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P. Wang et al. / Coastal Engineering 46 (2002) 175211
not clear, the two landwardmost ADVs are excluded
deviation and are included to demonstrate the degree
from the frequency analysis.
of alongshore variability.
4.1.2. Temporal variations and periodicities of long-
shore currents
4. Results and discussion
Overall, the frequency distribution of longshore
current was substantially different from the patterns
4.1. Temporal variations of surf-zone currents
of the cross-shore current and water-surface fluctua-
tions especially in the surf zone landward of gage 8
4.1.1. Temporal variations and periodicities of cross-
shore currents
a much lower frequency, between 50 and 100 s, than
that associated with either the peak incident waves or
density for the cross-shore current measured at 1/3
the 10- to 20-s low-frequency range observed in the
water depth from the bottom for both wave cases. The
cross-shore currents. The 50- to 100-s low-frequency
dimensionless power spectral density was computed
peak was an artifact of the data segmenting and
as
windowing applied in the present power spectral
PSDi
density analysis. No low-frequency cutoff was
i 1; 2; 3; . . .
7
PSDdimensionlessi
MaxPSD
imposed. Qualitative examination of the raw data
did not indicate apparent low-frequency variation
having 50- to 100-s period. It is worth noting that
where PSD(i) is the power spectral density of fre-
quency component i, and Max(PSD) is the peak
density instead of the magnitudes. The magnitudes of
spectral density. Fig. 7 illustrates the shape of the
the spectral density of the cross-shore current were
spectral density instead of the absolute magnitude.
much greater, typically over one order of magnitude
Overall, the spectral shapes are similar to those of
greater, than those of the longshore current.
water-level fluctuation (Fig. 3), as expected. At most
Across most of the mid-surf zone (gages 3 through
locations, the peak period of the cross-shore current
7), the variance of longshore current at the incident-
fluctuations was 1.5 s (0.67 Hz) and 3.0 s (0.33 Hz)
wave frequencies was small. A narrow spectral peak
for the spilling and the plunging cases, respectively,
occurred at approximately 1.5 s at ADV6 for the
with secondary low-frequency peaks from 11 s (0.09
spilling case. The energy carried by this narrow peak
Hz) to 21 s (0.05 Hz), respectively. The relative
was low. This peak is partially related to the small
spectral density at the low frequency dominates near
frequency interval used in the spectral analyses with
the shoreline in a pattern similar to the free surface.
the objective of fine spectral resolution. Secondary
These similarities are expected because the waves,
peaks occurred between 10 and 20 s for both wave
with a small incident-wave angle of 10j, dominated
cases, similar to the distributions of cross-shore
the cross-shore current. The increase of the low-
current and water-level spectral density. Near and
frequency components toward the shoreline is well
seaward of the breaker line (gages 8 through 10),
documented in both laboratory (e.g., Thompson and
spectral density at the incident-wave frequency
became apparent. Although the spectral shapes
Guza and Thornton, 1982).
resemble those of cross-shore current (Figs. 7 and
The two landwardmost ADVs were occasionally
8), the magnitudes of the longshore current variance
exposed to air due to the shallow and varying water
were much smaller.
depth, resulting in a considerable fraction (approxi-
Overall, the temporal variations of longshore cur-
mately 15% to 30%) of erroneous data in the form of
rent were not significantly influenced by the fre-
unrealistic spikes. These erroneous points were
quency of the wave-induced orbital motion across
removed during data analysis using the procedure
most of the surf zone, as indicated by the general
described in Hamilton et al. (2001) and Hamilton and
lack of the spectral peak at 0.67 Hz (1.5 s) and 0.33
Ebersole (2001). However, because the influences of
Hz (3.0 s), respectively. Temporal variations of long-
these spikes, or their removal on spectral analysis are
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