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 occur- ring in the inner surf zone usually work in concert

‘(Fax: 61 2 9351 0184) (Email: hughes@beryl.es.su.oz.au)

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 over-

sight (Horn and Mason, 1994; Turner, 1995).

Deterministic modeling of beach morphodynam-

0025-3227/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved.

PZZ SOOZS-3227(97)00014-5

92 M. G. Hughes et al. / Marine Geology 138 (1997) 91-103

its requires an appropriate quantitative description of the hydrodynamic and sediment dynamic pro- cesses 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 compari- son 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 hydro- dynamics and sediment transport have been avail- able 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 surrogate- flow velocity. There are only a few previous studies that present time series of flow velocities obtained in the swash zone. Kemp (1975) discusses some labo- ratory 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 time- averaged 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 sedi- ment 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 trans- port 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, eb0.5pjii3 T,

tan4 + tat@ = tan4 + tan/I = tan4 + tan/3

= ku3T,,

tan+ + tan/? (1)

where 1s is the immersed weight of bedload trans- ported 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 Geology 138 (1997) 91-103 93

total load transport rate qs:

11.8 z, -z, 48 = ~ -

( >

1.5

g(s-I) P (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 experi- ment 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 dis- cussed. The major indicator of morphological change in the beach environment is a change in beach slope. The sediment transport model pro- posed 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

period of 10 s. Swash oscillations occurred domi- nantly 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 devel- oped 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 meas- uring the flow depth and velocity (Fig. 2). Both the water level probes and flow meters were oper- ated continuously for the duration of the experi- ment with their analog output sampled and logged at 5 Hz. Only the results from the central instru- ment 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 nomi- nally 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 characteris- tics using algorithms contained in Nielsen and Cowell(l981).

94 M.G. Hughes et al. 1 Marine Geology 138 (1997) 91-103

-3.5-

PALM BEACH 23-7-1994 -4-I I 1 1 I 0 5 10 15 20 I 1 I

25 30 35 40 45 ! Distance (m)

Fig. 1. Beach profile showing location of instrument stations within the swash zone.

J

The water level probes were calibrated before and after the experiment and the average calibra- tion 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 mea- sured 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 experi- ment. 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 lers were spinning in the wind prior to the arrival period of 10 s, then the average difference between of the uprush) and are therefore not considered in sediment transport per unit meter beach width the analysis. The maximum instantaneous velocity during the uprush and the backwash is 7 x 10m5 measured was 5.11 m s-l and the time-averaged m3 per swash event. Assuming a porosity of 0.35 velocities ranged between 0.36 and 2.48 m s-l. the net immersed weight sediment transport per These velocities may appear large, but they have swash is then 0.074 kg m-’ in the onshore direc- been independently verified in a more recent tion. It will be shown that this is only a very small experiment by comparison with the swash front fraction of the sediment load actually carried by velocity measured using a co-located runup wire individual uprush events. (Masselink and Hughes, 1996).

3.2. Flow velocity, depth and discharge

The maximum and time-averaged uprush veloci- ties 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 inter- acting) and three were wind-affected (i.e. the impel-

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

96 M.G. Hughes et al. / Marine Geology I38 (1997) 91-103

-1.75- 8.55 13.00

-2 I I I 1 1 Cl 12 3

I 1 4 5 6 7 8 9 Distance (m)

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 back- wash 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, occa- sionally 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, indi- cated 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 Geology 138 (1997) 91-103 91

Table 1

Velocity and sediment transport data for 35 monitored

uprush events

Sample I I UFtl,, u Tu no. (kg m-l)’ (kg m-l)* (m s‘l) (m s-l) (s)

1 4.60 2.85

2 32.05 19.87

3 24.49 15.18

4* 4.72 2.93

5 31.83 19.73

6 7.62 4.72

7 9.64 5.98

8 24.06 14.92

9 3Y.64 24.58

lO# 5.92 3.67

11 17.28 10.71

12 45.39 28.14

13 40.50 25.11

14 1.39 0.86

15 12.57 7.79

16 54.73 33.93

17 6.33 3.92

18 9.17 5.69

19 9.18 5.69

20# 7.15 4.43

21 0.29 0.18

22* 4.36 2.70

23 9.13 5.66

24 81.09 50.28

25 7.42 4.60

26# 0.61 0.38

27 15.51 9.62

28 12.49 1.15

29 8.29 5.14

30 0.21 0.13

31 28.36 17.58

32 3.88 2.41

33 23.54 14.59

34 4.90 3.04

35 26.51 16.44

2.16 1.09 1.6

3.30 1.82 2.4

3.13 1.45 2.2

4.24 1.80 2.0

1.89 0.89 1.4

2.05 1.04 1.8

3.26 1.46 2.0

3.04 1.55 1.8

3.46 1.65 1.8

2.92 I .50 1.8

4.01 2.22 1.6

1.28 0.73 1.8

2.92 1.04 2.6

3.91 1.83 2.2

2.99 1.32 2.2

2.58 1.15 2.0

2.42 1.08 1.8

1.31 0.73 1.0

2.39 1.15 2.0

5.11 2.48 2.0

2.07 0.90 2.2

2.78 1.40 2.0

3.11 1.23 1.6

2.19 1.08 1.8

0.56 0.36 1.2

3.07 1.56 1.6

2.08 1.06 1.8

3.52 1.43 2.2

2.14 1.04 2.0

3.20 1.34 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 typi- cal uprush is two to three orders of magnitude greater than the average net transport per swash cycle. The relative magnitudes of sediment trans- port during the uprush and backwash of individual swash cycles was the subject of a more recent

experiment, which is reported in Masselink and Hughes (1996).

Both the bedload transport equation proposed by Bagnold ( 1963, 1966) and the total load trans- port 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 veloc- ity 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

98 M.G. Hughes et al. 1 Marine Geology 138 (1997) 91-103

3.2 , r

1.6 0.15 - 0.15

3 h

-: VJ

.!w 4

- 0.05 Y

-1.6

-0

-3.2 1, -0.3

3.2 - 0.15 0.3

1.6 h 7

i0

Y

-1.6

0.15 h 7

20

- 0.09

%

-L:

- 0.03 w

-0.15 -0

-3.2

4 02

2 0.1 h 7

i 0

0.09 h 7

lo Y

-2

%

e 0.03 w

-0.1

0

a.24 0 2 4 6 8 10

t (9

0 2 4 6 8 10

t (s)

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.

M.G. Hughes et al. / Marine Geology 138 (1997) 91-103 99

Table 2 4 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 5.41 f 1.06 0.54 2 3.50+0.42 0.80 3 1.83kO.23 0.78 4 0.82kO.15 0.59 5 0.34f0.08 0.36 6 0.14*0.04 0.16

0.01 I 0.01 0.1 1 10 100

ii3Tu

uu@+tanP (m3 s-‘)

Fig. 5. The measured total load transported during the uprush of 30 individual swash events plotted as a function of a Bagnold- type 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 predic- tions 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).

Ol 7

0 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.

If incident waves arrive with their crests normal to the shoreline and the beach face is planar and impermeable, then the uprush and backwash dis- charge 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 pres- ence 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 dis- charge. Alternatively, the imbalance in swash dis-

100 M. G. Hughes et al. / Marine Geology 138 ( 1997) 91 -I 03

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 pri- mary 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 labora- tory measurements of the total load sediment transport rate (bedload +suspended load).

M. G. Hughes et al. / Marine Geology 138 ( 1997) 91-103 101

(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 under- estimation 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 proba- bly 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 condi- tions 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

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 mea- sured 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 occur- ring 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 sus- pended load.

In the case of wave uprush Horn and Mason (1994) observed that “bedload” was largely pre- dominant, 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

102 M.G. Hughes et al. 1 Marine Geology 138 (1997) 91-103

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 trans- ported 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 jour- nal’s referees made several useful comments that have improved the content of this paper.

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