P. Wang et al. / Coastal Engineering 46 (2002) 175211
191
4.3. Spatial variations of surf-zone current
of Visser (1991). Longshore current profiles that
were nearly uniform with depth outside of a boun-
Along the middle 16 m of the test beach, the
dary layer were derived in a mathematical analysis of
longshore current, cross-shore current, and sediment
concentration showed little variation in the alongshore
The friction associated with the movable bed and its
direction. The following discussion focuses on spatial
rippled bedforms appears to have significant influen-
variations of the time-averaged current in the vertical
ces on the shape of time-averaged longshore current
and cross-shore directions. Typically, 10-min averages
profiles.
corresponding to the duration of the wave-generation
Because the current measurements could not be
drive signal were computed.
made reliably above the wave-trough level near
the water surface, the profiles shown in Figs. 12
4.3.1. Vertical and cross-shore variations of the time-
and 13 span approximately 65% to 80% of the still-
averaged longshore current
water depth. The depth-averaged longshore current,
Vertical profiles of time-averaged longshore cur-
Vd-average, was calculated as
rent were obtained at the 10 cross-shore locations
X Vi1 Vi hi1 hi
N 1
measured throughout the water column at most loca-
2
i1
tions across the surf zone for both the spilling (Fig.
8
Vdaverage
hhighest hlowest
urements obtained high in the water column at the
landwardmost ADV1, and at some of the other
where Vi is the current speed measured at the i
locations, could be influenced by the proximity to
level; hi is water depth at the i level; hhighest and
the surface and intermittent exposure of the sensor. In
hlowest are water depths at the highest and lowest
the upper portion of the water column, nearly 50% of
measurement levels, respectively; and N is the
the data points from ADV1 were removed due to
number of elevations where current measurements
unrealistic spikes.
were made. Because little is known about longshore
Except at the shallow ADV1 located at 1.1 m from
current near and above wave trough, no extrapola-
shoreline, the logarithmic curves fit the time-averaged
tion was conducted to incorporate the upper 20% to
longshore current profiles well. The average correla-
35% of the water column into the averaging proc-
tion coefficient of the least-square curve fitting, R2, is
ess; therefore, the depth-averaged current calculated
from Eq. (8) does not reflect this portion of the
0.96 for the spilling case, with a standard deviation of
0.025, or 2.6% of the mean (Fig. 12). Slightly greater
water column. Also, the bottom 1 cm was not
included in the averaging. If the near-surface long-
scatter was evident for the plunging case, with an
average R2 value of 0.89 and a standard deviation of
shore current follows the same logarithmic trend,
the present calculation (Eq. (8)) would result in an
0.066, or 7.4% of the mean (Fig. 13). The longshore
underestimate of the depth-averaged current speed.
current is driven by the radiation stress from the
The depth-averaged longshore current agreed well
obliquely incident waves; the variation over depth is
with the current speed measured at an elevation of 1/3
attributable to the effects of bottom stress and the
still-water depth from the bed, with the differences
depth-dependent forcing and mixing. Examination of
the detailed relationship between the wave forcing and
being within 15% at all cross-shore locations for both
spilling and plunging cases (Fig. 14). It is thus
boundary effects and the current-profile shape is
concluded that current measurements made at 1/3
beyond the scope of this paper.
depth from bed provide reliable representations of
Logarithmic mean longshore current profiles are
depth-averaged values, excluding the top portion of
in contrast to the fairly uniform profiles measured
the water column.
over a fixed concrete bed under regular and irregular
Cross-shore distribution patterns of mean long-
waves in the same facility (Hamilton and Ebersole,
shore current were remarkably similar for both the
2001). Relatively uniform longshore current profiles
were also measured in the fixed-bed laboratory study
spilling- and the plunging-breaker cases. In the cross-
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