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L. Erikson et al. / Coastal Engineering 52 (2005) 285302
1:10) was employed so that the chosen periods run
5. Results
in the laboratory were 1.3 s, 1.7 s, and 2.2 s
5.1. Measured run-up and swash depth
(prototype 4.1 s, 5.4 s, and 7 s). A summary of the
wave conditions is listed in Table 1. The wave
heights were set intentionally high in order to obtain
lengths, plotted against the left axis, and swash depths
well quantifiable results in the laboratory and model
measured at the SWS, plotted against the right axis,
extreme cases. The fourth column in Table 1 lists the
for the selected wave trains. Note that on this and
maximum wave height near the paddle in each group
similar figures the run-up is plotted in terms of run-up
and for each case. The greatest wave steepness (H0/
length, rather than run-up height (as was done by e.g.,
L0) is listed in column 5. Thffieffiffiffivffiaffilffiue of the surf
p ffi ffiffi ffi ffi
similarity parameter, n u= H0=L0 (where u is
different reference frames within which the measure-
the surf zone slope near the break point (Irribarren
ments were made. The run-up data were obtained in a
and Nogales, 1949)) varied for each wave within a
Lagrangian reference frame (following the swash front
given wave train suggesting a combination of spill-
motion) while the swash depth was obtained at the
ing and plunging waves in the surf zone.
initial SWS in an Eulerian reference frame (i.e., fixed).
The generated wave trains were constructed by
For the cases with tanb=0.07, the duration of the
multiplying sinusoidal waves of the chosen individ-
wave packets measured at the SWS decreased by
ual wave periods with a second sinusoidal wave
about 23% to 35% (from about 13 to 20 s measured
offshore to 10 to 13 s measured at the SWS). For all
column 3 of Table 1) such that each wave packet
four cases, the number of discernable peaks reduced
consisted of 10 waves. Offshore surface elevations
from 10 to between 5 and 7. The bdisappearingQ
measured at the most seaward gauge (about 14 m
waves appear to be a consequence of returning back-
from the SWS) are shown in Fig. 5 for the four
wash either colliding with incoming bores seaward of
cases presented in this paper. Water depths at the
the SWS or absorbing the incident bores at the SWS.
paddle were 0.56 for the B cases and 0.50 for case
A spectral analysis of the swash depth at the SWS
C1. The slightly more shallow water depth of case
was performed with a fast Fourier transform (FFT)
C1 in conjunction with the longer wave period 2.2 s
using the Welch method and 1024 data points sampled
caused the waves to shoal slightly at the offshore
at 25 Hz. The results are shown in Fig. 7 and indicate
location.
that although there is considerably high energy at the
Although more than a total of 100 wave trains
lower frequencies, much short wave energy is still
were run, results of only one wave train from each
present. The presence of short wave energy at the
case are presented here. The wave motion was
SWS supports the notion of using the bore collapse
highly repeatable and although the beach consisted
model, as opposed to a low-frequency standing wave
of movable sand, little sediment transport was
model (Section 1), to describe the run-up or shoreline
obtained so that results between subsequent bores
motion. The presence of the long wave energy (at the
only differed slightly. Wave trains were generated
low frequencies) is probably related to the up-rush/
with a half a minute lag for case C1 and a 3.5 min
back-wash interaction in the swash zone (Mase, 1994)
lag for the remaining cases between subsequent
and likely describes the envelope of the run-up
groups. This was done to minimize wave reflection
reached by individual bores as shown by Baldock et
in the tank and to simulate the passage of one vessel
al. (1997).
at a time. Analysis of the wave records was done on
Looking back at Fig. 6 it is clear that the run-up
sampled intervals spanning only the time of signifi-
(shoreline motion) is driven by the swash height at the
cant run-up and less than the time required for waves
SWS. Most of the peaks observed at the SWS are also
to reflect off the beach and paddle and return to the
observed in the shoreline motion. Cross-correlations
SWS. This procedure eliminated contamination of
between measured swash depth and run-up length are
the data by waves reflected off the board, but
shown in Fig. 8 and suggest that there is a similar
included the natural reflection of waves by the
variation with time and that the variation of the swash
beach.
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