| AUTHOR: | Ping Wang, Ernest R. Smith, and Bruce A. Ebersole |
| TITLE: | Large-Scale Laboratory Measurements of Longshore Sediment Transport Under Spilling and Plunging Breakers |
| SOURCE: | Journal of Coastal Research 18 no1 118-35 Wint 2002 |
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ABSTRACT
Total rates and cross-shore
distribution of longshore sediment transport under predominantly spilling and
plunging breakers were examined in the Large-scale Sediment Transport Facility
(LSTF) at the U.S. Army Engineer Research and Development Center. The input
waves were long-crested unidirectional irregular waves with broad spectra.
Taking advantage of the new state-of-the-art LSTF, a suite of parameters
including wave height, longshore current, longshore sediment flux, sediment
concentration, and their cross-shore distribution patterns were precisely
measured. The main objective of this study was to quantify the influences of
different forms of wave breaking on rates and patterns of longshore sediment
transport. A significantly greater total rate of longshore sediment transport
was measured under the plunging breakers than under the spilling breakers with
similar breaker height. The peak longshore transport rate was measured in the
swash zone for the spilling breaker case. In the case of plunging breakers, a
bi-modal distribution pattern was measured with one peak in the swash zone and
one in the vicinity of the breaker line. Similar rates of longshore transport
were measured in the surf-bore dominated mid-surf zone for both cases. The
suspended sediment concentration near the breaker line was approximately one
order of magnitude greater under the plunging breakers than under the spilling
breakers. Except in the inner surf zone, where faster current was measured
during the plunging case, a similar cross-shore distribution of longshore
current was measured for both plunging and spilling cases. Breaking type has
significant influence on the magnitude and pattern of longshore transport.
Parameters distinguishing dominant breaker types are important in improving the
accuracy of longshore sediment transport predictions.
ADDITIONAL INDEX WORDS:
Longshore sediment transport, nearshore sediment transport, physical modeling,
wave breaking, surf zone processes, sediment transport processes.
INTRODUCTION
Accurate predictions of the total
rate of longshore sediment transport and its cross-shore distribution in the
surf zone are central to many coastal engineering and science studies. Present
understanding and predictive tools are largely developed based on field studies
(KOMAR and INMAN, 1970; INMAN et al., 1981; KRAUS et al., 1982; BODGE and DEAN,
1987; DEAN, 1989; SCHOONEES and THERON, 1993; WANG et al., 1998a; WANG, 1998).
The dynamic and non-repeatable nature of the surf zone can introduce
considerable uncertainties in field measurements (WANG and KRAUS, 1999). The
non-controllable nature of field conditions increases the difficulties of
isolating and examining the contributions of, and interactions among, individual
parameters.
In contrast to field measurements, laboratory studies have the
advantages of being controllable and repeatable, allowing the isolation and
examination of the contributions of individual parameters. The convenience of
laboratory instrumentation enables the precise measurement of many parameters
such as wave height, current, sediment concentration, and their spatial and
temporal distribution patterns. The disadvantages of laboratory studies,
especially the three-dimensional physical models, are their substantially
reduced temporal and spatial scales and their limited capabilities of simulating
real-world situations even at small scales.
KAMPHUIS (1991a, b, c) conducted
a series of laboratory studies on longshore sediment transport. Irregular waves
ranging from 0.05 to 0.14m in significant wave height and 0.9 to 1.5s (one case)
in peak wave period were generated at 10 to 40 deg incident angles. Thirteen of
the 21 cases, or 62%, were conducted with waves having a peak period of 1.15s
(KAMPHUIS, 1991a). There is a gap between the coverage of laboratory longshore
transport measurements and field measurements, in terms of wave heights and
periods. The smallest waves encountered in field measurements are still much
higher than the highest waves in the laboratory measurements, with wave periods
much longer than the 1.15s. This gap raises the question of compatibility
between field and laboratory data and predictive relations developed using the
laboratory data. An overlap of wave conditions between field and laboratory data
would be valuable in examining the compatibility.
In an effort to challenge
the limitations of small scale and to bridge the gap between laboratory and
field measurements, the U.S. Army Engineer Research and Development Center
recently completed a Large-scale Sediment Transport Facility (LSTF). The LSTF is
specially designed for studies of longshore sediment transport (FOWLER et al.,
1995). The facility has the capability of simulating wave height and period that
are almost directly comparable to annual averages along many low-wave energy
coasts, for example, a majority of estuary beaches (NORDSTROM. 1992), and many
beaches along the Gulf of Mexico and the Great Lakes in the U.S. Detailed design
considerations, capabilities, and initial testing of the LSTF are described in
HAMILTON et al. (2001). This paper presents the results from the first phase of
the LSTF study.
Based on a series of laboratory studies and re-examination of
existing field data. KAMPHUIS (1991a) suggested an empirical formula for the
prediction of total longshore sediment transport rate, referred to as the
KAMPHUIS-91 formula in the following discussion. WANG et al. (1998a) found that
the KAMPHUIS-91 formula predicted consistently lower total longshore transport
rates than those predicted by the broadly used CERC formula (CERC, 1984) and an
earlier formula suggested by KAMPHUIS et al. (1986), referred to as the
KAMPHUIS-86 formula in the following. The lower prediction by the KAMPHUIS-91
formula, which is typically 1.5 to 3.5 times lower than predictions from the
CERC and KAMPHUIS-86 formulas, occurred over a range of low wave-energy
conditions with breaker height of less than 1m (WANG et al., 1998a). However,
the low predictions by KAMPHUIS-91 formula matched the measured values closer
than the CERC predictions for those low-wave conditions. On the other hand,
MILLER (1998, 1999) found that the predictions by the CERC formula matched storm
measurements with breaker height of nearly 4m closer than the KAMPHUIS-91
predictions, which were nearly one order of magnitude lower than the measured
rate.
Four types of breakers, including spilling, plunging, surging, and
collapsing, have been distinguished, largely based on visual observations
(PATRICK and WIEGEL. 1957; GALVIN, 1968; DEAN and DALRYMPLE. 1991; KOMAR, 1998).
As summarized in KOMAR (1998), a spilling breaker gradually peaks until the
crest becomes unstable and cascades down as "white water"--bubbles and foam. For
a plunging breaker, the shoreward face of the wave becomes vertical, curls over,
and plunges forward and downward, impinging onto part of the wave trough, with
the "white water" often penetrating the entire water column and impacting the
water-sediment interface directly. In surging breakers, the base of the wave
surges up the beach face so that the crest collapses and disappears. Collapsing
breaker is an intermediate condition between plunging and surging breakers. In
general, spilling breakers tend to occur on beaches of very gentle slope with
steep waves, while plunging breakers occur on steeper beaches with
intermediate-to low- steepness waves. Fine-scale laboratory studies indicated
that the characteristics of the turbulence generated under spilling and plunging
breakers were significantly different (TING and KIRBY, 1994, 1995, 1996).
Various criteria have been suggested to distinguish between the different types
of breaking (e.g., GALVIN, 1968; BATTJES, 1974). The criteria are typically some
form of a ratio between wave steepness and beach slope. SMITH and KRAUS (1991)
found that the presence of a bar could also influence the breaker type. Breaker
classifications tend to describe the end-member type. In reality, there is a
continuum of breaker type grading from one type to another. Also, describing the
breaking processes of irregular waves is difficult. There have been studies to
describe probabilities in wave breaking (THORNTON and GUZA. 1983; DALLY. 1990,
1992). These studies found that the commonly used Rayleigh distribution
describes the surf zone waves, which are composed of breaking and non-breaking
waves, well.
Numerous laboratory and field studies have found that suspended
sediment concentrations at the breaker line are strongly influenced by breaker
type (see the summary by VAN RIJN, 1993). Generally, sediment concentrations
measured under plunging breakers are significantly greater than that measured
under spilling breakers, given a similar breaker height (KANA, 1979; KANA and
WARD, 1980; NIELSEN, 1984; VAN RIJN and KROON, 1992; VAN RIJN, 1993). Since
sediment flux is the product of sediment concentration and current velocity, a
different sediment concentration should result in a different rate of sediment
transport given the same current velocity. Little is known about the influence
of the breaker type, and hence, different sediment concentrations, on the rate
and distribution pattern of longshore sediment transport.
The main objectives
of this first phase of the LSTF study were to investigate and quantify the
magnitude and distribution of longshore sediment transport under predominantly
spilling and plunging breakers. Two long-crested unidirectional irregular wave
conditions, one producing a predominantly spilling breaker and one a plunging
breaker, were investigated. The input waves were generated such that a similar
breaker height, but different breaker type, occurred. Wave height, longshore
current, depth-integrated longshore sediment flux, vertical profile of longshore
current, vertical profile of suspended sediment concentration, and the
cross-shore and longshore distribution patterns of all the above parameters were
measured.
METHODOLOGY AND INSTRUMENTATION
Detailed
discussions on the capabilities of the LSTF, as well as the procedures of
planning and executing longshore sediment transport measurements in the LSTF are
discussed in HAMILTON et al. (2001). The LSTF has dimensions of 30-m
cross-shore, 50-m longshore, and has walls 1.4m high (Figure 1). The
long-crested and unidirectional irregular waves were produced by four
synchronized wave generators oriented at a 10-deg angle to the shoreline. The
beach was arranged in a trapezoidal plan shape corresponding to the obliquely
incident waves. The beach is composed of approximately 150m[sup3] of very well
sorted fine quartz sand with a median grain size of 0.15mm. The sand beach was
approximately 25-cm thick over the planar concrete base and extended 27m
alongshore and 18m cross-shore, of which 15m were below still-water level and 3m
were above. The longshore current generated by the oblique incident waves was
circulated with 20 turbine pumps through 20 flow channels at the updrift and
downdrift ends. The influences of the lateral boundaries can be minimized by
properly circulating the wave-generated longshore current. Detailed procedures
to regulate the pumps for the longshore-current circulation are discussed in
HAMILTON and EBERSOLE (2001). Twenty 0.75-m wide and 6-m long bottom traps,
including 18 in the flow channels (except two of the most offshore ones) and 2
landward of the shoreline, were used to measure the depth-integrated longshore
sediment flux (Figure 1).
The LSTF hosts a suite of instrumentation. Details
on the capabilities and accuracy of the instrument are described in HAMILTON et
al. (2001). A brief summary of the instrumentation and sampling scheme specific
to this phase of the study is listed in Table 1. The sediment-flux measurements
using the downdrift bottom traps were conducted in 2 modes. Mode 1 consisted of
continuous weight sampling at a frequency of 4Hz during the wave run. Accuracy
of weight measurement during the wave run was influenced by vibration and
movement of the traps, which were forced by the wave motion. Mode 2 trap
measurements consisted of two discrete 100-s sampling periods before and after
the wave run. Accurate weights were obtained in quiescent water.
Wave height
and period were measured using capacitance wave gages sampling at 20Hz. The
Acoustic Doppler Velocimeters (ADVs) were used to measure current. The wave
gages and current sensors were co-located in the cross-shore direction. The wave
and current measurements were synchronized. The breaker angle was measured
visually using the digital compass in an electronic total station
transit.
Profiles of sediment concentration were measured using four arrays
of the innovative Fiber Optical Backscatter (FOBS) sensors. Each array consists
of 19 sensors. The vertical spacing of the sensors increased roughly
exponentially upward, ranging from a 1-cm spacing in the lower portion of the
array to a 6-cm spacing in the upper portion. The elevations of the FOBS sensors
are controlled by referring the sensors to the bottom one, which is deployed
directly on the bottom (HAMILTON et al., 2001). The FOBS sensors have a high
vertical resolution of 0.5cm (MILLER, 1999). The FOBS, which were recent
additions to the LSTF, were operated through a separate computer, independent of
the wave-current sampling system. There was an approximately 3-s delay of the
wave/current sampling relative to the sediment-concentration sampling.
Improvements are currently being made to synchronize the sediment concentration
and hydrodynamic measurements.
The beach profiles were surveyed using an
automated bottom-tracking profiler. The beach profiles were surveyed at 1-m
alongshore spacing in the middle of the test beach. A closer spacing of 0.5m was
used near the lateral boundaries to monitor the boundary influence. The profiler
was programmed to sample every 0.5cm in the cross-shore. This fine cross-shore
resolution allows measurements of bed ripples.
Transport measurements for
each of the wave conditions were conducted in segments. Eighteen test segments,
or wave runs, of 60- to 200-minute duration were conducted for the spilling case
and 13 segments of 40- to 100-minute duration were conducted for the plunging
case. Each segment was designed to focus on one of the following progressive
goals, with the final goal being acquisition of accurate and comprehensive
measurements of the longshore sediment transport rate and its cross-shore and
vertical distribution. The progressive goals listed in sequential order
included:
(1) obtain optimal settings for the pump-circulation system to
minimize boundary influence and circulate the longshore current;
(2) allow
the beach to reach equilibrium or stable shape;
(3) provide adequate sampling
coverage in the longshore and cross-shore directions;
(4) provide adequate
sampling coverage throughout the water column; and
(5) repeat key
measurements to ensure data quality and repeatability.
Each test segment
followed the same procedure to ensure data comparability. The procedure adopted
for each wave run was as follows:
(1) pre-run beach survey;
(2) pre-run
trap sampling (quiescent conditions);
(3) instrument check and
initialization;
(4) start sediment trap sampling;
(5) start longshore
current circulation;
(6) start waves;
(7) sampling of wave, current,
sediment concentration, and trap weight;
(8) stop waves;
(9) stop
longshore current circulation;
(10) wash sand off the traps' rubber seals
into the traps (HAMILTON et al., 2001);
(11) post-run sediment trap sampling
(quiescent conditions); and
(12) post-run beach survey.
Since the total
amount of longshore sediment transport during individual wave runs was only a
small fraction, less than 1%, of the total amount of approximately 150m[sup3] of
sand on the artificial beach, it was judged that continuous updrift sand
recharging during the wave runs was not necessary (HAMILTON et al., 2001). The
beach was typically replenished after 9 hours of wave activity for the spilling
case and after 3 hours for the plunging case. The wave basin was drained during
this operation. The purpose of the beach replenishment was twofold, to recharge
the sediment supply at the updrift end of the beach and to restore the beach to
one with straight and parallel contours. The replenishment was mostly
concentrated at the beach lying within 5m from the updrift boundary. The main
portion of the beach in the middle of the basin required little attention owing
partly to the uniform condition maintained by the longshore current circulation
system.
The principal temporal scale of this phase of the study was on the
order of 10 min, representing the averages of 400 waves (at peak period) during
the spilling case and 200 waves during the plunging case. It is generally
accepted that averages of 150 waves or more provide reliable representation
(NIELSEN, 1984; 1992). The main spatial scale was on the order of 0.75m, or the
width of the downdrift bottom traps. Parameters used in the present discussion
emphasized these particular temporal and spatial scales. Processes at finer
scales, such as temporal variations of currents and sediment concentrations at
the dominant wave frequencies, are discussed in another paper (WANG et al., in
review) and are beyond the scope of this paper.
WAVE AND BEACH CONDITIONS
THE INPUT WAVE CONDITIONS AND WAVE DECAY IN THE SURF
ZONE
Long-crested and unidirectional irregular waves with a
relatively broad spectral shape, representing typical sea conditions, were
generated. The broadly-used TMA spectrum (BOUWS et al., 1985) with the spectral
width parameter, gamma, set equal to 3.3 was used to define the incident wave
spectrum. Steep waves were generated to produce predominantly spilling breakers,
while low-steepness waves were generated to create predominantly plunging
breakers. The significant wave height (H[submo]) and peak wave period (T[subp])
were calculated using spectral analysis. A low-frequency cutoff at twice the
peak wave period, 3s for the spilling case and 6s for the plunging case, was
applied to ensure cross-shore compatibility. Energy at frequencies lower than
the cutoff represented a significant contribution to the overall energy near the
shoreline. This low-frequency motion, often referred to as the surf beat, might
have significant influence on the modulation of sediment transport in the
vicinity of the shoreline. It is beyond the scope of this paper to examine these
fine-scale processes.
The main breaker-line was located at about 13.1m from
the shoreline (gage 9, 2nd from offshore) for the spilling case (Figure 2). For
the plunging case, the main breaker-line was located at 11.6m (gage 8, 3rd from
offshore). Determination of the main breaker-line for irregular waves, and
therefore the breaker height, was somewhat subjective. In the present study, the
main breaker-line was determined to be at the location landward of which a
significantly accelerated rate of wave-height decay was measured (Figure 2).
This criterion was based on the comprehension that a dramatic wave-energy loss,
and therefore, wave-height decrease, should follow major wave breaking. Visual
observations during the wave runs supported use of this measure.
Similar
significant breaker heights of 0.26 and 0.27m were measured for the spilling and
plunging cases, respectively (Table 2). About 20 breaker angles were measured
during each of the segments of wave run after the beach reached a stable shape.
An overall average, from all the wave runs for each wave condition, was used to
represent the breaker angle. The average breaker angle for the spilling case was
6.5 deg with a standard deviation of 0.5 deg, or 8% of the mean. Similar average
breaker angle of 6.4 deg with a standard deviation of 0.6 deg, or 9%, was
measured for the plunging case. Except the very different forms of breaking, the
present two wave cases were characterized by similar breaker height and
angle.
A reasonable simplification of surf-zone longshore sediment transport
is to assume that sediment is being suspended by turbulence generated by
breaking waves and transported alongshore by the longshore current. Wave decay,
i.e., the decrease of wave height toward the shoreline, reflects the rate of
wave-energy dissipation. It is often assumed that a portion of the dissipated
wave energy is transferred to initiate sediment suspension. The faster the wave
energy is dissipated, the more the sediment is being suspended into the water
column, and hence the higher the longshore sediment flux. This approach has been
adopted to model the cross-shore distribution of longshore transport (BODGE,
1986; WANG, 1998).
The significant wave heights measured at the offshore most
wave gage, at about 2.5m from the wave generators, were rather similar, 0.26m
for the spilling case and 0.27m for the plunging case. The significant breaker
height measured for the spilling case was 0.26m, similar to the non-breaking
wave height measured at the offshore wave gage. The breaker height measured for
the plunging case was 0.27m, also similar to the non-breaking wave height
measured at the offshore gage. A sharp decrease of wave height was measured
directly landward of the main plunging breaker line, apparently related to the
dramatic wave-energy loss due to the turbulent plunging-type breaking. The wave
decay following the spilling breaking was much less dramatic. Rates of wave
decay in the mid-surf zone were rather similar for both the spilling and
plunging cases, as indicated by the similar wave height and similar cross-shore
trend of changing height (Figure 2).
Distributions of wave heights in the
alongshore direction were uniform during both the spilling and plunging cases.
During the spilling case, the alongshore variations, as indicated by one
standard deviation, at 11 transacts were mostly within 6% of the mean except at
the landward most gage, where 10% variation was measured (Figure 2). During the
plunging case, the alongshore variations measured at 4 transacts were less than
7% of the mean at all the gages. Due to much more active sediment transport
during the plunging case, the duration of each wave run was shorter than that of
the spilling case. The shorter wave runs resulted in less dense alongshore
sampling coverage during the plunging case than during the spilling case.
Maintaining satisfactory alongshore uniformity of both wave heights and
longshore current velocities is essential for accurate measurement of the
longshore transport rate.
The ratio of significant wave height to still water
depth, the breaker index, ranged mostly from 0.6 to 0.8 (Figure 2), similar to
the findings of other studies (KAMINSKY and KRAUS, 1994). A much greater value
was measured at the plunging breaker line, where the ratio reached almost 1,
followed by a sharp decline to slightly less than 0.6. The rapid increase of the
H[submo]/h ratio in the plunging breaker zone was caused by the sharp
water-depth decrease toward the bar crest while the wave height remained nearly
constant. A similar trend of landward increasing of the H[submo]/h ratio, from
slightly below 0.6 to nearly 0.8. was measured in most of the surf bore area for
both the plunging and spilling cases. This suggested that the rate of
wave-height decay toward the shoreline was slower than the rate of the
water-depth decrease. A rapid decrease of wave height was measured near the
shoreline during the spilling case, resulting in a sudden decrease of the
H[submo]/h ratio (Figure 2). The reason for this sudden wave-height decrease was
not clear, and this change did not occur during the plunging-breaker
case.
BEACH CONDITIONS
The 25-cm thick test beach
was initially constructed based on the equilibrium shape described by BRUUN
(1954) and DEAN (1977) in the form of
h = Ax[supm] (1)
where h is the still-water depth, x is the horizontal distance from the
shoreline. A is a dimensional scale parameter determined by sediment grain size,
and m is the empirical shape coefficient. The m value of 2/3 was used based on
DEAN (1977). For the present experiments, the A value was found to be 0.07 from
the sediment grain size based on DEAN (1991). The beach profile calculated using
Equation (1) was approximated with 3 planar beach segments for the convenience
of construction.
The test beach was composed of very well sorted quartz sand
with a median grain size of 0.15mm. Based on HALLERMEIER (1981), the terminal
settling velocity of this sand was calculated to be 1.8cm/s. A porosity of 0.4
was used to convert between weight transport rate and volume transport rate. A
relation between sediment suspension and wave orbital motion can be reflected in
the commonly used DEAN number, N[subo], defined as (DEAN, 1973)
N[subo] = H[subo] / wT (2)
where w is the sediment settling velocity, T is wave period, and H[subo] is
deep-water wave height, which can be calculated from the design wave conditions
using linear wave theory. The DEAN number was found to be 10.0 and 4.4 for the
spilling and plunging cases, respectively.
After a certain number of hours of
wave action, the beach profile reached stable, or equilibrium, shape. The
equilibrium profiles for the spilling and plunging cases are shown in Figure 3.
These profiles represent averages of 16 profiles in the middle section of the
test beach. In Figure 3 and the following relevant figures, the x-axis was
referred to the still-water shoreline of the initial constructed beach, which
was designed to be 3m from the basin wall. Overall, alongshore-averaged
shoreline changes measured during the 2 cases were small, generally less than
0.15m. Shoreline retreat was measured during the spilling case owing to the
steep erosive waves. The shoreline position was stable during the plunging
case.
The spilling-breaker experiment was conducted with the constructed
beach as the initial condition. Modest change of the beach-profile shape was
measured during the spilling breaker case, as compared to the original
power-function profile of Equation 1 (Figure 3). The inner surf zone was eroded
and modest and broad accumulation occurred in the vicinity of the breaker line.
The mid-surf zone from 5 to 9m from the shoreline remained remarkably stable.
The sand eroded from the inner surf zone was transported to and accumulated in
the vicinity of the breaker line. The beach reached stable shape after 14 hours
of wave action for the spilling breakers.
The plunging case was conducted
using the equilibrium beach conditions generated by the spilling breakers as the
initial profile. Considerable shape changes were measured for the plunging
breaker case, mainly in the vicinity of the plunging point, where a substantial
break-point bar developed (Figure 3). The equilibrium process took only 4 hours
for the much more energetic plunging breakers. Most of the changes occurred in
the vicinity of the plunging breaker line, while profile changes in other parts
were relatively minor. It is beyond the scope of this paper to examine the
detailed process of beach-profile evolution toward equilibrium. It was judged
that the beach reached equilibrium when the apparent trend of change measured
from the beginning of the wave run stopped or significantly slowed. In other
words, the equilibrium beach conditions were characterized by minor trendless
variations of profile shape instead of the progressive evolution toward the
stable shape as observed during the early hours of wave action. The steep toe of
the test beach, as limited by the dimensions of the wave basin, might have some
influences on wave breaking as compared to gentle beaches in the real
world.
Figure 4 shows examples of individual profiles (not averaged) surveyed
during the spilling and plunging experiments. Bed ripples were observed over the
entire surf zone under the spilling breakers except in the vicinity of the
shoreline (Figure 4). Most of the ripples were 0.7 to 1.2cm high and 6 to 10cm
long. Under the plunging breakers, ripples were measured in the middle of the
surf zone, while in the vicinity of the breaker line and shoreline, a relatively
featureless bed was observed. Most of the ripples were 1.0 to 1.5 cm high and 8
to 12cm long (Figure 4). For the convenience of discussion, the commonly used
nearshore zonation is divided as follows. The swash zone ranged from the
landward limit of uprush, seaward to the start of the planar bed, which roughly
coincides with the seaward limit of the backwash (Figure 4). For the spilling
case, the swash zone extended from 0.5m to -0.9m. For the plunging case, it
extended from 0.9m to -1.1m, about 43% wider than the spilling case. The breaker
zone ranged from 10 to 13m for the plunging case and 11 to 14m for the spilling
case (Figure 4). The mid-surf zone lies between the swash and breaker zones,
ranging from 0.5 to 11m for the spilling case and 0.9 to 10m for the plunging
case. Bed ripples were largely absent in the breaker zone for the plunging
breaker case. The relatively large bedforms on the seaward slope of the
breakpoint bar were irregular in orientations and different from the largely
shore-parallel bed ripples landward of the bar.
RESULTS AND DISCUSSION
LONGSHORE CURRENT
The current was measured
using the array of 10 ADVs mounted at the same cross-shore locations as the wave
gages (Figure 1, Table 1). The vertical current profiles were measured by
positioning the sensors at different elevations in the water column (HAMILTON et
al., 2001). Present and previous studies in the LSTF (HAMILTON and EBERSOLE,
2001) have shown that the depth-averaged longshore current can be represented
reasonably well by the velocity measured at an elevation of 1/3 water depth from
the bottom. In the following discussion, the depth-averaged velocity is
represented by a point measurement at this elevation in the water
column.
VERTICAL PROFILE OF LONGSHORE CURRENT
The
vertical current profile was measured by positioning the sensor at a different
water level during each 10-min sampling event. Therefore, a time difference of
approximately 15min (10min for sampling and 5min for positioning the bridge and
sensors) exists among the vertical measurements. Given that the wave and beach
conditions remained largely constant through the wave runs, especially after the
beach profile reached equilibrium, this time delay should not induce any
significant uncertainties in the measurement of current profiles. Details on the
measurement of velocity profiles are discussed in HAMILTON and EBERSOLE (2001)
and HAMILTON et al. (2001). The present discussion is focused on time-averaged
values over the 10-minute sampling interval.
Due to the lack of both field
and laboratory data, relatively little is known about the longshore-current
profile throughout the water column, especially near the bottom. Based mainly on
mathematical derivation and verified with limited laboratory data, DEIGAARD et
al. (1986) suggested that surf zone longshore current is relatively uniform
throughout the water column except in the immediate vicinity of the bottom.
SVENDSEN and LORENZ (1989) determined analytical expressions for vertical
varying longshore current for a long straight coast. Longshore-current profiles
measured in the LSTF over a fixed concrete bed confirmed a homogeneous profile
over much of the water column (HAMILTON and EBERSOLE, 2001).
The overall
shape of the longshore-current profile measured over the movable fine sand bed
was not homogeneous as derived mathematically and measured over the fixed
concrete bed. Logarithmic longshore-current profiles, with increasing velocity
with increasing elevation from the bed, were measured at all the cross-shore
locations under both the spilling and plunging breakers (Figure 5). The shape
and magnitude of the longshore current profile were rather similar under both
the spilling and plunging breakers. This seems to indicate that the breaker
types do not have significant influence on the vertical longshore current
structure in the surf zone. The similar longshore current was probably
controlled by similar breaker height and breaker angle (Table 2). The bottom
boundary layer over the movable bed with bed forms (except at the plunging
breaker line) should be thicker than that over the relatively smooth concrete
bed. This might contribute to the upward increasing velocity profile.
ALONGSHORE UNIFORMITY OF LONGSHORE CURRENT
As
discussed in VISSER (1991) and HAMILTON and EBERSOLE (2001), maintaining
alongshore uniformity of the longshore current is critical in minimizing the
boundary disturbance and producing the most accurate measurement of longshore
transport rate. It was necessary to accurately circulate the wave-generated
longshore current with pumps to maintain longshore uniformity. Detailed
procedures for examining the degree of longshore uniformity in longshore
currents are discussed in HAMILTON and EBERSOLE (2001). After a series of
iterations, a reasonably uniform longshore current pattern was achieved. The
magnitudes and cross-shore distribution of longshore-current velocity measured
at different alongshore locations over the middle 15-m test section of the wave
basin were rather similar (Figure 6), indicating a uniform condition alongshore.
Throughout most of the surf zone, the longshore currents generated by the
circulation pumps are in good agreement with currents generated by the oblique
incident waves (Figure 6).
CROSS-SHORE DISTRIBUTION OF LONGSHORE
CURRENT
Because the suspended sediment is transported alongshore
by the longshore current, the cross-shore distribution of longshore current has
a significant influence on the patterns of longshore sediment transport. The
cross-shore distribution of longshore current for both the spilling and plunging
cases are illustrated together in Figure 7. The cross-shore pattern plotted in
Figure 7 represents the average of measurements from the alongshore transacts
shown in Figure 6.
Slightly greater longshore current was measured in the
breaker zone from 10 to 13m for the plunging case than the spilling case (Figure
7). At the main spilling breaker line at around 13m, the longshore current was
relatively weak. A rapid increase was measured immediately landward of the
breaker line. A weak longshore return current (toward the updrift end of the
facility) was measured at the seawardmost ADV, indicating some re-circulation in
the basin. HAMILTON and EBERSOLE (2001) discussed in detail the procedures of
minimizing the return flow via optimal pump settings. The longshore current in
most of the surf-bore area remained rather constant at about 10 to 12 cm/s
during both spilling and plunging cases.
Two subtle peaks were measured
during both the spilling and plunging cases (Figure 7). For the spilling case,
one peak was measured just landward of the breaker zone and one just seaward of
the swash zone. For the plunging case, the seaward peak was located slightly
seaward of the peak for the spilling case and was inside the presently defined
breaker zone. Bi-model or broad cross-shore distribution patterns of longshore
current have been measured in the field by KRAUS and SASAKI (1979) and SMITH et
al. (1993). These patterns are quite different from the predictions from the
simple analytical model of LONGUET-HIGGINS (1970) for regular waves, which
predicts the peak longshore current just landward of the breaker line over a
plane beach. Some recent numerical models such as those of KRAUS and LARSON
(1991), SMITH et al. (1993), SLINN et al. (2000) are capable of incorporating
more complicated bottom profile and reproducing more complicated distribution
patterns. Due to the shallow and 100% variation of water depth in the swash
zone, current velocities could not be measured in this zone. However, dye
observations indicated strong longshore current, which was comparable to that
measured at the landward most current meter.
Overall, the differences in
magnitudes and patterns of longshore current between the spilling and plunging
cases were relatively minor. These, together with the similar longshore-current
profiles throughout most of the surf zone (Figure 5), indicate that different
breaker types did not significantly change the characteristics of longshore
current. The similar breaking wave height, angle, and wave-decay patterns may be
the dominant factors. Under both cases, peak longshore current was measured at
the landward-most gage just seaward of the swash zone. The reason for the
slightly greater longshore current measured near the shoreline during the
plunging case than during the spilling case was not clear. The swash zone, i.e.,
the zone of up- and down-rushing, was wider during the plunging case.
SUSPENDED SEDIMENT CONCENTRATION
For the
convenience of discussion, the suspended sediment is defined here as all the
particles that are in motion above the bed level, regardless of whether or not
the sediment is in frequent contact with the bed. This should not be confused
with the commonly used concepts of bedload and suspended load, which are
theoretically distinguished based on the frequency of the particles' contact
with the bed. The concepts of bedload and suspended load are helpful in
understanding the modes of sediment movement. Practically, they cannot be
measured separately. The suspended sediment referred to here should contain the
entire suspended-load and the portion of the bed-load that was not rolling on
the sediment surface. The following discussion is focused on the characteristics
of the time-averaged sediment concentration over the 10-min sampling
interval.
The overall magnitudes and shapes of the suspended sediment
concentration profile are significantly different in the breaker zone for the
spilling and plunging cases (Figure 8). Similar suspended sediment
concentrations were measured within 3cm from the bed during both the spilling
and plunging cases. Above 5cm from the bed, the suspended sediment concentration
in the breaker zone was more than one order of magnitude greater during the
plunging case than during the spilling case. Under the plunging breakers, the
sediment concentration remained fairly constant throughout the water column from
5cm to nearly 35cm above the bed, ranging from 1 to 3g/l. This seems to indicate
that the strong turbulent mixing under the plunging breakers dominated the
settling of the fine sand particles. This nearly homogeneous sediment suspension
was not measured under the spilling breakers. The rapidly decreasing
concentration with elevation above the bed indicates that vertical mixing under
the spilling breakers was not strong enough to suspend significant amounts of
sediment high into the water column.
The similar sediment concentrations
measured within 3cm from the bed at the spilling and plunging breaker line were
puzzling, given the very different hydrodynamic and bottom conditions. Almost
identical near-bed sediment concentrations were also measured by NIELSEN (1979),
and summarized in NIELSEN (1992, p. 219), for non-breaking waves and spilling
breakers. A conclusion was drawn that except for extreme case of plunging jet
hitting the bed, the pickup rate at the bed and hence the near-bed sediment
concentration was not affected by the spilling breaking. NIELSEN (1992) further
concluded that the main effect of the turbulence from wave breaking is a
vertical stretching of the concentration profile, i.e., much greater
concentration high in the water column. Our data from the LSTF indicated that
even when the plunging jet was hitting the bed, the near-bed sediment
concentrations were still remarkably similar. Almost identical near-bed
concentrations were also measured by BOSMAN (1982), and summarized in VAN RIJN
(1993, p. 8.18-8.19), under non-breaking waves, spilling breakers, and plunging
breakers. BOSMAN (1982) used direct pump-suction samplers over a flat bed in the
vicinity of the breaker line. No interpretation for the "approximately constant"
near-bed concentrations was provided.
The shapes of the suspended sediment
concentration profiles in the mid-surf zone, from about 1 to 9m from the
still-water shoreline, were similar during the plunging and spilling cases
(Figure 9). A slightly greater sediment concentration was measured during the
spilling case than during the plunging case. This is consistent with the similar
wave conditions measured in the surf-bore area (Figure 4). This also indicates
that the cross-shore mixing of the active sediment suspension from the plunging
breaker line at about 12m was limited to the narrow breaker zone between 10 to
13m and did not have significant influences on concentrations in most of the
mid-surf zone. The suspended sediment concentration decreased rapidly with
increasing elevation from the bed, indicating limited vertical mixing under the
surf bore.
Active sediment movement was observed in the swash zone, mostly in
a sheet flow mode, as reflected by the planar bed. The turbidity sensors could
not function properly in the very shallow water with depth variation of 100%.
Overall, the influences of breaker types on sediment suspension were limited in
the vicinity of the breaker line. Lateral mixing did not seem to play a
significant role in sediment suspension throughout the entire surf zone.
SEDIMENT FLUX
Depth-integrated longshore
sediment flux was measured by the 20 bottom traps at the downdrift end of the
wave basin. The traps are 0.75m wide and provide precise measurements of the
total sediment flux across this width. A disadvantage of the bottom traps is
that they cannot provide information on the vertical distribution of the
longshore sediment flux through the water column.
Sediment flux can also be
calculated from the sediment concentration and current measurements. By
definition, sediment flux, F(x, z, t), is the product of sediment concentration,
c(x, z, t), and particle velocity v(x, z, t),
F(x, z, t), = c(x, z, t), × v(x, z, t), (3)
where t is time, and x and z are cross-shore and vertical coordinates,
respectively. Because the sediment concentration and current measurements were
not exactly synchronized, the instantaneous sediment flux could not be
calculated from Equation 3. In the following, v(x, z) and c(x, z) values
averaged over the 10-min sampling interval were used to estimate a time-averaged
sediment flux. This simplification is acceptable if either longshore current or
sediment concentration is reasonably steady over time. Sediment concentration
varied greatly with time, dominated by the sediment suspension events that
typically followed the breaking of high waves. Detailed temporal variations of
sediment concentration and current and their relations are discussed in WANG et
al. (in review).
Figure 10 illustrates two examples of the temporal
variations of longshore current. For the spilling case (Figure 10, upper panel),
the standard deviation of the temporal average of the longshore current velocity
was 4.9cm/s, or about 38% of the mean. A slightly greater variation of 54% of
the mean was measured during the plunging case (Figure 10, lower panel). In
addition to this reasonably steady longshore current, WANG et al. (in review)
found that the temporal variations of longshore current and sediment
concentration seemed to be random relative to each other without any regular
phase-angle difference. Based on the above analyses, WANG (et al., in review)
suggested that the product of time-averaged sediment concentration and longshore
current should provide a reasonable estimate of longshore sediment flux.
VERTICAL DISTRIBUTION OF SEDIMENT FLUX
The
vertical profiles of sediment flux discussed in this section were calculated
based on Equation 3 using time-averaged sediment concentration and longshore
current. Realizing that the neglected contributions from time-variant portions
could not be quantified, the present discussion focuses on the trends of the
profiles and comparative magnitudes. Precise depth-integrated sediment flux, or
the total sediment transport rate per unit width, was measured at the downdrift
bottom traps. Within 3cm from the bed the measurements of sediment concentration
and longshore current were conducted at the same levels, at 1-cm intervals.
Minor differences (typically less than 3cm) in measurement levels existed in the
upper portion of the water column. Since the vertical gradient of sediment
concentration was much greater than that of the longshore current, the longshore
current was linearly interpolated to match the levels of the sediment
concentration measurements.
In the breaker zone, the longshore sediment flux
above 5cm from the bed was approximately one order of magnitude greater during
the plunging case than during the spilling case (Figure 11). This was controlled
by the much greater sediment concentration (Figure 8), because the
longshore-current profiles were similar (Figures 5 and 7). The longshore
sediment-flux profile under the plunging breakers was fairly homogeneous
throughout the water column above 5cm from the bed. The relatively mild
upward-decreasing sediment concentration was compensated by the
upward-increasing longshore current. Under the spilling breakers, sediment flux
decreased with distance above the bed, dominated by the rapid upward-decreasing
sediment concentration. Under the plunging breakers, the longshore sediment flux
throughout the entire water column at the breaker line (at 11.6m from the
shoreline) was consistently less than the flux immediately landward (at 10.1m).
This was because the longshore current at the breaker line was smaller than that
immediately landward (Figure 7).
In the mid-surf zone, slightly greater
sediment flux was measured during the spilling breaker case than during the
plunging breaker case (Figure 12). This was caused by the slightly greater
suspended sediment concentration measured in the surf-bore area during the
spilling case (Figure 9). Except in the vicinity of the plunging breaker line,
the majority of sediment transport occurred close to the bed. This is because
the sediment concentration was one or two orders of magnitude greater near the
bed, overcoming the weaker near-bottom longshore current. For the present 2
cases, over 75% of the total longshore sediment flux occurred within 5cm from
the bed in the mid-surf zone. However, at the plunging breaker line at 11.6m,
only 29% of the total longshore flux occurred within 5cm from the bed, and over
70% of the longshore flux occurred high in the water column. The near-bed
longshore flux increased to 46% of the total immediately landward of the
plunging breaker line at 10.1m from shoreline. At the spilling breaker line, 73%
of the total longshore flux occurred within 5cm from the bed, similar to the
surf-bore area.
CROSS-SHORE DISTRIBUTION OF LONGSHORE SEDIMENT
FLUX
The depth-integrated longshore sediment flux over a 0.75m
cross-shore section of the beach measured at the downdrift traps is used here to
discuss the cross-shore distribution patterns. The trap measurements are direct
and accurate. The cross-shore distribution patterns of the depth-integrated
longshore sediment flux were quite different during the plunging and spilling
cases (Figure 13). The cross-shore distribution of longshore sediment transport
was far from being uniform. For the spilling case, the peak longshore transport
was measured in the swash zone. Two transport peaks, one in the swash zone and
one in the breaker zone, were measured during the plunging case.
For both
cases, significant sediment transport was measured in the swash zone. The swash
zone is characterized by a planar bed regime, as compared to the rippled
surf-bore area (Figure 4). The planar bed was apparently generated by the
extremely active interaction between the up- and down-rush and the bottom
sediment. For the spilling case, about 27% of the total longshore sediment
transport occurred in the narrow swash zone (Figure 13). The 1.4-m (0.5 to
-0.9m) width of the swash zone was approximately 10% of the total surf-zone
width of 14.0m (including 0.9m landward of the still-water shoreline reached by
the uprush). For the plunging case, about 34% of the total longshore sediment
transport occurred in the swash zone, which was approximately 15% (0.9 to -1.1m)
of the total surf-zone width of 13.1m (including 1.1m landward of the
still-water shoreline reached by the uprush). A substantial amount of longshore
sediment transport occurred landward of the still-water shoreline, especially
during the plunging case. The peak longshore flux was measured in the trap just
landward of the still-water shoreline (Figure 13). Nearly 28% of the total
longshore sediment transport occurred landward of the still-water shoreline
during the plunging case. During the spilling case, less than 5% of the total
transport was trapped landward of the still-water shoreline. Visual observations
during the experiments indicated that the uprush was much more active during the
long-period plunging case than that during the spilling case. This was probably
responsible for the much greater sediment flux above the still-water
shoreline.
Active sediment transport in the swash zone was also observed in
several field and laboratory studies (KRAUS et al., 1982; BODGE and DEAN, 1987;
KRAUS and DEAN, 1987; KAMPHUIS, 1991a; WANG, 1998). Instantaneous sediment
concentrations of up to 110 g/l, far greater than that in any other portions of
the surf zone, have been measured by ZAMPOL and INMAN (1989) in the swash zone.
The swash zone usually has the coarsest sediment as compared to that on the dry
beach and in other parts of the surf zone (DAVIS et al., 2000). One explanation
of the coarse swash zone sediment is that fine grains are being moved away by
the active transport leaving the relatively coarse sediment on the bed (WANG et
al., 1998b). Little is known about quantitative swash zone processes. The main
obstacle is the technical difficulty of conducting accurate measurements in this
dynamic narrow zone with 100% variation of water depth. This is an area of
continued research at the LSTF.
A substantial and relatively broad peak of
longshore sediment flux was measured in the vicinity of the plunging breaker
line (Figure 13). This peak was related to the active sediment suspension
throughout the entire water column induced by the turbulent plunging-type
breaking. Nearly 35% of the total longshore sediment transport occurred in the
3-m wide breaker zone from 10 to 13m. This zone represented 23% of the total
surf-zone width of 13.1m. Combined with the swash-zone peak, nearly 70% of the
total longshore transport occurred in the breaker and swash zones. These two
areas together occupied less than 40% of the total surf zone width. Active
sediment suspension and transport in these two zones are also indicated by the
planar bed regime. In the swash zone, the planar bed was caused by active sheet
flow motion. At the plunging breaker line, the planar bed seemed to be induced
by a combination of the sheet flow and strong turbulence, which also resulted in
active sediment suspension high into the water column. No transport peak was
measured at the spilling breaker line.
Similar magnitude and distribution
pattern of the longshore sediment flux were measured in the mid-surf zone for
both the spilling and plunging cases (Figure 13). The similar sediment fluxes
are consistent with the similar distribution patterns of wave height and decay
(Figure 2) and longshore current (Figure 7) in the mid-surf zone. These indicate
that the breaker types did not have significant influence on the surf bore
dynamics in the mid-surf zone. A gradual trend of increasing sediment flux
toward the shoreline was measured. According to the energy-dissipation model of
DALLY et al. (1985), an increasing ratio of breaker height to water depth
(Figure 4) would result in an increased rate of energy dissipation, which could
contribute to the increasing magnitude of longshore sediment flux toward the
shoreline. The dynamics and energy dissipation of spilling breakers and surf
bores are described reasonably well by the surface roller theory (SVENDSEN,
1984a, 1984b). Both these models were developed based on the understanding of
the spilling type of breaking. Considerable modifications may be necessary to
adopt these models to describe plunging breakers.
TOTAL RATE OF SURF-ZONE LONGSHORE SEDIMENT
TRANSPORT
The total rate of longshore sediment transport in the
surf zone is an important and commonly used parameter in coastal research and
engineering projects. One of the goals of the LSTF is to improve the accuracy of
predictions of the total rate of longshore transport (FOWLER et al., 1995). A
commonly used tool for predicting the total rate of longshore transport is the
CERC formula (CERC, 1984)
I[subl] = K[subl] / 16[root]{Begin Greek}gr{End
Greek}g[sup3/2]H[sup5/2[sub[subsb]sin(2theta[subb]) (4)
where I[subl] is the
submerged-weight transport rate, gamma is the breaker index, often taken to be
0.78, rho is the density of the water, g is gravitational acceleration, H[subsb]
is significant breaking wave height, theta[subb] is wave breaker angle, and
K[subl] is an empirical coefficient. Based on the original field study by KOMAR
and INMAN (1970), the Shore Protection Manual (CERC, 1984) recommended a K[subl]
value of 0.39. BODGE and KRAUS (1991) re-examined the derivation and suggested a
lower K[subl] value of 0.32. SCHOONEES and THERON (1993, 1994) re-examined the
46 most reliable of the 240 existing field measurements that have been compiled
to determine a K[subl] value of approximately 0.41. The physical foundation of
the CERC formula is that the rate of sediment transport is proportional to a
measure of the wave-energy flux.
Based on similar field data, KAMPHUIS et al.
(1986) developed an empirical formula, which includes the beach slope and
sediment grain size
Q = 1.28(H[sup3.5[sub[subsb]m) / (d)sin(2theta[subb]) (5)
where d is sediment grain size, and m is beach slope. With additional
laboratory study and further analysis of the existing field data, KAMPHUIS
(1991a) modified the 1986 formula, adding the influence of peak wave period,
T[subp]
Q = 6.4 ×
10[sup4]H[sup2[sub[subsb]T[sup1.5[sub[subp]m[sup0.75]d[sup-0.25]sin[sup0.6](2thetab])
(6)
The Q in Equation 6 is the total volume transport rate in the units of
m[sup3]/yr. It is noted that the dependence on grain size and wave height were
greatly reduced in the newer Equations 6 as compared to Equation 5. The
influences of beach slope and incident wave angle were also reduced. The
coefficients in the above forms of KAMPHUIS-86 and -91 formulas were determined
using metric units.
KRAUS et al. (1988) adopted a different approach as
compared to those above, which assume a proportionality between longshore
transport rate and longshore wave-energy flux. KRAUS et al. (1988) assume that
the total rate of longshore sediment transport in the surf zone is proportional
to the longshore discharge of water:
Q [varies] K[subd](R - R[subc]) (7)
where K[subd] is an empirical coefficient that may relate to sediment
suspension, R[subc] is a threshold value for significant longshore sand
transport, and R is called the discharge parameter and is proportional to the
average discharge of water moving alongshore. In the LSTF, R is accurately
measured. In the field, R can be calculated as
R = nV[subls]x[subb]H[subb] (8)
where n is a constant, V[subls] is the average longshore current velocity,
x[subb] is the surf-zone width, and H[subb] is the breaker height. Based on
field data collected using streamer sediment traps at Duck, North Carolina,
KRAUS et al. (1988) suggested a K[subd] value of 2.7 and R[subc] value of
3.9m[sup3]/s.
In the LSTF, the total rate of longshore sediment transport was
obtained by simply summing the sediment flux measured at all the traps. The
total rate measured during the spilling case was 2,660m[sup3]/yr, substantially
less than the total rate of 7,040m[sup3]/yr measured during the plunging case.
The breaking wave was about 4% higher during the plunging case, 0.27m versus
0.26m during the spilling case (Table 2). Despite the slightly lower waves
generated at the wave board, the more significant shoaling of the long-period
waves resulted in slightly higher breakers. The 4% higher breaker could not
explain the fact that measured total longshore sediment transport rates differed
by a factor of 2.65. The much more active sediment suspension under the plunging
breakers and the greater transport in the wider swash zone apparently
contributed to the greater rate of total transport.
The measured total
transport rates were substantially lower than the predictions from the CERC
formula (Equation 4) and the KAMPHUIS-86 formula (Equation 5) for both the
spilling and plunging cases (Table 3). The KAMPHUIS-91 (Equation 6) formula, on
the other hand, under-predicted the measured rates for both cases. The empirical
K[subl] value of 0.39 as recommended by the Shore Protection Manual (CERC, 1984)
was used in Equation 4.
The CERC formula over-predicted the total rate for
the spilling condition by over 700%, while for the plunging breakers; the
over-prediction was less than 250%. This inconsistency of the CERC formula under
different breaker types indicates that a simple reduction (or increase) of the
K[subl] value as examined by BODGE and KRAUS (1991), SCHOONEES and THERON (1993,
1994), and WANG et al. (1998a) cannot completely solve the problem. In other
words, the comprehension that the total rate of longshore sediment transport is
proportional to a measure of the longshore wave-energy flux at the main breaker
line might not be complete. The KAMPHUIS-86 formula also had a similar
inconsistency. The spilling case was over-predicted by more than 300%, while the
plunging case was over-predicted by less than 30%.
By incorporating wave
period to a power of 1.5, the KAMPHUIS-91 formula produced more consistent
predictions for the different breaker types, as compared to the measured values.
Wave period, which is linked to the wavelength through the dispersion relation,
has significant influence on wave steepness and hence breaker type. Wave period
also seems to have considerable influence on the range of up-rush and down-rush,
which in turn influences the transport rate in the swash zone. The KAMPHUIS-91
formula under-predicted the spilling and plunging cases by 17% and 24%,
respectively. The consistent under-prediction, if confirmed with more data, can
be resolved by adjusting the empirical coefficient.
Different comprehension
and parameterization were used in the KRAUS et al. (1988) formula. The threshold
value R[subc] of 3.9m[sup3]/s, which was determined from an Atlantic Ocean surf
zone, is too large for application in the laboratory beach. Since the main
purpose of the present comparison is to examine the consistency of predictions
for different breaker types, and also because little is known about the factors
controlling R[subc], this parameter is ignored here. The recommended K[subd]
value of 2.7 is still used. The longshore discharge was measured directly in the
LSTF through the circulation pumps (HAMILTON and EBERSOLE, 2001). It was not
necessary in this case to use Equation 8 to calculate the total discharge.
Predictions from the KRAUS-88 formula are also compared in Table 3. The
predicted value compared well with the spilling case, but under-predicted the
plunging case by 55%. As discussed in KRAUS et al. (1988), the coefficient
K[subd] is related to sediment suspension. Based on discussions in the previous
sections, sediment suspension in the vicinity of the spilling and plunging
breaker lines was substantially different. The inconsistency in the prediction
using the method of KRAUS et al. (1988) was caused by neglecting the different
magnitudes of sediment suspension and using a constant K[subd] value. The
K[subd] value for plunging breakers should be greater due to the much more
active sediment suspension. Similar to the situation encountered by using the
KRAUS-88 formula, the inconsistency of the CERC formula and KAMPHUIS-86 formula
probably arose for a similar reason. The significantly improved consistency of
the KAMPHUIS-91 formula was likely caused by the incorporation of wave period,
which has significant influence on the breaker type and swash transport.
CONCLUSIONS
In the vicinity of the breaker
line, sediment suspension was much more active under the plunging breakers than
under spilling breakers. High in the water column, at elevations greater than
5cm from the bed, suspended sediment concentration was more than one order of
magnitude greater under the plunging breakers than under spilling breakers of
similar breaking wave height. The greater sediment suspension was apparently
related to the much more turbulent plunging-type breaking, as also reflected in
a steep rate of wave-height decay immediately following the breaking of the
plunging waves. This substantial difference was not measured in the mid-surf
zone dominated by surf-bore motions, where slightly greater suspended sediment
concentrations were measured under the spilling breakers. The surf-bore motions
seemed to be independent of the breaker type.
Cross-shore distribution of the
depth-averaged longshore current, as well as the vertical profile of the
current, was not significantly influenced by breaker type. Similar vertical
profile and depth-averaged longshore current were measured during the spilling
and plunging breakers. These were probably controlled by the similar breaker
height and angle, and the cross-shore pattern of wave decay. During both the
spilling and plunging cases, the peak longshore current was measured just
seaward of the swash zone at the landward-most current meter 1.1m from the
still-water shoreline. Longshore current in the swash zone could not be measured
due to the shallow water with 100% depth variation. Visual observations of dye
movement indicated that longshore current in the swash zone was of the similar
magnitude as that measured at the landward-most current meter. A subtle
secondary peak was evident just shoreward of the main breaker line in both
cases.
Influenced by the different suspended-sediment concentrations, the
total rate and cross-shore distribution of longshore sediment transport were
significantly different during the plunging and spilling cases. Nearly 170% more
longshore sediment transport was measured for the plunging-breaker case than for
the spilling-breaker case, although the plunging-breaker height was only 4%
higher than the spilling-breaker height. The cross-shore distribution of
longshore sediment transport was far from being uniform. During the
spilling-breaker case, peak longshore transport was measured in the swash zone.
During the plunging-breaker case, two transport peaks were measured, one in the
swash zone and one in the vicinity of the breaker line. Substantial amounts of
longshore sediment transport were measured in the swash zone during both cases.
Interestingly, in the mid-surf zone dominated by surf-bore motions, the measured
transport rates were rather similar for both the spilling and plunging cases. In
other words, the much greater rate of total longshore transport measured for the
plunging case than for the spilling case was mainly contributed by the much more
active sediment suspension and transport in the breaker zone and more transport
in the wider and more active swash zone.
The commonly used CERC formula
predicted inconsistent total longshore sediment transport rate under the
spilling and plunging breakers. It may be necessary to adjust the empirical
K[subl] for different breaker types. By including wave period, which has
significant influence on breaker type, the KAMPHUIS-91 formula produced
consistent predictions for both the spilling and plunging cases, although
underestimated by about 20%. Results from the present study suggest that breaker
type has a significant influence on the total rate of longshore sediment
transport and its cross-shore distribution pattern. Parameterization of
predictive formulas should include factors that reflect the breaker type.
In
terms of breaker height and angle, the two most commonly used parameters in
predicting longshore sediment transport rate in the surf zone, the present
laboratory data are directly comparable to some of the field measurements under
low-wave energy conditions. Although not directly examined in this paper,
valuable knowledge could be learned through a comparison of laboratory and field
data.
ADDED MATERIAL
Ping Wang#, Ernest R. Smith##, and Bruce A.
Ebersole##
# Department of Geology
University of South Florida
Tampa,
FL 32620
U.S.A.
## U.S. Army Engineer Research and Development
Center
Coastal and Hydraulic Laboratory
3909 Halls Ferry
Road
Vicksburg, MS 39180
U.S.A.
ACKNOWLEDGMENTS
David Hamilton, William
Halford, David Daily, and Tim Nisley provided technical support for this study.
We thank Carl Miller and Reggie Beach for providing the FOBS sensors. The paper
benefited greatly from the constructive reviews by Dr. Mark Schmeeckle, Dr. Jane
Smith, and an anonymous reviewer. Ping Wang is jointly funded by the U.S. Army
Engineer Research and Development Center and the Louisiana Sea Grant College
Program. Permission to publish this paper was granted by the Headquarters, U.S.
Army Corps of Engineers.
Table 1. LSTF instrumentation and sampling scheme
for this study.
Parameter To
Be Measured Instrument Type Sampling Rate
Wave Capacitance gage 20Hz
Current Acoustic Doppler Velocimeter (ADV) 20Hz(Fn##)
Sediment concentration Fiber Optical Backscatter (FOBS) 16Hz
Water depth Bottom-tracking profiler every 5mm cross-shore
Sediment flux Bottom sediment traps mode 1: 4Hz
mode 2: 1Hz No. Of
Parameter To Sampling Cross-Shore Vertical
Be Measured Duration Locations Profile
Wave 10min 10(FN#) N/A
Current 10min 10(FN#) Yes
Sediment concentration 10min 7 Yes
Water depth between wave runs 3660 N/A
Sediment flux continuous 20 No
100s 20 No
FOOTNOTES
# The 10 locations were 1.1, 27,
4.1, 5.7, 7.1, 8.5, 10.1, 11.6, 13.1, 15.6m from the still-water shoreline,
starting from ADV (or gage) #1 to ADV (or gage)
# 10.
## The ADVs were
synchronized with the wave gages.
Table 2. Summary of wave and surf zone
conditions.
Spilling Plunging
Breaker Case Breaker Case
Design conditions at the wave generator
Water depth (m) 0.9 0.9
Significant wave height (m) 0.25 0.23
Peak wave period (s) 1.5 3.0
Wavelength (m) 3.4 8.7
Wave celerity (m/s) 2.2 2.9
Wave angle (deg) 10 10
Breaking wave conditions
Significant breaker height (m) 0.26 0.27
Breaker angle (deg) 6.5 6.4
Breaking water depth (m) 0.46 0.28
Breaker index 0.57 0.96
Surf zone conditions
Surf zone width(FN#) (m) 14.0 13.0
Surf zone slope(FN##) 1:28 (0.035) 1:43 (0.023)
FOOTNOTES
# The surf zone width also includes
the uprush zone above the still-water shoreline.
## The overall surf zone
slope is calculated as the plane slope from the breaker point to the still water
shoreline.
Table 3. Comparison among measured and predicted total rate of
long-shore sediment transport.
Spilling Case Plunging Case TRANSPORT RATES (m[sup3]/yr) Measured (m[sup3]/yr) 2,660 7,040 CERC formula (m[sup3]/yr) 22,030 23,850 KAMPHUIS-86 (m[sup3]/yr) 10,760 9,100 KAMPHUIS-91 m[sup3]/yr) 2,200 5,360 KRAUS-88 (m[sup3]/yr) 2,670 3,150 RATIOS OF PREDICTED VERSUS MEASURED CERC/measured 8.28 3.39 KAMPHUIS-86/measured 4.05 1.29 KAMPHUIS-91/measured 0.83 0.76 KRAUS-88/measured 1.00 0.45 PERCENTAGE OVER (+) OR UNDER (-) PREDICTION CERC +728% +239% KAMPHUIS-86 +305% +29% KAMPHUIS-91 -17% -24% KRAUS-88 0% -55%
Figure 1. The LSTF during the plunging case, showing the downdrift traps in
the flow channels (bottom), the instrument bridge (top), and the cross-shore
array of flow meters, wave gages, and turbidity sensors.
Figure 2. Patterns
of the surf-zone wave decay under the spilling and plunging breakers. The error
bars represent the ranges of alongshore variations.
Figure 3. Equilibrium
beach profiles under the spilling and plunging breakers, averages of the 16
profiles in the middle section of the test beach.
Figure 4. Examples of beach
profiles showing the distribution of bed ripples and planar bed.
Figure 5.
Time-averaged longshore current profiles at various cross-shore locations under
the plunging and spilling breakers.
Figure 6. Alongshore uniformity of
longshore current and the rates of pump circulation, legend numbers indicate
alongshore locations in meters.
Figure 7. Cross-shore distribution of
longshore current under the spilling and plunging breakers.
Figure 8.
Suspended sediment concentration in the breaker zone. Numbers in the legends
denote distance to the still-water shoreline.
Figure 9. Suspended sediment
concentration in the mid-surf zone, an example at 5.7m from shoreline.
Figure
10. Steadiness of longshore current, 200-s segments of the 600-s recording are
shown. Upper: spilling case at 8.5 from shoreline; lower: plunging case at 8.5m
from shoreline.
Figure 11. Sediment-flux profiles in the breaker zone.
Numbers in the legends denote distance to the still-water shoreline.
Figure
12. Sediment-flux profiles in the mid-surf zone. Numbers in the legends denote
distance to the still-water shoreline.
Figure 13. Cross-shore distribution of
longshore sediment transport under the spilling and plunging breakers.
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