Morphodynamics of a bar-trough surf zone

Marine Geology, 70 (1986) 251--285

251

Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

MORPHODYNAMICS OF A BAR-TROUGH SURF ZONE*

L.D. WRIGHT', P. NIELSEN 2, N.C. SHI' and J.H. LIST'

'Virginia Institute of Marine Science, School of Marine Science, College of William and Mary, Gloucester Point, VA 23062 (U.S.A.) ~Department of Coastal and Oceanographic Engineering, University of Florida, Gainesville, FL 32611 (U.S.A.) (Received May 13, 1985; revised and accepted May 21, 1985)

ABSTRACT Wright, L.D., Nielsen, P., Shi, N.C. and List, J.H., 1986. Morphodynamics of a bar-trough surf zone. Mar. Geol., 70: 251--285. A field study was made of the distinguishing morphodynamic processes operating in a surf zone which perennially exhibits accentuated bar-trough topography (the "longshorebar-trough" and "rhytmic-bar-and-beach" states as described by Wright and Short, 1984). Characteristic features of the morphology include a shallow bar with a steep shoreward face, a deep trough, and a steep beach face. This morphology, which is favored by moderate breaker heights and small tidal ranges, strongly controls the coupled suite of hydrodynamic processes. In contrast to fully dissipative surf zones, the bar-trough surf zone is n o t at all saturated and oscillations at incident wave frequency remain dominant from the break point to the subaerial beach. The degree of incident wave groupiness does not change appreciably across the surf zone. Infragravity standing waves which, in dissipative surf zones, dominate the inshore energy, remain energetically secondary and occur at higher frequencies in the bar trough surf zone. Analyses of the field data combined with numerical simulations of leaky mode and edge wave nodal--antinodal positions over observed surf-zone profiles, indicate that the frequencies which prevail are favored by the resonant condition of antinodes over the bar and nodes in the trough. Standing waves which would have nodes over the bar are suppressed. Sediment resuspension in the surf zone appears to be largely attributable to the incident waves which are the main source of bed shear stress. In addition, the extra near-bottom eddy viscosity provided by the reformed, non-breaking waves traversing the trough significantly affects the vertical velocity profile of the longshore current. Whereas the bar is highly mobile in terms of onshore-offshore migration rates, the beach face and inner regions of the trough are remarkably stable over time. INTRODUCTION

Beach and surf-zone systems which frequently or predominantly exhibit a combination o f high-relief straight or rhythmic bars, deep troughs, and relatively steep subaerial beach faces (Fig.l) are c o m m o n in nature. Such beaches are morphologically and dynamically intermediate between the fully dissipa*Contribution No. 1233 from the Virginia Institute of Marine Science. 0025-3227/86/$03.50

© 1986 Elsevier Science Publishers B.V.

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Fig.1. Plan and profile configurations and major features of the longshore-bar-trough and rhythmic-bar-and-beach stat~. Both of t h e s e s t a t e s a r e characterized by accentuated bartrough topography. tire states which have wide, low-gradient surf zones and flat subaerial beach faces (Wright et al., 1982a; Wright and Short, 1984) and the highly reflective states which lack surf zones and consist of steep subaerial beaches with high runup (Wright et al., 1979a, b; Wright and Short, 1983, 1984). Beaches fronted by accentuated longshore bar-trough or rhythmic bar topographies possess elements of both the dissipative and reflective extremes. However, they are far more complex than either of the two extremes in terms of their morphology, hydrodynamic process signatures, and temporal behavior. Nearshore bars assume a wide variety of forms and occur in response to different mechanisms. They have been the subjects of numerous studies, some recent examples of which include those by Sonu (1973), Greenwood and Davidson-Arnott {1975, 1979), Short (1975, 1979a, b), Chappell and Eliot (1979), Wright et al. (1979a, b, 1982b), Goldsmith et al. (1982), Wright {1982}, Bowman and Goldsmith (1983), Wright and Short {1983, 1984}, Katoh (1984), Symonds and Bowen (1984), Sunamura and Takeda (1984), and Sallenger et al. (1985). Despite the complexities of bar-trough beach and surf-zone systems, there are commonalities, recurrent in space and time, with respect to morphology, hydrodynamic processes, and temporal behavior patterns. The purpose of this paper is to examine prominent morphodynamic features utilizing observational data from a field site in southeastern Australia.

253 SITES A N D METHODS

Most of the field data on which this paper is based were obtained from an exposed, moderate- to high-energy, microtidal sandy beach in southeastern Australia. The Australian sites have been described most recently by Wright and Short (1984). The major site of relevance here is Eastern Beach on the Gippsland coast of Victoria (Fig.2), although some data from Moruya, N.S.W., and Narrabeen, N.S.W. (near Sydney) are included in the discussion. The Eastern Beach site is part of the long uninterrupted beach of East Gippsland ("Ninety-Mile Beach"); it is described in detail by Wright et al. (1982b). Well-developed straight or rhythmic bar-trough topography prevails for most of the time. Storm waves dominate the energy regime: the frequent passage of southwesterly or southeasterly gales causes highly variable and rapidly changing wave conditions. Owing to frictional dissipation over the wide, shallow, and rough shelf, inshore wave heights are substantially lower than those offshore (Wright and Short, 1984). The waves typically break at oblique angles generating strong longshore currents. Spring tide range averages 1.5 m. Sediments composing the beach and surf zone bed are predominantly quartz ranging in size from 0.30 mm {1.72 ~) in the outer surf zone to 0.45 mm (1.13 ~) in the swash zone. The main experiments on Eastern Beach were c o n d u c t e d in late Autumn (May) of 1981. Surveys of the beach and surf zone at Eastern Beach were carried out using a conventional theodolite and a surveying level. A specially designed staff permitted the staff handler to operate in the surf zone to water depths of a b o u t 4 m. Surveys were extended seaward of the surf zone using a R a y t h e o n Model D E 7 1 9 surveying echo sounder. Horizontal positions for bathymetric surveys were determined b y theodolite angles from shore. At the main Eastern

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254

Beach experiment site, a survey grid was established consisting of six profiles spaced at intervals of 50 m alongshore. These lines were surveyed daily over the experiment period. Benthic currents seaward of the Eastern Beach surf zone were recorded from depths (h) of 10 and 20 m using a pair of InterOcean Model 195 M recording electromagnetic current meters. These instruments employ Marsh McBirney two-component electromagnetic current sensors with a range of 0--3 m s-1 and a precision of +2 cm s-1. We used a sampling interval (At) of 2 s, a burst duration of 15 rain, and an interval of 1 h between the start of each burst. The instruments were m o u n t e d on tripods weighing 220 kg with sensors situated at elevations of 1 m above the bed. Significant wave heights and peak periods at h = 20 m and h = 10 m were estimated from velocity spectra using linear wave theory. Additional data on deepwater waves near the shelf break (h = 90 m, ~ 8 0 km seaward) were obtained from an offshore oil platform (ESSO Australia's Kingfish B). Within and near the surf zone, strain-gage-type pressure transducers with 0--5 bar range absolute were used to measure pressure from which water surface elevation was estimated by simple hydrostatic conversion. Horizontal surf zone currents were measured by means of small, low inertia bidirectional ducted-impellor flow meters (Sonu et al., 1974; Bradshaw et al., 1978). Flow meters were m o u n t e d orthogonally to obtain time series of u and v (x and y components of velocity). Pressure transducers and flow meters were m o u n t e d together on masts with 50 kg flat bases in various arrays. Several such installations were deployed simultaneously. Figure 3 shows the shore-normal instrument array used in m a n y of the runs. Signals from the sensors were transmitted by cables to a mobile van housing a chart recorder, multiplexing digital tape recording facilities and minicomputers. The field monitoring system has been described by Bradshaw et al. (1978). Sensors were sampled simultaneously at intervals (A t) of 1--1.5 s. Data were corrected for frequency response characteristics (Nielsen and Cowell, 1981). Vertical profiles of suspended sediment concentration in the Eastern Beach surf zone were measured using the suction sediment sampler developed by Nielsen (1983, 1984a). -2INSTRUMENT

LOCATIONS

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255 Analyses included computing instantaneous and time-average vector resultants and performing spectral and cross-spectral analyses to determine the magnitudes of currents and surface oscillations corresponding to different frequencies and forcings. A fast Fourier transform was used to c o m p u t e spectral estimates. A phase angle of 90 ° (~/2) between water surface elevation, 77, and shore-normal current, u, at any given frequency was used as a test for the existence of surf zone standing waves at t h a t frequency. Current and surface oscillation amplitudes related to different frequency bands were determined from the total variance within that band. THE OCCURRENCE OF BAR-TROUGH STATES Of the six c o m m o n l y occurring beach states discussed b y Wright et al. (1979a) and more recently by Wright and Short (1984), the intermediate "longshore bar-trough" (Fig.la) and "rhythmic bar and beach" (Fig.lb) states are the most complex and enigmatic. Moreover, our observations in different parts of the world suggest that these states are more c o m m o n than either the fully dissipative or fully reflective extremes. On beaches subject to a large range of temporal variability, these states develop from a preceding dissipative profile in an accretionary sequence as the subtle bars of the dissipative state (e.g. Wright et al., 1979a, b, 1982a) migrate shoreward and become accentuated (e.g. Sunamura and Takeda, 1984). However, certain nearshore environments favor the persistence, virtually year-round, of the intermediate bar trough states. In these environments, the absolute widths of the surf zone and trough may vary widely but the general s t a t e tends to oscillate back and forth between the "longshore bar t r o u g h " state and the "rhythmic bar and b e a c h " state. This is the case for Eastern Beach as well as for Duck, N.C., in the mid-Atlantic Bight. It appears that, to a rough first-order approximation the existence of these states depends on the height, Hb and period, T, of the breakers and on the fall velocity, ws, of the sediment which can be combined into a single dimensionless parameter suggested b y Dean (1973): = Hb/(WsT)

(1)

Analyses of a 6.5 year time series of daily beach state observations from a highly dynamic time-varying beach (Narrabeen, N.S.W., Australia; Wright et al., 1985a) indicated that the "longshore bar trough state" is favored b y ~2 = 4.7 + 0.93 and the "rhythmic bar and beach" state most c o m m o n l y prevails when ~ = 3.5 + 0.76. In contrast, the fully dissipative state is only maintained when ~ > 5.5--6.0. At Eastern Beach, ~2 varies between 2.5 and 5.5 around a modal value of ~ 4 . 0 (Wright and Short, 1984). Tide range imposes an additional constraint on the maintenance of the longshore bar trough and rhythmic bar and beach states. Additional analyses of Short's 6.5 year time series of daily beach state observations from Narrabeen Beach (discussed b y Wright et al., 1985a, b) reveal that the bartrough states are typically associated with tide ranges on the order of 1 m or

256 less and are precluded when tide range exceeds 1.5 m even if the 12 values are within the necessary range. Notably, environments like those of Eastern Beach and Duck, N.C., where the bar trough topography is maintained for most of the time experience spring tide ranges which do not exceed 1.5 m. Although bars of various configurations frequently occur in the presence of high ranges, such bars are typically more subtle and rounded and lack the accentuated form described in the following section. GENERAL MORPHODYNAMIC CHARACTERISTICS Morphodynamically, the reflective and dissipative extremes of beach and surf-zone states are distinguished on the bases of the parameter: e = ab~2/g

tan2~

(2)

where ab is local breaker amplitude, ¢o is wave radian frequency (2~/T), ~ is beach slope, and g is acceleration of gravity (Guza and Inman, 1975). The fully dissipative beaches studied by Wright et al. (1979a, b, 1982a) and Wright and Short {1984) were characterized b y e values ranging from 30 to 500; values typically less than about 2.5 define highly reflective conditions. At a first order, breaker types also depend on e: breakers are usually of the spilling t y p e when e > 20, they are plunging when 2.5 < e < 20, and they are surging when e < 2.5 {natural data on breaker transitions show considerable scatter; Cowell, 1982). Intermediate beach states, particularly the longshorebar-trough and rhythmic bar and beach states, possess b o t h dissipative and reflective elements; e varies spatially. Universally, the longshore bar-trough state is distinguished by its high bartrough relief combined with a relatively steep beach face. Waves initially break over the bar by plunging or spilling and the bar region is moderately to highly dissipative {i.e. e is moderate to high). In contrast to the fully dissipative extreme, however, the broken waves cease their decay after passing over the steep inner edge of the bar and reform within the deep trough (Fig.4). The much steeper beach face is typically reflective with respect to the partially dissipated and subsequently reformed waves and e is commonly in the vicinity of 2.0. Runup is consequently relatively high. In terms of the shorenormal segregation of a dissipative bar and reflective beach face, the rhythmic bar and beach state are similar to the bar-trough state. However, rhythmic longshore undulations of the crescentic bar and the subaerial beach distinguish the rhythmic bar and beach state and maintain weak to moderate rip circulation. The rips are persistently located in embayments. Spacings between shoreline protrusions, crescentic bar horns and rips are typically on the order of 200--300 m {Short, 1979a, b; Wright et al., 1979a, b; Wright and Short, 1983, 1984). Figure 5 shows the profile configuration of the beach and surf zone of Eastern Beach as it appeared in the early phases of the experiment period. Figure 6 shows the plan configurations near the beginning and end of the experiment. A ground view of the study site is shown in Fig.4. Although the

257

Fig.4. V i e w o f e x p e r i m e n t a l site s h o w i n g o u t e r and inner breaks.

absolute width of the trough varied considerably over the experiment period, the main features as shown in Fig. 5 remained consistent. Waves broke over the shallow bar by plunging or spilling and breaker heights were on the order 0.6--1.2 m. The inner edge of the bar descended abruptly into the trough which was 1.5--2.0 m deep. The beach face was steep and maintained a gradient of tan # = 0.10. Over the step at the base of the beach there was a violent shore break (Fig.7a) followed by an explosive surge of high runup on the beach face (Fig.7b}. To distinguish the characteristics of the outer primary break and the shore break, it is necessary to define two scaling parameters, e, an outer (or surf) value es c o m p u t e d from the primary breaker amplitude and the local gradient of the bar crest and a beach-face value, eb, c o m p u t e d on the basis of the shore break amplitude and the beach gradient. These parameters had values of es = 30--100 and eb = 1.5--3.0 indicating, dissipative and reflective conditions, respectively (Fig.5). Consistent with observations of bar-trough topographies elsewhere (e.g. Moruya Beach, N.S.W.; Wright, 1982) the profile between the upper limit of

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258 m

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Fig.6. Plan configuration of the bar, trough and beach at the experiment site and locations of survey lines (a) May 5, 1981, and (b) May 16, 1981. t h e b e a c h face a n d t h e inner edge o f t h e b a r c o n f o r m e d well to an e x p o n e n tial m o d e l o f t h e f o r m :

h = h= (1 -- e-~x)

(3)

where h is local depth, x is distance seaward and h= is the asymptotic depth at which d h / d x ~ O. For the Eastern Beach case shown in Fig.5, h~ = 1.7 m and ~ = 0.06. The distance from the limit of runup to the inner edge of the bar (trough width) was about 100 m during the first few days of the experiment but decreased to 50 m as the bar migrated toward the shore. In plan view, the beach and surf zone exhibited long crescentic bar and beach rhythms with an average longshore wave length of 250 m separating successive shoreline protrusions, bar crescents and rips (Fig.6). Rips occupied the regions of shoreline embaymentswhich were also the regionsof maximum trough width. In addition to the large-scale longshore rhythms, the steep beach faceexhibited beach cusps spaced at intervals of about 35--40 m. These cusps were best developed along sections fronted by the most pronounced bar-trough relief and were poorly developed in rip bays.

259

Fig.7. A relatively high and violent shore break over the step (a) was followed by an explosive surge of high r u n u p on the steep beach face (b). GENERAL PROCESS SIGNATURE OF THE SURF ZONE

The more important modes of fluid motion which contribute to the Shear stresses T and net water transport, V in surf zones include: (1) oscillatory flows corresponding directly to the incident waves; (2) oscillatory or quasioscillatory flows corresponding to standing waves and edge waves at frequencies lower than incident wave frequencies, particularly those at subharmonic (period twice incident wave period) and infragravity (period >30 s) frequencies; and (3) net circulations generated by wave-energy dissipation, specifically longshore currents, rips, and net return flows. Our observations of different surf zones show that the relative velocity magnitudes of these different modes of motion depend on morphodynamic state and also vary with location within the system (Wright, 1982; Wright and Short, 1984}.

260

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histograms are proportional to amplitudes.

In highly dissipative surf zones, shoreward decay of incident waves is consistently accompanied by shoreward growth of infragravity standing waves. In the inner surf zones of such beaches, currents assoqiated with infragravity standing waves are 2 to 3 times stronger than the orbital velocities of incident waves and are also usually dominant over mean currents (Wright et al., 1982a). On reflective beaches, incident waves and subharmonic edge waves are strongly dominant and mean currents and infragravity oscillations are very weak (Wright et al., 1979a; Wright, 1982; Wright and Short, 1984). F o r any given set of wave conditions, the strongest rips and associated feeder currents occur in association with the intermediate transverse bar and rip state. It is in the presence of the longshore-bar-trough and rhythmic bar and beach states that the most complex process signatures prevail (Wright, 1982; Wright and Short, 1984). Under these m o r p h o d y n a m i c conditions, important roles are played b y all of the modes of motion. In a succession of experimental runs, water surface, ~ (pressure) and horizontal current, u and v time series were recorded at different longshore and shore normal positions within the surf zone. From statistical and spectral analyses of these time series, we have estimated the velocity amplitudes corresponding to the incident waves and to subharmonic and infragravity standing waves, the velocities of mean currents, and the significant heights o f water surface oscillations at the different frequencies. The results of these analyses from several of the more important runs are listed in Table 1 together with the positions and depths of the sensors.

262

An example of a "process signature cross section" is shown in Fig.8 based on data from 11 May across profile 6 after the bar had migrated shoreward. The upper histograms show absolute significant heights of oscillations at incident wave (Hs), subharmonic (/'/sub) and infragravity (Hm) frequencies. The lower histograms show the corresponding u and v velocity amplitudes. It is apparent from Fig.8 that in contrast to highly dissipative surf zones (Wright et al., 1982a), motions at incident wave frequency are dominant at all locations. However, there is a shoreward growth of subharmonic and infragravity motions and mean currents are significant. INCIDENT WAVES AND SURF

The dominance, right up to the beach face, of energy in the frequency band of the incident waves {0.05--0.33 Hz, 3--20 s) is a distinguishing characteristic of bar-trough surf zones. Figure 9 shows examples of time series

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Fig.9. Examples of pressure (n) time series from different positions (x) across the surf zone (from run LE 4). (A) unfiltered time series showing combined swell plus high-frequency wind waves; (B) filtered time series showing swell with group amplitudes superimposed.

263

of unfiltered waves (~), the 10--20 s filter c o m p o n e n t of incident waves, and a time series following the amplitude of swell waves at four stations (locations shown in Fig.3) across the surf zone. The swell time series shown in Fig.9 correspond to oscillations in the 10--20 s period band and were obtained b y band-pass filtering the raw time series. Time series of wave amplitudes, G(t), were generated by removing the low-frequency components (T > 2 0 s) with a high-pass filter, taking the absolute value I~l of each point in the series, applying a low-pass filter to remove the incident waves, and multiplying the resultant values by ~/4 to correct for a non-symmetrical mean. What remains is essentially a time series of the running means of approximately half the amplitudes of the waves in a group o f two or more waves. The resulting G(t) time series is similar in principle to the " s m o o t h e d instantaneous wave energy history" (SIWEH) obtained by the m e t h o d of F u n k e and Mansard (1979) except that we remove the long period components and use [7[ instead of 7:. We c o m p u t e d t w o time series of G(t): one, Gw(t) for all waves in the period band 3--20 s and one, G,(t), for swell groups applicable to swell in the period band 10--20 s. F r o m these time series, a dimensionless grouping factor, G', expressing the amplitude variability relative to the time averaged amplitude can be estimated from: G'

=

[2 Vat G(t)]l/:

(4)

where brackets indicate time averaging and Var G(t) is the variance of G(t). In this analysis, (G(t)) and Vat G(t) were c o m p u t e d from records 3000 s long. Since the series G(t) is a running mean of 1/2 the wave amplitude, (G(t)) is equivalent to 1/4 the mean wave height. Extremes of G' are 0 for waves of uniform height and 1 for a simulated "completely g r o u p y " wave train in which the amplitude alternately varies from zero to some recurrent maximum. Separate values, G~ and G's can be c o m p u t e d for the total incident wave spectrum and for swell. Table 2 lists the corresponding grouping factors at four stations across the Eastern Beach surf zone. Note that G's is always larger than G' w since a narrower band of difference frequencies leads to more regularity in the amplitude modulation. From Fig.9 and Table 2 it is apparent that wave height as well as groupiness experience only slight variations from the bar crest to the step. A slight TABLE 2 Cross-shore variations in wave height, Hs, total incident wave groupiness, Gw and swellband groupiness, G s Run LE4

x (m) Hs (m) G~G~

115 90 0.59 0.44 0.33 0.36 0.69 0.67

LE5

70 35 0.36 0.45 0.36 0.35 0.65 0.66

115 90 70 0.57 0.49 0.42 0.34 0 . 3 2 0.32 0.69 0.68 0.68

LE6

35 0.52 0.34 0.68

115 0.60 0.32 0.74

90 70 0.51 0.45 0.33 0.35 0.79 0.'/8

35 0.52 0.32 0.75

264 decrease in height between the outer station and the middle of the trough was followed by subsequent shoaling over the inner margins of the trough with the result that the waves at the shore break were consistently slightlyhigher than the waves over the outer edge of the trough. Within the trough the waves did not break again before reaching the step region and were not at all borelike. The degree of wave groupiness is nearly constant from the bar to the step, consistent with a progression of reformed incident waves through the trough. This contrasts sharply with the conditions in flat dissipative surf zones where breaker and bore heights are locally depth limited in accordance with H b = ~h (Wright et al., 1982a), and incident wave groupiness would be expected to decay landward. The bar-trough surf zone is clearlynot saturated landward of the bar. Another important characteristic is the comparative constancy, over time, of the significant (and rms) heights of the waves which traversed the trough and reached the beach face despite appreciable variations in deepwater height, H~. S o m e of the reduction in temporal variability must certainly have been attributable to frictional dissipation of higher waves seaward of the breaker zone (Wright et al., 1982b; Wright and Short, 1984). M u c h of it, however, must have resulted from the tendency for the depth over the bar crest to limit the height of the waves which cross the bar. It m a y be reasonably surmised that the m a x i m u m possible shore break height should be proportional to bar-crest water depth. The outermost sensor (Fig.3) also shows relatively little temporal variability of wave height. However, it must be pointed out that the sensor was situated approximately beneath the average breaker position. The largest waves broke seaward of the sensor and were thus partially dissipated by the time they reached the sensor. SURF-ZONE STANDING W A V E S A N D INFRAGRAVITY E N E R G Y

Infragravity energy is important in all natural surf zones and it takes the form of standing surf-zone oscillations (Holman, 1981; Huntley et al., 1981; Guza and Thornton, 1982; Wright, 1982; Wright et al., 1982a; Wright and Short, 1984). Theoretically, these long-period (20--300 s) standing oscillations may exist as either (a) leaky mode standing waves in which the reflected energy is radiated back to sea, or (b) trapped mode edge waves which may be either progressive or standing alongshore (Guza and Davis, 1974; Guza and Inman, 1975; Holman, 1981; Huntley et al., 1981). In fully dissipative surf zones where bar-trough topography is subtle or absent, the infragravity energy is strongly dominant near the beach face and is primarily at low frequency (periods of 100--200 s; Wright et al., 1982a). The tendency for infragravity energy to be subordinate in the presence of pronounced bar-trough topography is evident from Table 1 and Fig.8 and has been previously reported (Wright, 1982; Wright and Short, 1984). Furthermore, infragravity energy peaks are centered at much higher frequencies in bar-trough surf zones than in fully dissipative surf zones. This was noted earlier for other bar-trough examples (Wright et al., 1979a; Wright, 1982; Wright and Short, 1984) as

265 well as for Eastern Beach, however, these distinctive infragravity signatures have remained enigmatic. In analyzing and reanalyzing the Eastern Beach data set we posed the following questions: (1) What are the unique features of infragravity oscillations in the presence of bar-trough topography? (2) How likely is it that the surf zone infragravity motions are locally forced by the groupiness of the breaking waves as hypothesized by Symonds et al. (1982) and Symonds and Bowen ( 1 9 8 4 ) a n d concluded by Huntley and Kim (1985)? (3) Do the dominant standing waves have antinodes over the bar and nodes in the trough as would be expected for resonance in equilibrium with the topography and as suggested by Symonds and Bowen (1984) and Katoh (1984)? and (4) Are the lower frequencies suppressed and if so why? Normally incident leaky mode standing waves are typically two~iimensional standing waves with longshore wave numbers of k] = 0. The longshore wave number kl of an edge wave of m o d e n is related to edge wave radian frequency coe by a dispersion relationship which has a simple analytical solution for linear (Eckart, 1951) and exponential (Ball, 1967) inshore profiles. Eckart's (1951) now familiar dispersion relationship for linear beaches with slope ~ is: ~.De2 --

g k l ( 2 n + 1) t a n ~

(5)

Ball's (1967) form for an exponential profile is somewhat more elaborate; however, neither a linear profile nor an exponential profile is a valid approximation to pronounced bar trough topography. Numerical procedures must be used to estimate kl over pronounced bar-trough relief. Linearization of the equation of wave motion in the surf zone expressed in terms of the velocity potential ¢ has the form:

The velocity potential • is related to water surface displacement, 7, xc o m p o n e n t velocity u, and y - c o m p o n e n t velocity v by: =

lab gat'

u

a¢ 3x'

v

a¢ by

We assume x to be shore normal and y to be shore parallel. In both leaky m o d e and trapped mode standing waves, the local amplitude a(x) of water surface (W) oscillations alternates between maxima at antinodes (u minima) and minima (or zero for pure standing wave) at nodes (u maxima). The first antinode of all frequencies is the beach face where the oscillations of ~ are manifest as runup with vertical amplitude a0. The offshore variation in dimensionless amplitude f(x) = a(x)/ao expresses the alternation between nodes and antinodes. The corresponding space and time variation in velocity potential for both leaky and trapped m o d e standing waves has the form: ¢ = g ao~(X) cos (klY - - cot) CO

(7)

266

For normally incident leaky modes kl = 0. Replacing x, h, and kl with the non~dimensionalized quantities: x * = xco2/g,

h* = hw2/g,

kl*= klg/co 2

and substituting eqn.(7) into (6) we obtain: d dx*

h* d~

dx*

(k*2h * -- 1)~ = 0

(8)

The boundary conditions for the dimensionless amplitude function ~ are [(0) = 1, d~/dx*lx =0 = --1/tan ~ at the beach face, and ~(x) remains finite as x -~ ~. This last condition imposes the constraint that only certain values of the longshore wave number kl are possible for a given frequency, w; the relationship between kl and co is, of course, the dispersion relation. The analytical solutions which exist for ~ and k~ (e.g. Eckart, 1951; Ball, 1967) only apply to linear and exponential profiles. F o r complex bar-trough topography such as we are dealing with here, eqn.(8) must be solved numerically. In the analyses which follow, we utilize numerical solutions obtained b y means of an algorithm which was developed to search for edge wave wavenumbers for the full range of likely mode numbers, n, over observed natural profiles. The procedure permits the shore-normal variability of ~(x) to be determined and, hence, the theoretical positions of nodes and antinodes to be accurately estimated. Our numerical scheme was also applied to linear and exponential profiles in order to compare the results against the known analytical solutions. For the results presented here, the error index was set at 0.01% which, for the simple cases, gives edge wave wavenumbers to within 0.01% of that given b y the analytical solution. Examples of power spectra and cross spectra of T and u from different locations within the trough of Eastern Beach are presented in Fig.10. Frequencies which are standing exhibit phase angles of n/2 between T and u. In the case shown in Fig.10, long-period (T = 12--14 s) swell is dominant and appears to be partially standing. Pronounced standing wave motions are present at infragravity frequencies including frequencies which might be subharmonics of the swell. The sharp valleys in 77spectra accompanied b y peaks in u at the same frequency indicate the presence of a standing wave node at that particular frequency and offshore (x) position. Because of these peaks and valleys, which are inevitable features of standing wave spectra from locations other than the first antinode (runup), it is difficult to discern whether or n o t there are any real energy peaks at specific frequencies. We have attempted to overcome this problem b y estimating '%otal~energy" spectra which combine the potential (related to ~) and kinetic (related to u and v) energy into a single spectral estimate, St(f), for each frequency f using: St(f) = h [Su(f) + Sv(f)] q- g S T ( f )

(9)

where S u ( f ) , S v ( f ) , and ST (f) are, respectively, the separate spectral estimates of u, v and W at frequency f. Figure 11 compares a total energy spectrum (encompassing only the infragravity frequencies) from a fully dissipative surf

267

~

STANDING

RUN L [ I

x • 7ore h ,ll3m

i

r~, u(m2s '1

xh ~90m =08m

JO°

.%//~1 i~I II

GIPPSLIINO ]1 NAT,I$$1 RUN L[4

=d

GIPPSLAND 11 HILHI$!

I0 STANDING

TROUGH f /

~ i~

//%~ulm2s'') ' % BAR (INNER EDGE) ~ i ^

,o ~~

~ q~ms,

,

OO5

,~ ~ 1 ~

~

\.J~fX " V ' ~v V ~, / X '

Ol O15 02 ;REQUENCY (Hz)

OZ5

03

005

Ol O15 02 FREQUENCY (Hz}

025

O05

Ol O15 O2 FREQUENCY (Hz)

025

03

08 O6

o

I-C . Or 015 O2 FREQUENCY (Hz)

-

Z ] _ ± ~ -

OO5

180 r

. . . . .

O25

O3 180o

9~ t .leo°

.,8o°i

~

Fig.10. Power spectra and cross spectra of n and u from time series recorded simultaneously in (left) the trough and (right) over the inner edge o f the bar (At ffi 1.5 s, d.f. = 12).

I00--

/

i/~" ",\\

/

\ X

/

~

DISSIPATIVE

SURF Z O N E

\ ~ . f "--/-, \

'N ,¢

BAR - TROUGH

\

SURF ZONE

0

I

.01

I

.02

I

.03 FREQUENCY

i

.04 (hz}

I

.05

I

.06

\

.017

Fig.11. Comparison of a "total energy" power spectrum of low-frequency energy (f < 0.07 Hz) from bar-trough surf zone (Eastern Beach) with that from a fully dissipative surf zone (Goolwa; Wright et al., 1982).

268

zone (Goolwa; Wright et al., 1982a) with a total energy spectrum from the pronounced bar-trough topography of Eastern Beach. In the bar-trough case, most of the standing wave energy is associated with a family of discrete and relatively sharp peaks at frequencies higher than 0.02 Hz. In the dissipative surf zone, the infragravity energy is not only much more dominant but occurs primarily in a wide frequency band centered around 0.01 Hz. In contrast to the theoretical model proposed by Symonds and Bowen (1984) and to the field results obtained by Huntley and Kim (1985) from an unbarred beach, the dominant infragravity oscillations observed in the Eastern Beach surf zone cannot be explained in terms of local forcing by the grouping of the incident waves. Figure 12 shows smoothed spectra of infragravity currents (u) in the trough compared to spectra of group (or envelope) amplitudes near the break point. The two spectra are not at all similar and the coherence is very low across the entire frequency band of the dominant infragravity energy (e.g. from 0.01 to 0.05 Hz). There is moderately high coherence at lower frequencies (<0.01 Hz) suggesting the possibility that the longer period motions may be forced. However, infragravity energy at these low frequencies is secondary in the bar-trough surf zone. Alternatively, it appears much more likely that infragravity oscillations are controlled by the inherited geometry of the bar-trough topography as originally suggested by Wright et al. (1979a) and Chappell and Wright (1979). We applied the numerical procedure previously described to estimate the shorenormal variation of ~ for leaky mode standing and edge wave modes over the observed complex topography. Figure 13 shows the predicted x positions of the first nodes and second and third antinodes for different periods. The first antinode is always at the beach face (x = 0) regardless of frequency. The IO 0

u

IN T R O U G H

'N

IO - 2

"x

E

LOW-PASS FILTERED SERIES

"---.

NEaR

BREAK ~

~0/ x

0

112 O o o

.01

.02

.03 FREQUENCY ( h z )

05

,04

COHERENCE 2 ,

,

Fig.12. Power spectra and coherence squared of low p ~ - f i l t e r e d shore normal currents (u) in trough (solid) and group amplitudes near break point (broken). Note low c o h e r e n c e throughout the frequency region of the dominant infragravity energy in u (0.02-0.04 Hz).

269

I00

80

.~ 6O

~40 CL

20

1.0 E 2.0 3.0 4.0 0

20

40

60 OISTANC F

80

IO0

120

140

z (m)

Fig.13. Predicted shore-normal positions (x) of the first nodes and second and third antinodes as functions o f standing wave periods. The upper boundary of each of the shaded bands is the normally incident leaky m o d e case; the lower boundary represents the solution for the lowest possible edge wave mode. Solutions for higher m o d e edge waves lie between the upper and lower boundaries of the bands. upper boundary of each band in Fig.13 represents the leaky mode solution, and the lower boundary represents the lowest possible edge wave mode. Other edge wave modes lie between the upper and lower boundaries. As suggested by Symonds and Bowen {1984) resonance should be enhanced at frequencies which have antinodes over the bar and suppressed at frequencies which would have their first nodes over the bar. Observed nodal positions, which were readily identified from spectra like those shown in Fig.10 are plotted in Fig.14 in relation to the predicted positions of the first and second nodes. There is seen to be a high degree of consistency between runs and a good correspondence between predictions and observations. Within the frequency band of the d o m i n a n t standing wave energy, the nodes are situated within the trough. Shorter period standing waves corresponding to the longest period swell (16--17 s) have first and second nodes in the trough. Total energy spectra observed at two different locations within the trough at high and low tide on the same day are shown in Fig.15. The spectra are superimposed on bands which embrace the frequency regions of predicted possible nodes and antinodes over the bar. The widths of the bands reflect uncertainty as to what is defined as the bar crest as well as differences related to whether a leaky mode or edge wave model is used. As expected, predicted

270

tlO I00 OBSERVED

Ist N~DE -

NODES

90

v

A'I I I LP'.~*."

~

.,~IllI?'+" ,~(>~"

Le 4

•

f.40-

.

~'II IUJ'j'l~*

3,0-

•

2rid N O D E x

x

x

i

20-

o-

e~ ' ' ~ ' ~ ' - - ~ ° ° ~

I~ \ ~

" INSTRUMENT

STATIONS

c

0

20

40

60 BO D I S T A N C E x (m)

I00

120

Fig.14. Observed and predicted shore-nom,.a] positions of standing wave (leaky mode and edge wave) nodes. tOX =

---

I

70m

X = 90m

l I

A

l

I

24s

HIGH TIDE

/" -\ *N .C I--

I0-

/l,..~ /'X'JI

\

//

2rid ~NTt,;;OE

lit NODE SEAWARD OF I N N E REDGE O F BAR

~;.; L-o'~ ~ OVER BA,,

/

3VER BAR

/

;'St

/

)

LOW TIDE

.;,

.;z

• 3

FREQUENCY

.04

.05

06

C"

(hz)

Fig.15. Total energy spectra o f standing wave energy ( f < 0 . 0 7 H z ) at t w o l o c a t i o n s (x = 70 m, x = 9 0 m ) in the trough at high tide ( A ) and l o w tide (B). Predicted f r e q u e n c y bands for the occurrence o f t h e s e c o n d and third a n t i n o d e s over the bar and 1st n o d e over the bar are s h o w n (d.f. = 12).

271 and observed infragravity frequencies are lower at low tide. There are other important features. First, at high tide, a low-frequency infragravity peak is present within the "node-over-the-bar" zone, b u t a distinct energy trough is present in this region at low tide when the depth over the bar is shallower and the suppressing effects of the bar are presumably more pronounced. At the opposite frequency extreme, standing waves at the period of the long period swells have their 2nd or 3rd antinodes over the bar, depending on m o d e number. Within the "2nd antinode over the bar" band, there are distinct peaks which recurred consistently during both high and low tides. Leaky mode standing waves or edge waves of mode 3 or higher at the frequency of the lower-frequency peak (35--45 s) are predicted to have their 2nd antinodes over the bar. Standing waves corresponding to the higher-frequency peak can only have antinodes over the bar if they are mode 1 edge waves; otherwise, they should have their second nodes over the bar. The predicted cross-shore variations in dimensionless amplitude f of different modes corresponding to the frequencies of the two prominent low tide peaks (T = 40 and 26 s) are shown in Fig.16. Assuming the 40 s standing wave to be a m o d e 3 edge wave (which satisfies the resonance condition of a node in the trough, antinode over the bar), the corresponding longshore wave length would be about 500 m which is close to twice the longshore spacing of rips and other larger scale surf zone features. This is consistent with the notion that rhythmic longshore features are related to edge waves standing alongshore and are therefore spaced at one-half the edge wave length. The 26 s peak in this example could be a subharmonic of the swell, the specific frequency selected from the possible range by the trough dimensions. The m o d e 2 edge wave model predicts an antinode over the shoreward edge of the bar, while the m o d e I edge wave mode predicts an antinode over the seaward edge of the bar. Note that, considering the natural topography, the amplitude of the 2nd antinode over the bar is larger than the first antinode at the beach face. This result is consistent with the spectra shown in Fig.15 b u t is n o t anticipated from the analytical linear profile solution of Eckart (1951) or the exponential profile model of Ball (1967). We draw the following conclusions concerning infragravity energy and standing waves in the presence of pronounced bar-trough surf-zone topography: (1) infragravity energy is lower than incident wave energy; (2) the dominant infragravity energy occurs at higher frequencies than in dissipative surf zones; (3) the dominant infragravity oscillations are not locally forced b y the groupiness of the incident waves; (4) the trough is the locus of the dominant standing wave nodes; (5) frequencies low enough to have their first nodes over the bar are suppressed, though less so at high tide than at low tide; and (6) the dominant infragravity oscillations have antinodes over the bar. We must emphasize that in cases where pronounced bar trough topography prevails, the bar itself has experienced some accretionary evolution and is typically shoreward of its initial high-energy position. The bar-position governs the infragmvity motions just described rather than the reverse. It is likely, however, that the dominance of standing wave nodes in the trough

272 LEAK+ NODE . . . . . . . . NOD[ 0 l O G [ WIvE -----NOD~ I lOBE w & v l .... MODE I lOBE wAVE " M O 0 [ $ lOBE W&V[

~2~~-I::::::::::::~RO~H: 0

.

4

~'o

v

T

4o

40S

T=

so

,6

,~o

v

,~o

,,o

1

,~o

I

0-

~2-

T = 26s T ~OUGH

io

,'o

:

"i:

~o

~o

,Go

DISTANCE: • ( m )

~,o

.

:

~

,:,o

,~,o

Fig.16. Predicted shore-normal variation in the dimensionless amplitudes, ~ = a/ao, of leaky mode standing waves and different edge wave modes corresponding to the observed 40 s (A) and 26 s (B) peaks from the total energy spectra in Fig.15.

plays an important role in maintaining trough depth. The shoreward migration of the bar causes an increase in resonant frequency. SURF-ZONE CIRCULATION AND NET CURRENTS

The net (time-averaged) circulation features observed in the Eastern Beach surf zone were of three general types: (1) vertically segregated shore normal drifts; (2) horizontally segregated rip circulation; and (3) longshore currents. The vertically segregated drifts were prominent over the bar and within the trough in regions away from rips. This form of circulation was similar to that described for the dissipative surf zone at Goolwa, South Australia, by Wright et al. (1982a) and was characterized b y net onshore transport in the surface layer and net offshore transport near the bottom. Onshore wind stress probably played a role in maintaining this form of circulation. The nature of this circulation is illustrated by the results of a vertical profile of shore-normal

273

(u) velocity measured in the trough where the depth was 2.0 m. Figure 17 shows the time series of u, filtered with a 100 s filter to remove wave effects, from 0.04, 0.22, 0.45 and 0.91 m above the bed. Closest to the bed, flow is seen to be exclusively offshore whereas it is predominantly onshore at and above 0.91 m above the bed. Onshore transport prevailed throughout the upper meter of the water column. As indicated by the values of time averaged near b o t t o m velocities (~u)) in Table 1, flows below 0.30 m above the bed were seaward throughout the study period. Since onshore transports in the upper half (or more} of the water column were substantially stronger than seaward transports near the bed, it may be concluded that the depth-averaged water transport was shoreward in the vicinity of this profile which was situated near a shoreline protrusion. This excess onshore transport was accomodated by the net horizontal circulation pattern shown in Fig.18. Water flowed alongshore within the trough and turned offshore as a wide rip in the region of profile 4. Within the rip, flow was seaward at all depths. Unfortunately, we were unable to obtain a vertical velocity profile in the rip owing to the strong current drag on the vertical mast. Near b o t t o m (0.20 m above the bed) velocities of up to 0.30 m s-I were recorded and dye tracking of surface flows indicated stronger surface flows. However, the observed rip velocities were substantially weaker than those which normally occur in association with the transverse bar and rip type of topography (Wright and Short, 1984). Despite the fact that the rip was not excessively strong, it was nevertheless effective in causing seaward bedload Icm/min , +-0-5m/s , 2V , IOOsec. FIIter I minute 01

~ 0"9 time

0

0

Z= 0 . 4 5 m

A^

/~

H%t

j~

-0"1 -0'2

01 ~= 0-22m

-0.2

-0-1

'-0-2 Fig.17. Shore-normal current (u) time series from four elevations showing vertical segregation o f onshore (upper level) and offshore (lower levels) flows. An electronic filter w i t h a 100 s time constant has been applied to remove incident waves.

274

EASTERN BEACN,GIPPSLAND,¥1C. 5 MAY,1981 200

(~)

o

o-~

BREAK

Hi, = I ' 0 - 1"5m

150

100

50

0

50

100

150

200

250m

Fig.18. Observed plan-view circulation in the Eastern Beach surf zone. transport of sand as evidenced by the presence of seaward-migrating dune bedforms. For a few days during the experiment period, strong longshore currents prevailed within the trough related in part to oblique wave incidence and in part to local pressure gradient forces "feeding" the downdrift rip. We succeeded in obtaining vertical velocity profiles of these currents, some examples of which are shown in Fig.19. Although longshore currents over simple topography have been the subject of considerable attention (e.g. Longuet-Higgins, 1970a, b; Komar, 1975, 1976; Kraus and Sasaki, 1979; Gourlay, 1982) there is very little field data on the nature of longshore currents within pronounced troughs or on the vertical current structure. Some more detailed analysis and discussion of our data are therefore warranted. Time-averaged longshore current velocities ((v)) near the surface exceeded 0.5 m s-1 in some runs; at 0.075 m above the bed (above the level of ripple troughs) velocities were still as high as 0.25 m s-~ (Fig.19). Although these longshore velocities were on the same order of magnitude as the wave orbital velocities, the b o t t o m boundary layer was apparently dominated by the waves which acted in the shore normal direction orthogonal to the longshore currents. This is indicated by two lines of evidence: (1) the bedforms were fully developed, sharp-crested wave induced ripples (heights, ~r = 0.08 m; lengths, X~ = 0.5 m) with long crests aligned shore-paraUel; and (2) vertical profiles of suspended sediment concentration (discussed further in the next

275 /X

1 0 S E C FILTER,SAMPLED 100 SEC FILTER,SAMPLE I-1 100 SEC FILTER,SAMPLE x FAST,SAMPLE INTERVAL o FAST,SAMPLE INTERVAL

EVERY 6 SECS. INTERVAL 1 MIN. INTERVAL 1 MIN. 6SECS. 6SECS.

;l(m) I-0 O

,~.

0"8

0"6

0"4

0-2

0"1

0.2

0.3

0.4

0-5 (m/s) >

Fig.19. Vertical profile of time-averaged longshore current velocity, ,as recorded within the trough of Eastern Beach in a succession o f runs. The position of the lowest flow meter is shown.

subsection) were perfectly exponential similar to those observed under pure wave m o t i o n and concentration magnitudes were not significantly larger than would be expected from waves alone. The longshore current profiles were not at all logarithmic (Fig.19) and it appears that t h e y were strongly influenced by the vortices generated by the wave oscillations over the ripples. Between the elevations of z = 0.07 and 0.30 m above the bed, which is the domain of the vortices shed by the ripples, the longshore current velocity was nearly constant. This is understandable since, for a constant time averaged longshore shear stress, T, the velocity gradient, d(v)/dz, must adjust to the total eddy viscocity, vt, t h a t is: d(v) d z = ~lPvt

(10)

and hence be small where vt is large. The wave induced vortices cause a very large exchange of m o m e n t u m for a given shear rate, and thus produce a large e d d y viscosity. Grant and Madsen (1979) have presented a theoretical model for wave-current interactions near rough beds which describes this effect and Grant et al. (1983) have analyzed observed effects on b o t t o m stress over the continental shelf. The strong effect of the vortices within the trough is probably related to the fact t h a t the axes of the vortices are oriented parallel to the direction of the longshore current. The b o u n d a r y layer structure is different in rip currents where wave oscillations parallel the mean flow producing a "roller e f f e c t " . In order to model the current flow near the bed of the trough, we will consider the mean longshore flow as a steady current which only inter-

276

acts with the waves by way of the total eddy viscosity, vt, which consists of two components (vt = vw + vc): a component vw attributable to the waves and a component vc attributable to the current. Equation (10) relating the time averaged longshore velocities to shear stress then becomes: d(v) p(vw + re) ~ = z(z)

(11)

The eddy viscosities, vw and vc are related to vertical velocity fluctuations. Assuming the distribution of shear stress to be linear: z(z) = r~(1 - - z / h )

(12)

where re is the longshore shear stress at the bed, the contribution of the longshore current to eddy viscosity is:

vc = C~v.~z(1 - - z / h )

(13)

where v. ~ is the friction velocity related to the longshore current v.~ = ~

(14)

For " p u r e " steady flow, the constant Ca is equal to Von Karman's constant (K = 0.4). The wave-induced eddy viscosity Vw can be evaluated from Lundgren's ( 1972) empirical formula: vw =

Cwu,wZ z

1 + 1.34(0.5f,,,,) ~/4 T exp

(15)

(z/8)

where f~ is the friction factor (Jonsson, 1967; Swart, 1974; Lofquist, 1980), 5 is boundary layer thickness, u.w is wave friction velocity and Cw is a constant pertaining to wave effects. Equation (15) was obtained by Lundgren {1972) from analyses of boundary layer measurements subsequently published by Jonsson and Carlsen (1976). We note that vw is initially proportional to z but then decays exponentially with z farther from the boundary with a length scale of decay equivalent to the boundary layer thickness 5. Exponential decay was observed by Nakato et al. ( 1 9 7 7 ) a n d MacDonald (1977) in measurements of vertical velocity fluctuations, Wrms, in oscillatory boundary layers. Their measurements also show t h a t the vertical length scale, l, of suspended sediment concentration profiles [c(z) = Coe-Zn; where Co is concentration at the bed] are virtually identical to those of the velocity distribution. Although we have no measurements of Wrms, we do have direct field measurements of c(z) {discussed further in the next subsection) obtained simultaneously with the longshore current profiles. We can use these data to obtain an estimate of the length scale, l [since c(z) showed consistent expo-

277 nential decay with z] from: =

--

~ 0.093 m

(16)

The length scale, l, can then be used to replace 8 in eqn.(15). By replacing 5 with l, and inserting vc and Vw as obtained from eqns.(13) and (15) into (11) we get: d(v> _ v2,c(1 - - z / h ) dg

v w + v c

or:

(V2>

J

Pw Jr Pc

dz

(17)

2 1

where (vl> and are the longshore velocities at two elevations, zl and z2, respectively. If Cw and C, are known, eqn.(17) will determine v.c from any pair of measured velocities. However, we cannot assume Cw = Cc = K = 0.4 since this will greatly underestimate the relative importance of vw and lead to a poor prediction of the velocity profile as iUustrated in Fig.20. However, if we set Cw = 0.4 and adjust Cc and v.c a good fit is obtained for Cc = 0.1 and v.c = 0.024 m s-1. Alternatively, as shown in Fig.20, an equally good fit is f o u n d for the combination Cc = 0.4, Cw = 7.4 and V.c = 0.10 m s-~. The resulting profiles of vw, vc, and Pt are shown in Fig.21. Our available empirical basis is insufficient to permit reliable prediction of longshore current profiles. However, the qualitative implications are that wave~enerated vortices shed from ripples have a paramount influence on longshore current profiles. The longshore bed shear stresses corresponding to the two alternative parameter sets (C~, Cc and V.c) described above differ by a factor of ~ 1 7 . Independent measurements of %, are needed to indicate which set of parameters is most appropriate. Z

(m) 1.0

/ I

C¢ : Cw :0"4, l v,¢ = 0'029 m/s/ /

o'., 0.2

/'~..~..~ /

C¢ =0"1, Cw=O'4, V~¢=0"024 m/s

0.3 o.4 0% (m/s) Fig.20. Predicted and observed longshore velocity profiles.

278

Z(m) 1-0 .

.

.

.

.

~W ~C

....

0"5

../"/ ~'--~~~-, (m's")

;z = I

I

i0 -3

I

--

2 x l 0 "3

Fig.21. Vertical distribution of total (vt), wave induced (Vw) and current induced (Vc) eddy viscosity.

SEDIMENT SUSPENSION IN THE TROUGH The observed presence of wave-formed ripples within the trough together with the observed tendency for wave oscillations to dominate the boundary layer suggests that oscillatory flows at incident wave frequency should dominate the entrainment and suspension of sediment. Recent laboratory and field studies indicate that oscillatory flows over rippled beds cause predominantly suspended load transport (albeit close to the bed) and that suspended sediment concentrations can be modelled as functions of b o t t o m orbital velocities (aso~), sediment fall velocity, ws, and ripple height ~ (Nielsen et al., 1979; Nielsen, 1979, 1983, 1984a, b; Nielsen et al., 1982). The conventional method of expressing suspended sediment concentration profiles is in terms of the one~limensiop~l diffusion equation: dc

E " ~ + wsc = O or:

d In c dz

-

ws E

(18)

where E is diffusivity, c is suspended sediment concentration and w~ is sediment fall velocity (e.g. Nielsen, 1979, 1983; Nielsen et al., 1982). However, recent work b y Nielsen (1983, 1984a) suggests that a more meaningful approach is to consider c in terms of the vertical length scale, l, in the form: c( z ) = Co exp (--z /l)

(19)

where Co is the concentration at the ripple crest level (z = 0) and l is as defined by eqn.(16) and is related to the diffusivity by: l(z)

E(z) -

Ws

(20)

279 Nielsen (1979, 1984a) and Nielsen et al. (1982) have shown that Co is a function of the skin friction Shield's parameter: e' = ~ / ( p , -

p)~pD, =

0.5 pfw(a,~) 2 (p, _ p)gO,

(21)

where, as previously fw is the f r i c t i o n factor, a s is orbital semi-excursion, o~

is wave radian frequency Ps and p are sediment and water densities and Ds is grain diameter. The length scale, l, relative to ripple height, ~r, is a function of (asco/w,) where ws is sediment fall velocity (Nielsen et al., 1982; Nielsen, 1983). Using the suction device described b y Nielsen (1983, 1984a), we obtained 12 concentration profiles from the Eastern Beach surf zone. Examples of concentration profiles from separate runs are shown in Fig.22. The results of these measurements are strictly comparable to field results from other beaches as well as laboratory results (e.g. Nielsen et al., 1982). The length scale, l, relative to ripple height, ~r, fits the relationship: - I- = 1.43 -- 1.25 exp 17r

--0.0011

(22)

from which we can predict l if we know or can estimate ripple height, ~ . Nielsen (1981) showed that ~ is largely a function of the mobility number: ~-

p(as~°)2 (p, -

(23)

p)~D,

Available data suggests: n_~ = 0.23 a, 1 + 0.022 exp (~/16)

(24)

Figure 23 shows the relationship b e t w e e n values o f l as predicted from eqns.(22) and (24) and values observed in the laboratory and in the Eastern Beach surf zone. Although there is appreciable scatter, the fit is reasonably I

v

'

I

r

r

v

,

I

'

0.6 ,

clz)

05 0-4

"-0"3

~,

T E S T 57 T E S T 58

o

T E S T 59

o

T E S T 60

0

0-2 o

0.1

o

~ o

K o

x

~ o

0

i

I

i

I

i

I

iO-S

i

i

I

10-4

o

i

~i

10-3

c (m31m 3)

Fig.22. Suspended sediment concentration profiles from Eastern Beach.

280

20

.

10

~ R~P

c~ I-0

Z

N

R : Eoslem Beech Field dote Loborolory dolo : I " Nokolo et o11977

P

0'4 0"2

'~" %"

N M

~

!

~M / v .,.M M

L~ M I " Nielsen(1979)

/ 0'2

/

°P 04

I'0

2

PREDICTED ~..

4

1 iO

20

(cm)

Fig.23. Comparison between predicted and observed values of the vertical length scale I. Observations from Eastern Beach are indicated.

good. We conclude that despite the complexity of processes in the presence of the longshore bar-trough and rhythmic bar-and-beach morphodynamic states, suspended sediment concentrations can probably be modelled in terms of entrainment by incident waves alone. TEMPORAL VARIABILITY OF INSHORE MORPHOLOGY

The temporal variability of beach and surf-zone forms largely expresses temporal variability of breaker conditions, including height, period, direction of incidence and groupiness. In many cases, the morphologic changes involve changes in beach state. Some beaches, particularly those fully exposed to high-energy but temporally variable waves can experience changes which take them through the full range of states from reflective to dissipative (Wright and Short, 1984; Wright et al., 1985a, b). However, for reasons noted earlier, beaches like Eastern Beach and the beach at Duck, N.C., do not change state appreciably but simply tend to alternate between the rhythmic-bar-and-beach state and the longshore-bar-trough state. However, despite the fact that temporal variations in s t a t e are small, the longshore-bartrough and rhythmic bar and beach states are among the most mobile and profile changes are large and rapid (e.g. Mason et al., 1984; Sallenger and Holman, 1985). The most prominent changes are associated with onshore--offshore migrations of the bar. Figure 24 shows a series of beach--surf-zone profiles measured at Eastern Beach over the period 5--16 May 1981. During the earlier phases of this period (5--8 May) comparatively low breakers caused an

281 (m) 6

Dune

5 4

~rp

3

EASTERN

-I -2

-

5 - 16 MAY, 1981

Erosion

~

egoCuspHorn "~,,~

0

BEACH

-/6/5

=Bor Migrotion

MLW

-

15/5

,do DISTANCE

,;o

16/5

2Go~

SEAWARD

Fig,24. Temporal variations in the beach and surf-zone profile at Eastern Beach, May, 1981. onshore bar migration rate of nearly 10 m per day. With increasing breaker heights after 8 May, onshore migration slowed and halted. Longshore migration of the rip and of crescentic bar "horns" accompanied onshore bar migration (Fig.6). Much longer time series of bar crest, trough and subaerial beach positions at Duck, N.C. have been obtained by Sallenger et al. (1985) and by CERC-FRF personnel (Mason et al., 1984). From Fig.24 it is apparent that by far the greatest changes are related to the bar crest position and trough width; the mobility of the subaerial beach is strikingly low. The Duck data also indicate that whereas the bar is subject to migrations over horizontal distances of about 200 m, the beach face advances and retreats across a zone only about 20 m wide. Changes in the gradients of the subaerial beaches at both Eastern Beach and Duck are also relatively small. The lowered mobility of the beach face is probably due, at least in part, to the filtering effects of the bar and trough system to prevent large temporal fluctuations in shore break amplitude. Cut of the subaerial beach, when it occurs, is generally accompanied by accretion on the segment of the profile immediately below the step. In the Gippsland example, there appears to be relatively little exchange of sediment across the trough between the bar and the beach. The maintenance of standing wave nodes in the trough may provide a barrier to cross-shore sediment exchange and may inhibit the tendency for the bar to weld to the beach. Temporal variations in bar position are generally accompanied by temporal variations in bar-trough profile shape. When the bar is farther offshore following a period of high energy, it is roughly symmetrical in shape and the bar crest-to-trough amplitude is at a minimum. As the bar migrates shoreward its amplitude increases, the trough depth-to-width ratio increases dramatically and the asymmetry of bar cross-section increases. It seems reasonable to believe that the shoreward migration of the bar is a simple response to the waves breaking over the seaward slope of the bar as suggested by Sunamura and Takeda (1984). Under the moderate- and low-energy conditions which permit the shore-

282 ward bar migration, the infragravity motions are not strongly forced and the accentuated bar-trough morphology can control the frequency and longshore wave number of the standing waves. Presumably, during high energy events, external forcing of the lower-frequency infragravity motions is strong enough to overwhelm the suppressing effects of the bar. Cause and effect roles are then reversed and it is likely that the seaward movement of the bar simply represents an equilibrium readjustment whereby the bar becomes reestablished as a broader, more subtle feature beneath the antinodal region of the dominant (forced) infragravity band. SUMMARYAND CONCLUSIONS The accentuated bar-trough beach and surf-zone states are common in nature; in environments such as those discussed herein, these states may persist year round. Bar-trough morphology of this sort is much more than a simple perturbation of an otherwise linear or exponential surf-zone profile. Many of the simplifying assumptions (e.g. roughly linear profile, saturated surf zone) which approximately hold in fully dissipative or unbarred surf zones, are invalid in the presence of accenttmted bar-trough morphology. Moreover, unlike the morphology of high energy dissipative surf zones, the surf zone morphology of the pronounced bar trough states is not simply the passive respondent to hydrodynamic forces. By significantly selecting and altering the surf zone processes, this morphology plays a fundamental role in its own maintenance. More than the morphology, distinctive though it may be, it is the form-coupled modes and patterns of surf-zone water motions that give the bar-trough states their unique signature. From the foregoing, we must underscore the following general points: (1) The "longshore-bar-trough" and '~thythmic-bar-and-beach" morphodynamic states, both of which are characterized by highly accentuated bartrough topography, are favored by the combination of moderate breaker heights and small tidal range. (2) The accentuated bar-trough morphology results in a process signature which is dominated by oscillatory motions at incident wave frequency across the entire width of the surf zone. (3) Because of the dominance of the incident waves, it is the incident waves which cause most of the sediment resuspension in the surf zone. Similarly, the waves are probably the main source of the eddy viscosity in the bottom boundary layer. (4) Standing waves and edge waves at infragravity and near-infragravity frequencies are energetically secondary, but are probably fundamental in determining the net drift patterns of water and sediment and, thereby, influencing surf-zone morphology. Suppression, by the bar, of the lowerfrequency standing waves, which have the greatest potential for being forced, may be responsible for lowering the infragravity energy. Frequencies which yield the resonant condition of antinodes over the bar and nodes in the trough are favored.

283 (5) T h e bars associated w i t h t h e s e states e x h i b i t high m o b i l i t y c h a r a c t e r i z e d b y rapid a n d e x t r e m e migrations. H o w e v e r , t h e m o b i l i t y o f t h e intertidal b e a c h face is surprisingly low. This m a y r e f l e c t t h e ability o f t h e standing wave n o d e s in t h e t r o u g h t o act as a w e a k barrier t o cross-shore e x c h a n g e o f s e d i m e n t b e t w e e n t h e bar a n d t h e beach. In a d d i t i o n , b a r - t r o u g h readjustm e n t s p r o b a b l y a b s o r b changes in b r e a k e r height a n d t h e r e b y r e d u c e t h e t e m p o r a l variability o f s h o r e b r e a k a m p l i t u d e . ACKNOWLEDGEMENTS This s t u d y has b e e n s u p p o r t e d b y t h e O f f i c e o f Naval Research, Coastal Sciences P r o g r a m Task N R 3 8 8 - 1 8 9 , C o n t r a c t N 0 0 0 1 4 ~ 3 - K - 0 1 9 8 . Beach a n d s u r f - z o n e surveys were c o n d u c t e d b y A.D. S h o r t a n d J. Mackaness. Essential a n d c o m p e t e n t assistance w i t h t h e field e x p e r i m e n t s was also p r o v i d e d b y M.P. Bradshaw, F.C. C o f f e y , P.J. Cowell, M.O. G r e e n , G. L l o y d a n d B.G. T h o m . We are grateful t o E S S O Australia f o r f u n d i n g assistance f o r t h e field s t u d y a n d f o r m a k i n g available d a t a o n o f f s h o r e wave conditions. T h e m a n u script was t y p e d b y C.D. Gaskins. REFERENCES Ball, F.F., 1967. Edge waves in an ocean of finite depth. Deep-Sea Res., 14: 79--88. Bowman, D. and Goldsmith, V., 1983. Bar morphology of dissipative beaches: an empirical model. Mar. Geol., 51: 15--33. Bradshaw, M.P., ChappeU, J., Hales, R.S. and Wright, L.D., 1978. Field monitoring and analysis of beach and inshore hydrodynamics. Proc. 4th Aust. Coastal and Ocean Eng. Conf., Adelaide, S.A., pp.171--175. Chappell, J. and Eliot, I.G., 1979. Surf-beach dynamics in time and space --an Australian case study, and elements of a predictive model. Mar. Geol., 32: 231--250. Chappell, J. and Wright, L.D., 1979. Surf zone resonance and coupled morphology. Proc. 16th Int. Conf. Coastal Eng., Hamburg, 1978, pp.1359--1377. Cowell, P.J., 1982. Breaker stages and surf structure. Tech. Rep. 82/7, Coastal Studies Unit, University of Sydney, Sydney, N.S.W., 239 pp. Dean, R.G., 1973. Heuristic models of sand transport in the surf zone. Proc. Conf. on Engineering Dynamics in the Surf Zone, Sydney, N.S.W., pp.208--214. Eckart, C., 1951. Surface waves on water of variable depth. Wave Rep. 10, Scripps Inst. of Oceanogr., Univ. of Calif., La Jolla, Calif., 99 pp. Funke, E.R. and Mansard, E.P.D., 1979. On the synthesis of realistic sea states in alaboratory flume. Natl. Research Council, Canada, Rep. LTR HY 66. Goldsmith, V., Bowman, D. and Kiley, K., 1982. Sequential stage development of crescentic bars: Hahoterim Beach, Southeastern Mediterranean. J. Sediment. Petrol., 52: 233--249. Gourlay, M.R., 1982. Nonuniform alongshore currents and sediment transport -- a one dimensional approach. Res. Rep. No. CE31, Dept. of Civil Eng., Univ. of Queensland, 67 pp. Grant, W.D. and Madsen, O.S., 1979. Combined wave and current interaction with a rough bottom. J. Geophys. Res., 84: 1797--1808. Grant, W.D., Williams, A.J., Glenn, S.M., Cacchione, D.A. and Drake, D.E., 1983. High frequency bottom stress variability and its prediction in the CODE region. Woods Hole Oceanographic Institution, Tech. Rep.83-19, 71 pp. Greenwood, B. and Davidson-Arnott, R.G.D., 1975. Marine bars and nearshore sedimen-

284 tary processes, Kouchibouguac Bay, New Brunswich. In: J. Hails and A. Cart (Editors), Nearshore Sediment Dynamics and Sedimentation. Wiley, New York, N.Y., pp.123-150. Greenwood, B. and Davidson-Arnott, R.G.D., 1979. Sedimentation and equilibrium in wave-formed bars: a review and case studies. Can. J. Earth Sci., 16: 312--332. Guza, R.T. and Davis, R.E., 1974. Excitation of edge waves by waves incident on a beach. J. Geophys. IRes., 79: 1285--1291. Guza, R.T. and Inman, D.L., 1975. Edge waves and beach cusps. J. Geophys. Res., 80: 2997--3012. Guza, R.T. and Thornton, E.B., 1982. Swash oscillations on a natural beach. J. Geophys. Res., 87: 483--491. Holman, R.A., 1981. Infragravity energy in the surf zone. J. Geophys. Res., 86: 6442-6450. Huntley, D.A. and Kim, C.S., 1984. Is surf beat forced or free? Abstracts, 19th Int. Conf. Coastal Eng., Houston, Texas. Huntley, D.A., Guza, R.T. and Thornton, E.B., 1981. Field observations of surf beat. 1. Progressive edge waves. J. Geophys. Res., 86: 6451--6466. Jonsson, I.G., 1967. Wave boundary layers and friction factors. Proc. Int. 10th Conf. Coastal Eng., Tokyo, 1966, pp.127--148. Jonsson, I.G. and Carlsen, N.A., 1976. Experimental and theoretical investigations in an oscillatory turbulent boundary layer. J. Hydraul. Res., 14: 45--60. Katoh, K., 1984. Multiple longshore bars formed by long period standing waves. Rep. of the Port and Harbour Res. Inst., 23(3). Komar, P.D., 1975. Nearshore currents-generation by obliquely incident waves and longshore variation in breaker height. In: J.R. Hails and A. Cart (Editors), Nearshore Sediment Dynamics and Sedimentation. Wiley, New York, N.Y., pp.17--45. Komar, P.D., 1976. Beach Processes and Sedimentation. Prentice-Hall,Hemel Hempstead, 429 pp. Kraus, N.C. and Sasaki, T.O., 1979. Effect of wave angle and lateralmixing on the longshore current. Coastal Eng. Jpn., 22: 59--74. Lofquist, K.E.B., 1980. Measurement of oscillatory drag on sand ripples. Proc. Int. 17th Conf. Coastal Eng., Sydney, N.S.W., pp.3087--3106. Longuet-Higgins, M.S., 1970a. Longshore currents generated by obliquely incident sea waves, 1. J. Geophys. Res., 75: 6 7 7 8 - 6 7 8 9 . Longuet-Higgins, M.S., 1970b. Longshore currents generated by obliquely incident sea waves, 2. J. Geophys. IRes., 75: 6 7 9 0 - 6 8 0 1 . Lundgren, H., 1972. Turbulent currents in the presence of waves. Proc. Int. l l t h Conf. Coastal Eng., Vancouver, p p . 6 2 3 - 6 3 4 . MacDonald, T.C., 1977. Sediment suspension and turbulence in an oscillating flume. CERC Tech. Pap. No.77-4. Mason, C., Birkemeier, R.A., Holman, R.A. and Sallenger, A.H., 1984. A comprehensive experiment on storm-related coastal processes. Abstracts 19th Conf. Coastal Eng., Houston, Texas, pp.166--167. Nakato, T., Locher, F.A., Glover, J.R. and Kennedy, J.F., 1977. Wave entrainment of sediment from rippled beds. J. Waterways, Harbours Coastal Eng. Div., A.S.C.E., 13(WWI): 83--100. Nielsen, P., 1979. Some basic concepts of wave sediment transport. Series Paper 20, Inst. of Hydrodynamics and Hydraulic Eng., Tech. Univ. of Denmark, Lyngby, 160 pp. Nielsen, P., 1981. Dynamics and geometry of wave generated ripples. J. Geophys. Res., 86: 6 4 6 7 - 6 4 7 2 . Nielsen, P., 1983. Entrainment and distribution of different sand sizes under water waves. J. Sediment. Petrol., 53: 423--428. Nielsen, P., 1984a. Field measurements of time-averaged suspended sediment concentrations under waves. Coastal Eng., 8: 51--72. Nielsen, P., 1984b. On the m o t i o n of suspended sand particles. J. Geophys. Res., 89: 616-626.

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