P. Wang et al. / Coastal Engineering 46 (2002) 175211
207
depth-averaged velocity (approximately equal to 1/3-
surface were neglected from the calculation, one
depth velocity) and concentration (approximately
would expect the calculated results to be less than
equal to 1/5-depth concentration) will almost always
the trapped quantities in all cases. For the spilling
result in greater total flux than that derived from a
case, the total sediment flux measured at the bottom
more accurate integration of the sediment-flux profile.
traps across the section of beach from 2.7 to 11.6 m
(from the shoreline) was 1200 m3/year, the same as
The total longshore transport rate across the section
the 1200 m3/year calculated from the profiles of time-
obtained from the depth-averaged fluxes were 4400
m3/year for the spilling case and 4500 m3/year for the
averaged longshore current and sediment concentra-
tion. However, for the plunging case, the total sedi-
plunging case, compared to the measured rates of
ment flux was 3600 m3/year for the traps and 2500
1200 m3/year for the spilling and 3600 m3/year for the
m3/year, or approximately 30% less, for the calculated
plunging case. The closer match for the plunging case
is likely to be a coincidence.
rate from 2.7 to 11.6 m. The underprediction resulted
The total rates of longshore sediment transport
from the lower calculated values across the mid-surf
measured at the downdrift traps were substantially
zone.
different for the spilling and the plunging cases, 1200
Given the uncertainties involved in using the time-
vs. 3600 m3/year for the section of beach from 2.7 to
averaged longshore current and sediment concentra-
tion, and the neglect of transport in the bottom 1 cm
11.6 m from the shoreline. The rate for the spilling
and top 20% to 35% of the water column, the
case was 33% of the plunging-case rate although the
calculated total longshore transport rate may carry
breaker height and breaker angle were similar (Table
considerable uncertainty of up to 30% to 40%.
Uncertainties associated with the estimate of local
ences between the total transport rates across the
longshore sediment flux, especially the small values
entire surf zone for the two cases.
in the mid-surf zone, can be as high as 200%. Based
on a simultaneous field measurement of longshore
4.5.2. Cross-shore sediment flux
current and sediment concentration, Beach and Stern-
Similar time-shifted calculations of instantaneous
berg (1992) concluded that the product of time-aver-
sediment flux, as described above, were conducted in
aged longshore current and concentration yields a
the cross-shore direction. Cross-shore flux is much
reasonable estimate of longshore sediment flux at
more significantly influenced by individual wave
the measurement point.
motions than longshore flux. Large variations of over
The longshore flux was also calculated as the
100% were obtained when comparing the flux
product of depth- and time-averaged current and the
obtained from the product of time-averaged cross-
mean concentration over the measured portion of the
shore current and time-averaged sediment concentra-
water column, and compared with the measured
tion with the time averages of the shifted instanta-
values at traps from 2.7 to 11.6 m from shoreline.
neous flux for both spilling (Fig. 26, upper panel) and
This calculation (denoted as ``depth-averaged calcu-
plunging (Fig. 26, lower panel) cases. Compared to
lation'' in Fig. 25) yielded greater sediment fluxes
longshore flux, the variations in the cross-shore flux
than computed from integration of the sediment-flux
were much greater. Although it is not clear which of
profile. For the spilling case, sediment flux obtained
the shifted values represents the true flux, and it is
from the depth-averaging calculation was significantly
possible that the product of time-averaged velocity
greater than the flux measured at the downdrift bottom
and concentration may coincide with the true flux, this
traps. For the plunging case, the depth-averaging
occurrence is neither likely nor reliable given the large
calculation resulted in considerable overprediction in
and variable differences.
the vicinity of the breaker line, while the match in the
The present experiments were conducted after a
mid-surf zone was reasonable. Because sediment
series of preexperiment runs that were designed to
concentration decreases much more rapidly away
establish optimal pump settings to circulate the wave-
from the bed than the increase of longshore current
generated longshore current (Hamilton and Ebersole,
at most of the cross-shore locations, and the neglect of
2001) and to allow the beach profile to reach an
the top 20% to 35% of water column, the product of
equilibrium shape. Because the beach reached quasi-
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