid element.
accounted for in the ballistic model. An overview of
If g, b, f and yh are constant, then Eq. (1) can be
the model and modifications done for this study are
integrated using separation of variables to yield the
presented in the following section and simulation
(a)
initial still-water
z
shoreline (SWS)
x
2
1
3
xs
4
2
uo 1
Time
(b)
2
1
3
4
2
1
Time
Fig. 1. Sketch illustrating two phenomena accounted for in the swash interaction model. (a) Catch-up and absorption, and (b) up-rush and back-
wash collision.
Previous Page
