ELSEVIER
MarineGeology
138(1997)91L103
Flow velocity and sediment transport in the swash zone
of a steep beach
Michael G. Hughes a,1, Gerhard Masselink b, Robert W. Brander ’
a Department of Geology and Geophysics (FOS), University of Sydney, Sydney, NSW2006, Australia
b Centre for Water Research, University of Western Australia, Nedlands , WA 6907, Australia
’ Coastal Studies Unit, Department
qf Geography (HO3), University of Sydney, Sydney, NS W2006, Australia
Received 5 October 1995; received in revised form 10 February 1997; accepted 10 February 1997
Abstract
Detailed measurements of flow velocity and total sediment load were obtained in the swash zone on a steep beach.
Swash motion was measured using ducted impeller flow meters and capacitance water level probes. During wave
uprush, the onshore flow increased almost instantaneously from zero to its maximum velocity after the arrival of the
leading edge of the swash lens and subsequently decreased gradually to zero for the remainder of the uprush. During
backwash, the offshore flow increased steadily from zero to its maximum towards the end of the backwash and
dropped rapidly to zero as the beach fell “dry”. The duration of backwash was typically longer than that of uprush
and maximum water depth on the beach was attained just prior to the end of the uprush. The total sediment load
was measured for 35 individual wave uprush events using a sediment trap. The amount of sediment transported by a
single uprush was typically two to three orders of magnitude greater than the net transport per swash cycle (difference
between uprush and backwash) inferred from surveys of beach profile change. The measured immersed weight total
load transport rate displayed a strong relationship with the time-averaged velocity cubed, which is consistent with
equations for both bedload transport and total load transport under sheet flow conditions. The Bagnold (1963, 1966)
bedload transport model was tested against our field data and yielded Zb=ZG3TU/(tan~ + tar@), where Zb is the
immersed weight of bedload transported during the entire uprush (kg m-l), k is a coefficient (kg m-4 s’). ti is the
time-averaged flow velocity for the uprush (m s-l), T, is the uprush duration (s), 4 is the friction angle of the
sediment and /I’ is the beach slope. The empirically determined value for the coefficient k was 1.37 +O. 17. 0 I997
Elsevier Science B.V.
1. Introduction
Erosion and accretion
of the beach face, and
hence lateral movement
of the shoreline position,
are a direct result of net sediment transport in the
swash zone. Sediment transport
processes occurring in the inner surf zone usually work in concert
‘(Fax:
61 2 9351 0184) (Email:
0025-3227/97/$17.00
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0 1997 Elsevier Science B.V. All rights reserved.
PZZ SOOZS-3227(97)00014-5
with those in the swash zone, but it is ultimately
wave uprush that places sediment on the beach
and backwash that removes sediment from it. It is
surprising,
therefore,
that so few investigations
have examined the processes that govern sediment
transport
in the swash zone. Only recently has a
resurgence of interest begun to address this oversight (Horn and Mason, 1994; Turner, 1995).
Deterministic
modeling of beach morphodynam-
92
M. G. Hughes et al. / Marine Geology 138 (1997) 91-103
its requires an appropriate quantitative description
of the hydrodynamic and sediment dynamic processes that control spatial and temporal gradients
in the net sediment transport rate and consequently
morphological change. Clearly, such modeling
efforts require field data for model development,
r&nement and verification, especially where our
understanding of the physics is limited. In comparison to the surf zone, field measurements of the
hydrodynamic and sediment dynamic processes
operating in the swash zone are rare (Horn and
Mason, 1994). This largely reflects the general
perception that field measurements in the swash
zone are technically difficult to obtain, particularly
during periods when significant morphological
change is occurring. While there is a great deal of
truth in this perception, the state of the art is not
yet suthciently advanced to suggest that there is
no need for such measurements under less energetic
conditions, particularly since this is frequently
when the important process of beach recovery
occurs. It is fair to say that what is presently
needed most to advance our understanding of
beach morphodynamics is more field data from
the swash zone since, in a general sense, theoretical
and numerical models for predicting swash hydrodynamics and sediment transport have been available for some time (see Kobayashi, 1988 for a
review).
One of the most important hydrodynamic
parameters for sediment transport is the near bed
shear stress or its frequently used surrogateflow
velocity. There are only a few previous studies that
present time series of flow velocities obtained in
the swash zone. Kemp (1975) discusses some laboratory examples, whereas Schiffman (1965), Kirk
( 1971) and Beach and Sternberg ( 1991) present
field measurements from a variety of natural
beaches. Jago and Hardisty (1984) and Hardisty
et al. (1984) report field measurements of timeaveraged velocities for the uprush and backwash
separately.
While theories for sediment transport have been
available for some time, direct measurements of
sediment transport for individual waves in the
swash zone are limited. The use of monochromatic
waves in the laboratory enabled Sunamura (1984a)
to estimate the net total load transported during
a swash cycle with a reasonable degree of accuracy
from profile changes. There are also a number of
field studies that use profile changes to infer sediment transport rates (see Horn and Mason, 1994
for a review), but these cannot be used to deduce
sediment transport rates for individual swash
events due to the spectrum of input waves. To
date only Jago and Hardisty ( 1984), Hardisty et al.
( 1984) and Horn and Mason ( 1994) report field
measurements of bedload transport for individual
swash events. The latter authors, together with
Beach and Sternberg ( 1991), also present field
measurements of the suspended sediment transport rate.
There is still some debate as to whether the
mode of sediment transport in the swash zone is
principally bedload or suspended load (Komar,
1978; Horn and Mason, 1994) thus it is uncertain
which of the available transport formulae are most
appropriate. Hardisty et al. ( 1984) measured what
they considered to be bedload transport in the
swash zone in order to calibrate the following
bedload transport formula based on Bagnold
(1963, 1966):
Ib =
et.OTu
e,z,ZiT,
eb0.5pjii3T,
tan4 + tat@ = tan4 + tan/I = tan4 + tan/3
=
ku3T,,
tan+ + tan/?
(1)
where 1s is the immersed weight of bedload transported during the entire uprush, et, is a bedload
efficiency factor, o is the fluid power, T, is the
uprush duration, 4 is the friction angle of the
sediment (tan 4 =0.63), fi is the beach slope, z, is
the bed shear stress, U is the time-averaged flow
velocity, p is the water density,fis a friction factor
and k is a coefficient that incorporates the value
of eb, p andf(i.e. k=+e,pf).
Note that Eq. 1 suggests the bedload transport
rate is proportional to the time-averaged velocity
cubed. Interestingly, Wilson (1987) argued, on
both theoretical and empirical grounds, that the
total load transport rate in sheet flow is also
proportional to the velocity cubed. He proposed
the following equation to calculate the volumetric
M. G. Hughes et al. /Marine
total load transport rate
11.8
48 = ~
g(s-I)
z, -z,
1.5
( P >
qs:
(2)
where z, is the critical shear stress required for
sediment motion and s is the ratio of sediment to
fluid density. Note that this is a modified form of
the classic Meyer-Peter and Miiller ( 1948) bedload
transport equation in which the constant 8 is
replaced by 11.8.
This paper presents results from a field experiment aimed at obtaining concurrent measurements
of flow velocity and sediment transport in the
swash zone. The need for such information to
develop, refine and verify morphodynamic models
of the beach environment has already been discussed. The major indicator of morphological
change in the beach environment is a change in
beach slope. The sediment transport model proposed by Bagnold (1963, 1966) is of particular
relevance here, since bed slope is represented in
the transport equation (Eq. 1). This simplifies the
simulation of such morphodynamic phenomenon
as the equilibrium balance between hydrodynamic
asymmetry and gravity on the beach face (e.g.
Hardisty, 1986; Turner, 1995), which can be used
to explain the often reported relationship between
beach slope and wave/sediment characteristics (e.g.
Sunamura, 1984b; Wright and Short, 1984). For
this reason Eq. 1 will be calibrated against the field
data reported here.
2. Field site and methods
The field experiment was conducted on Palm
Beach in Sydney (Australia) at approximately high
tide on 23 July 1994. During the experiment the
beach morphology was characterised by a steep
beach face (tan p = 0.12) and a low-gradient low
tide terrace (tan /I = 0.01) (Fig. 1). The beach
face was composed of medium-sized sand. A
surface sample collected from the mid-swash
yielded a mean grain diameter of 0.3 mm. Incident
swell waves approached the beach with their crests
parallel to the shoreline and were character&d by
a visually-estimated breaker height of 0.5 m and a
Geology 138 (1997) 91-103
93
period of 10 s. Swash oscillations occurred dominantly at incident wave frequencies. Most waves
broke on the seaward edge of the low tide terrace
by spilling and then either: (1) reformed before
breaking again by plunging just seaward of the
beach face, resulting in bore collapse and then
swash; or (2) evolved directly into a fully developed bore that collapsed upon reaching the beach
face to produce swash.
A transect was established across the beach face
in a shore-normal direction and bed elevation rods
were installed at 1 m intervals. The rods were
monitored hourly. The beach morphology from
the berm crest to the outer surf zone was surveyed
at the beginning and end of the field experiment
using standard surveying techniques.
Three instrument stations were installed in the
mid-swash region at a separation distance of 1 m.
Each station consisted of a capacitance water level
probe (Hughes, 1992) and two ducted impeller
flow meters (Nielsen and Cowell, 1981) for measuring the flow depth and velocity (Fig. 2). Both
the water level probes and flow meters were operated continuously for the duration of the experiment with their analog output sampled and logged
at 5 Hz. Only the results from the central instrument station (Station 2) will be discussed here,
since this was where the sediment trap was
deployed.
The flow meters were installed as close to the
bed as possible, nominally 1 cm above the bed.
This required occasional adjustments during the
course of the experiment. The internal diameter of
the flow meter duct is 5.5 cm, thus the flow velocity
measurements represent the vertical zone nominally l-6 cm above the bed. It was observed that
consistent flow velocities were still being recorded
even when the duct was only partly submerged.
The flow meter also continued to function in the
latter stages of the backwash when a slurry of
sand and water was moving through the duct.
Some reservations are appropriate with regard to
the reliability of flow velocities recorded in the
latter stages of the backwash, when water depths
are less than ca. 2.5 cm. The flow meter records
were corrected for frequency-response characteristics using algorithms contained in Nielsen and
Cowell(l981).
M.G. Hughes et al. 1 Marine Geology 138 (1997) 91-103
94
-3.5-4-I0
PALM BEACH 23-7-1994
1
1
I
5I
10
15
20
30
25
Distance (m)
I
35
1
40
I
45
! J
Fig. 1. Beach profile showing location of instrument stations within the swash zone.
The water level probes were calibrated before
and after the experiment and the average calibration curve was applied. Hughes (1992) reported
the likely error in estimating swash depth using
these probes to be about 15%.
Concurrent with the collection of hydrodynamic
data, the total load (bedload and suspended load)
of sediment carried up the beach by individual
uprush events was measured with a sediment trap
similar to the “streamer traps” deployed by Kraus
( 1987) (Fig. 2). The opening of the sediment trap
was 0.1 m wide and 0.5 m high, with a small sill
present at the bottom of the trap opening to
properly convey sediment into the trap. No scour
of the beach was observed upstream of the trap.
Sediment that passed through the opening was
collected in a 1.5 m long net with a mesh size of
100 pm. The net was laid out landward of the trap
to avoid interference of the flow. The length of the
net was sufficient to enable unrestricted through
flow of water since no piling up of either water or
sediment was observed in front of the trap. The
trap was held in place adjacent to Station 2 for
the duration of the uprush, at the end of which it
was lifted out of the water and the sediment was
transferred to storage bags for transport back to
the laboratory. The total sediment load was measured for 35 individual uprush events. The sand
collected by the sediment trap was washed, dried
and weighed in the laboratory and the dry weight
was converted to an immersed weight assuming a
sediment density of 2650 kg mW3 and a water
density of 1028 kg rne3.
3. Results
3.1. Morphology
Measurements of the beach morphology before
and after the field experiment indicated only minor
changes (Fig. 3). The beach profile landward of
Station 2 underwent an average deposition of
approximately 1 cm, which equates to an overall
increase in sediment volume of around 0.1 m3 per
unit meter beach width. Hourly morphological
measurements obtained from the bed elevation
rods demonstrated that this morphological change
occurred gradually over the course of the experiment. Taking the time between the first and last
h4.G. Hughes et al. /Marine
Geology 138 (1997) 91-103
Fig. 2. Photograph showing the total load trap being deployed, as well as the configuration of instrument stations containing flow
meters and water level probes.
survey as 4 hours and assuming an average swash
period of 10 s, then the average difference between
sediment transport per unit meter beach width
during the uprush and the backwash is 7 x 10m5
m3 per swash event. Assuming a porosity of 0.35
the net immersed weight sediment transport per
swash is then 0.074 kg m-’ in the onshore direction. It will be shown that this is only a very small
fraction of the sediment load actually carried by
individual uprush events.
3.2. Flow velocity, depth and discharge
The maximum and time-averaged uprush velocities for the 35 swash events where sediment load
was measured are listed in Table 1. Of these, two
were overrunning swashes (i.e. two waves interacting) and three were wind-affected (i.e. the impel-
lers were spinning in the wind prior to the arrival
of the uprush) and are therefore not considered in
the analysis. The maximum instantaneous velocity
measured was 5.11 m s-l and the time-averaged
velocities ranged between 0.36 and 2.48 m s-l.
These velocities may appear large, but they have
been independently verified in a more recent
experiment by comparison with the swash front
velocity measured using a co-located runup wire
(Masselink and Hughes, 1996).
Three examples of flow velocity, U, swash depth,
h, and swash discharge rate per unit beach width,
q, are shown in Fig. 4. The swash discharge rate
was obtained from the product of the velocity and
depth records. In all cases, when the moving
shoreline or leading edge of the swash lens arrived
at the instrument station, there was an almost
instantaneous acceleration in flow velocity to its
M.G. Hughes et al. / Marine Geology I38 (1997) 91-103
96
-1.75-2 I
Cl
8.55
13.00
I
12
I
3
1
1
4
5
6
Distance (m)
I
7
1
8
9
0
Fig. 3. Beach profiies in the swash zone at the beginning (8.55 hr) and end (13.00 hr) of the experiment, obtained by monitoring of
bed elevation rods. The position of instrument Station 2 is also shown.
maximum followed by a more prolonged decrease
to zero. Zero velocity at the end of the uprush
always occurred after the time of maximum water
depth. In contrast, at the start of the backwash
the flow velocity increased relatively slowly
towards its maximum, which occurred towards the
end of the backwash. After the maximum backwash velocity was reached the velocity decreased
to zero relatively rapidly as the water depth
reduced to zero. Close inspection of the velocity
and depth records in Fig. 4 indicates that, occasionally at the end of the backwash, the flow
meters were recording zero velocity before the
water depth had gone to zero. This situation arises
when the impeller of the flow meter becomes fully
emerged while there is still a thin layer of backwash
flowing beneath it. The true time that the velocity
becomes zero at the end of the backwash should
be interpreted as the time when the depth
becomes zero.
The swash event shown in Fig. 4a,b represents
a situation where the total uprush discharge, indicated by the area under the curve in Fig. 4b, is
approximately equal to the total backwash dis-
charge. The event shown in Fig. 4c,d represents a
situation where the total uprush discharge is
noticeably larger than the backwash discharge,
whereas the reverse situation is shown in Fig. 4e,f.
It is apparent from these examples that neither the
maximum velocity for the uprush and backwash
or the total discharge for the two are necessarily
equal. Moreover, the fact that maximum velocity
for the uprush in these examples exceeds the
maximum for the backwash does not necessarily
mean that total uprush discharge will be greater
than backwash discharge. This is due to the longer
duration of the backwash.
3.3. Sediment transport in the uprush
The total load of sediment transported during
the uprush for 35 individual swash events are listed
in Table 1. The measurements,
expressed as
immersed weight, range from 0.13 kg m-l to
50.28 kg m-l. Clearly, large amounts of sediment
are moved on the beach face during a single wave
uprush. The survey data suggest a net onshore
sediment transport of 0.074 kg mP1 per swash
M.G. Hughes et al. /Marine
Table 1
Velocity
and
uprush events
sediment
transport
data
for
35
monitored
Sample
no.
I
(kg m-l)’
I
(kg m-l)*
UFtl,,
(m s‘l)
u
(m s-l)
Tu
(s)
1
2
3
4*
5
6
7
8
9
lO#
11
12
13
14
15
16
17
18
19
20#
21
22*
23
24
25
26#
27
28
29
30
31
32
33
34
35
4.60
32.05
24.49
4.72
31.83
7.62
9.64
24.06
3Y.64
5.92
17.28
45.39
40.50
1.39
12.57
54.73
6.33
9.17
9.18
7.15
0.29
4.36
9.13
81.09
7.42
0.61
15.51
12.49
8.29
0.21
28.36
3.88
23.54
4.90
26.51
2.85
19.87
15.18
2.93
19.73
4.72
5.98
14.92
24.58
3.67
10.71
28.14
25.11
0.86
7.79
33.93
3.92
5.69
5.69
4.43
0.18
2.70
5.66
50.28
4.60
0.38
9.62
1.15
5.14
0.13
17.58
2.41
14.59
3.04
16.44
2.16
3.30
3.13
1.09
1.82
1.45
1.6
2.4
2.2
4.24
1.89
2.05
3.26
3.04
1.80
0.89
1.04
1.46
1.55
2.0
1.4
1.8
2.0
1.8
3.46
2.92
4.01
1.28
2.92
3.91
2.99
2.58
2.42
1.65
I .50
2.22
0.73
1.04
1.83
1.32
1.15
1.08
1.8
1.8
1.6
1.8
2.6
2.2
2.2
2.0
1.8
1.31
0.73
1.0
2.39
5.11
2.07
1.15
2.48
0.90
2.0
2.0
2.2
2.78
3.11
2.19
0.56
3.07
2.08
3.52
2.14
3.20
1.40
1.23
1.08
0.36
1.56
1.06
1.43
1.04
1.34
2.0
1.6
1.8
1.2
1.6
1.8
2.2
2.0
2.6
* Overrunning
swash.
#Wind affected record
1 Dry weight.
’ Immersed weight.
cycle (difference between uprush and backwash),
averaged over the course of the experiment. Thus
the amount of sediment transported during a typical uprush is two to three orders of magnitude
greater than the average net transport per swash
cycle. The relative magnitudes of sediment transport during the uprush and backwash of individual
swash cycles was the subject of a more recent
Geology 138 (1997) 91-103
91
experiment, which is reported in Masselink and
Hughes (1996).
Both the bedload transport equation proposed
by Bagnold ( 1963, 1966) and the total load transport equation for sheet flow proposed by Wilson
(1987) suggest the sediment transport rate should
scale with velocity cubed. To determine the best
relationship for the data presented here a linear
least squares regression analysis was performed
according to
I= cii” T,
(3)
where I is the measured immersed weight of the
total load transported during the uprush (kg
m-r), c is the regression coefficient (units depend
on n), u is the measured time-averaged velocity
(m SC’), 7’” is the measured uprush duration (s)
and n was varied between 1 and 6. The regression
coefficients and R2-values for each value of n are
listed in Table 2. The best result is for the model
II = 2 (i.e. sediment transport rate scales with velocity squared), however, there is no significant
difference between the models n = 2 or n = 3 since
both are significant at the 0.5% level (Blalock,
1981; pp. 419-420).
Given the importance attached to Bagnold’s
bedload transport model in previous studies of the
swash zone, our data have been plotted in Fig. 5
to determine the coefficient k in Eq. 1. The data
suggest a k value (and 95% confidence interval ) of
1.37 f 0.17 kg m 4 s2. The k value does not appear
to depend on flow velocity (Fig. 6).
4. Discussion
The flow velocity records reported here show
that the swash process is not symmetrical, i.e. the
backwash is not simply the reverse of the uprush.
The distinguishing features of flow in the swash
zone are: ( 1) when the moving shoreline or leading
edge of the swash lens arrives at a position on the
beach face, the flow velocity increases from zero
(on the “dry” beach) to the value of the shoreline
velocity virtually instantaneously; (2) throughout
the remainder of the uprush the flow velocity
steadily decreases to zero; (3) flow velocity during
the backwash gradually increases from zero to its
M.G. Hughes et al. 1 Marine Geology 138 (1997) 91-103
98
3.2 ,
r
0.15
1.6
- 0.15
h
-:
3
VJ
.!w
4
Y
-
0.05
-1.6
-0
-0.3
-3.21,
- 0.15
3.2
0.3
1.6
h
7
-
%
i0
Y
- 0.03
0.15
h
7
0.09
-L:
20
w
-1.6
-0.15
-0
-3.2
4
02
2
0.1
0.09
h
7
h
7
lo
%
0.03
Y
-2
e
i
0
w
-0.1
0
a.24
0
2
4
6
t (s)
8
10
0
2
4
6
t (9
8
10
Fig. 4. Examples of the flow velocity, depth and discharge at Station 2 for three individual swash events. (a) and (b) show an example
where the uprush and backwash discharge are equal, (c) and (d) show an example where the uprush discharge is greater than the
backwash discharge, and (e) and (f) show an example where the uprush discharge is less than the backwash discharge.
99
M.G. Hughes et al. / Marine Geology 138 (1997) 91-103
Table 2
Results of least squares regression analysis for the equation Z=
cii”Z’,, where Z is the measured immersed weight of sediment
transported during the uprush (kg m-r), c is the regression
coefficient (units depend on n), I is the measured time-averaged
flow velocity (m s-r) and T, is the measured uprush duration (s)
n
c
R2-value
1
2
3
4
5
6
5.41 f 1.06
3.50+0.42
1.83kO.23
0.82kO.15
0.34f0.08
0.14*0.04
0.54
0.80
0.78
0.59
0.36
0.16
4
Ol
0
7
1
2
3
U (m s-l)
Fig. 6. The estimated k value for 30 individual swash events
plotted as a function of the time-averaged flow velocity.
0.01
I
0.01
0.1
1
ii3Tu
10
100
(m3 s-‘)
uu@+tanP
Fig. 5. The measured total load transported during the uprush
of 30 individual swash events plotted as a function of a Bagnoldtype bedload transport formula (see Eq. 1).
maximum towards the end of the backwash; (4)
once the maximum backwash velocity is reached,
the velocity drops rapidly to zero (as the beach
goes “dry”); (5) backwash duration is typically
longer than uprush duration; and (6) maximum
water depth occurs before the end of the uprush.
These observed features are consistent with predictions by the non-linear shallow water theory for
swash behaviour following bore collapse (e.g. Shen
and Meyer, 1963; Hibberd and Peregrine, 1979;
Hughes, 1992).
If incident waves arrive with their crests normal
to the shoreline and the beach face is planar and
impermeable, then the uprush and backwash discharge per unit width of beach are expected to be
equal. The maximum flow velocity for the uprush
and backwash are not necessarily equal, however,
since the flow duration and acceleration pattern
for the two are different. There are a number of
possible reasons for the inequality between uprush
and backwash discharge observed in our data.
Either swash infiltration or the presence of a
localised elevation of the beach face (e.g. cusp
horn), causing flow divergence, will lead to local
uprush discharge being greater than backwash
discharge. Either beach face seepage or the presence of a localised depression of the beach face
(e.g. cusp bay), causing flow convergence, will lead
to local uprush discharge being less than backwash
discharge. No measurements
were made of
infiltration or seepage rates, so it is not possible
to assess the importance of these processes in our
data set. The beach face in the vicinity of the
instruments appeared planar, but some subtle
topography may have caused the minor flow
convergence/divergence necessary to produce the
observed differences in uprush and backwash discharge. Alternatively, the imbalance in swash dis-
M. G. Hughes et al. / Marine Geology 138 ( 1997) 91 -I 03
100
charge may be offset by the existence of a
secondary wave (e.g. sub-harmonic edge wave)
with a frequency different from that of the primary wave.
The velocity time series shown here in Fig. 4 are
similar in appearance to those shown in fig. 4 of
Schiffman (1965), fig. 7 of Kirk (1971) and fig. 3.8
of Kemp (1975). All of these studies are from
beaches where the swash was primarily driven by
incident waves that had broken prior to reaching
the beach face. A comparison of the time series
presented here with that shown in fig. 5 of Beach
and Sternberg (1991) is less consistent. Some of
the swash events are similar, whereas others are
clearly different. For those that are different, the
rise to maximum uprush velocity is much slower
in Beach and Sternberg’s data, so that the record
for the uprush is approximately
symmetrical,
rather than saw-toothed. Beach and Sternberg’s
measurements are from a highly dissipative beach
where infragravity waves dominated the inner surf
zone, thus there is some suggestion that the velocity
field produced by incident swash and infragravity
swash may be of a fundamentally different nature.
Visual observations made during the experiment
indicate that the sediment transport we measured
was occurring under sheet flow conditions i.e.
several layers of the bed were mobilised throughout
the uprush. Wilson (1988) indicated that fully
developed sheet flow conditions exist when the
non-dimensional shear stress or Shields parameter
is greater than 0.8. It is not possible to calculate
the actual Shields parameter for our data, since
we did not measure the boundary shear stress. A
lower limit for our data can be estimated, however,
if we calculate the mean skin friction Shields
parameter 8’ (following Nielsen, 1992; p. 104):
(j’=
0.5$?
gD(s-
1)
(4)
where f is a friction factor, U is the time-averaged
horizontal flow velocity, g is the gravitational
acceleration,
should be noted, however, that Wilson’s semi-empirical
transport equation (Eq. 2) is actually calibrated using laboratory measurements of the total load sediment transport rate
(bedload +suspended load).
M. G. Hughes et al. / Marine Geology 138 ( 1997) 91-103
(density=2650 kg me3) in sea water (density=
1028 kg mw3), then the immersed weight transport
rate is 0.61 times the dry weight transport rate.
The k value found by Hardisty et al. then becomes
6.17, which is still nearly a factor 5 larger than the
value reported here.
The difference between our k value and that of
Hardisty et al. (1984) could be a result of the
different methods used to measure water velocity.
It is possible that the swinging vane used by
Hard&y et al. did not respond adequately to the
rapid accelerations that occur in the early stages
of uprush (Fig. 4). This would lead to an underestimation of the time-averaged flow velocity and
an overestimation of the k value. Alternatively,
the difference in k values could be due to grain
size effects. The fact that the k value is independent
of swash velocity (Fig. 6) indicates that it is also
independent of wave energy and therefore is probably constant for a given site. The k value is
expected, however, to vary between sites through
the effect of grain size on the friction factor, which
is represented in k (see Eq. 1). Hardisty (1983)
re-evaluated existing laboratory data and found
that k was strongly dependent on grain size in the
medium sand range. The two beaches studied by
Hardisty et al. were composed of sand with mean
grain diameters of 0.23 mm and 0.66 mm. The
sediment diameter at Palm Beach was 0.3 mm,
which is within the range of their data set.
Unfortunately Hardisty et al. did not report the
data from their two beaches separately, so it is not
possible to determine if the k value correlates with
differences in grain size between the three beaches.
If sediment transport under sheet flow conditions occurs principally as suspended load, then
the relationship between our measurements and
Bagnold’s bedload transport equation (Eq. 1) is
fortuitous and our k value becomes somewhat
artificial. Horn and Mason (1994) measured the
“bedload” (< 1 cm above the bed) and “suspended
load” (> 1 cm above the bed) separately for a
number of swash events on four beaches in the
UK. Unfortunately their definition of the sediment
transport modes is based on trap design rather
than the underlying physics. Wilson (1987, 1988)
showed that the thickness of the sediment layer
mobilised during sheet Ilow is lOOD, thus in the
101
case of the swash zone on sandy beaches the
thickness will typically be of the order of 10 to 30
times the grain diameter. This means that if the
sediment transport that Horn and Mason measured was occurring under sheet flow conditions
(no velocity data were presented to enable an
assessment of this), then their “bedload” quantities
probably represent the entire transport load occurring in the sheet flow layer. In light of the previous
discussion, what they have termed as “bedload”
might also be interpreted by some to be suspended load.
In the case of wave uprush Horn and Mason
(1994) observed that “bedload” was largely predominant, but the proportion of the total transport
occurring as “suspended load” increased under
certain conditions. In light of the results reported
here this increase in “suspended load” is likely to
be related to either a continual exchange between
the sheet flow layer and the water column above
or advection from elsewhere in the swash zone.
One likely source for advected sediment is the base
of the beach where large amounts of sediment are
often entrained into suspension during the bore
collapse/wave
plunge
process
(James
and
Brenninkmeyer, 1977). If a significant amount of
the material in suspension in the swash zone is a
result of advection from entrainment mechanisms
occurring at the base of the beach face, then a
somewhat different approach to modeling sediment
transport in the swash zone will be required, since
the equilibrium-type transport equations discussed
here will be inadequate on their own.
5. Conclusion
The following observations have been made
concerning swash kinematics on a steep beach.
During wave uprush, flow velocity increases almost
instantaneously from zero to its maximum after
arrival of the leading edge of the swash. Flow
velocities decrease steadily to zero during the
remainder of the uprush. Maximum water depth
on the beach is attained just prior to the end of
the uprush. Flow velocity during the backwash
increases gradually from zero to its maximum
towards the end of the backwash. A rapid drop in
M.G. Hughes et al. 1 Marine Geology 138 (1997) 91-103
102
backwash velocity occurs just before the beach
becomes “dry”. The duration of the backwash is
typically longer than that of the uprush.
The total load (bedload + suspended load)
transport rate during the uprush phase of the
swash cycle displayed a strong relationship with
the time-averaged velocity cubed. This result is
consistent with models for both bedload transport
(Bagnold, 1963) and total load transport in sheet
flow (Wilson, 1987). Our data compares well with
a bedload transport model for the swash zone
proposed by Hardisty et al. (1984) and based on
the work of Bagnold (1963, 1966):
tan4 + tan/?
(5)
where Ii, is the immersed weight of bedload transported during the entire uprush (kg m-l), k is a
coefficient (kg m -4 s’), U is the time-averaged flow
velocity for the uprush (m s-i), T, is the uprush
duration (s), 4 is the friction angle of the sediment
and /I is the beach slope. Least squares regression
analysis yielded a
Acknowledgements
The authors greatly appreciate the assistance of
Mathew Potter (University of Sydney), Aart
Kroon (University of Utrecht), Anne Sorber
(University of Utrecht) and Judith Bosboom
(Technical University of Delft) in conducting the
field experiment. The sediment traps were built by
Graham Lloyd (University of Sydney). The journal’s referees made several useful comments that
have improved the content of this paper.
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