Observations of bedforms on a dissipative macrotidal beach
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Field measurements of wave ripples and megaripples were made with a Sand Ripple Profiler in the surf and shoaling zones of a sandy macrotidal dissipative beach at Perranporth, UK in depths 1–6 m and significant wave heights up to 2.2 m. A frequency domain partitioning approach allowed quantification of height (η), length (λ) and migration rate of ripples and megaripples. Wave ripples with heights up to 2 cm and wavelengths ∼20 cm developed in low orbital velocity conditions (u m < 0.65 m/s) with mobility number ψ < 25. Wave ripple heights decreased with increasing orbital velocity and were flattened when mean currents were >0.1 m/s. Wave ripples were superimposed on top of megaripples (η = 10 cm, λ = 1 m) and contributed up to 35 % of the total bed roughness. Large megaripples with heights up to 30 cm and lengths 1–1.8 m developed when the orbital velocity was 0.5–0.8 m/s, corresponding to mobility numbers 25–50. Megaripple heights and wavelengths increased with orbital velocity but reduced when mean current strengths were >0.15 m/s. Wave ripple and megaripple migrations were generally onshore directed in the shoaling and surf zones. Onshore ripple migration rates increased with onshore-directed (+ve) incident wave skewness. The onshore migration rate reduced as offshore-directed mean flows (undertow) increased in strength and reached zero when the offshore-directed mean flow was >0.15 m/s. The migration pattern was therefore linked to cross-shore position relative to the surf zone, controlled by competition between onshore-directed velocity skewness and offshore-directed mean flow.
KeywordsSurf zone ripples megaripples ripple migration Sand Ripple Profiler dissipative beach
In sandy marine environments, ripples on the seabed develop in a variety of conditions and make an important contribution to bottom boundary layer hydrodynamics and sediment transport (Dyer 1986). However, the conditions for their development and migration on macrotidal dissipative beaches are not well understood.
In wave-dominated conditions, ripples may develop with a typical wavelengths λ of ∼0.05–0.5 m and heights η of ∼0.01–0.1 m (e.g. Nielsen 1992; Gallagher et al. 2005). They are typically symmetrical in shape (Masselink and Hughes 2003), and their steepness indicates their classification as either post-vortex ripples with η/λ < 0.15 or vortex ripples with η/λ = 0.15 (Bagnold 1963). In unidirectional currents, bedforms evolve as shear stress increases, through a sequence of low stage flat bed ripples, current dunes, upper stage plane bed and finally antidunes (Dyer 1986; Nielsen 1992). Ripples in unidirectional flows scale with typical lengths of 0.1 to 0.2 m and heights up to 0.06 m (Allen 1968). Yalin (1964) parameterized ripple length from the grain size (λ = 1,000 D) and ripple height as η = λ/7. Current dunes have typical wavelengths of 0.6 to 30 m and heights of 0.06 to 1.5 m. Dune length is governed by water depth h, as λ = 2 π h, and dune height scales to maximum of h/6 (Yalin 1964). In high flows and shallow depths, under supercritical flow conditions, bedforms may migrate against the flow direction, in which case they are known as antidunes (Dyer 1986).
Approaching the surf zone from offshore, wave ripples that typically form in deeper water give way to megaripple features in the surf zone, which have larger wavelengths and heights (Clifton et al. 1971). Typical heights of the megaripples are 0.1 to 1 m, and lengths are 0.5 to 5 m (Gallagher et al. 1998; Gallagher 2003). In megaripple-dominated surf zones, field measurements show that the bed roughness (i.e. bedform height) is largest at moderate mobility numbers (Gallagher et al. 2003). Wave orbital velocity is a key parameter in determining bedform type. Hay and Mudge (2005) identified that megaripples existed when root mean square (RMS) wave orbital velocities were approximately >0.28 m/s, while linear transition ripples existed when RMS orbital velocities were in an approximate range 0.19 to 0.31 m/s. Bedform type was independent of wave velocity skewness, velocity asymmetry and longshore current strength (Hay and Mudge 2005). Megaripples are reported as three-dimensional, and although they may take on a regular alongshore structure, they may develop as lunate features (Hay and Mudge 2005) or as hummocks and holes in a less regular distribution (Gallagher 2003).
Field measurements indicate that megaripple wavelengths do not conform well to the predictive capability of conventional models (Gallagher et al. 2003). Self-organization theory suggests that nearshore bedforms including cusps, ripples and megaripples either grow or remain stable in size, depending on the forcing conditions (Clarke and Werner 2004; Gallagher 2011). Where hydrodynamic conditions do result in bedform modification, the timeframe for change may be long (Soulsby 1997), leading to the potential for the hydrodynamic conditions to be out of equilibrium with the seabed. This may also result in different sorts of bedforms existing at the same time. Dyer (1986) and Blondeaux et al. (2000) identified that in conditions with both waves and currents, the bed may display features of both wave and current ripples. Thornton et al. (1998) observed bedforms in an alongshore trough/rip channel from a large range of conditions at the Duck94 field experiment and found that mild waves and weak currents led to wave ripples, but storm waves and strong longshore currents led to megaripples. Thornton et al. (1998) also identified that newly formed wave ripples co-existed with residual bedforms, to create complex patterns of topography.
The migration rate of ripples has been suggested to depend on mobility number (Vincent and Osborne 1993; Traykovski et al. 1999). The direction of transport and the migration rate has also been shown to follow the wave skewness (Gallagher et al. 1998; Crawford and Hay 2001). Doucette (2002) made visual observations of ripple migration rates on a coarse sandy beach (D 50 = 0.7 mm). The beach was sea breeze dominated, and ripples with heights of 0.05–0.15 m and lengths of 0.3–1.2 m were found to migrate onshore at rates of up to 0.2 cm/min. Masselink et al. (2007) investigated variations in ripple migration rates across the surf zone on a coarse grained sand beach (also D 50 = 0.7 mm) at Sennen, UK and found that migration rate depended on cross-shore location. Ripple heights of 0.05 m and lengths of 0.35 m were recorded. Migration rates varied from 0.1 cm/min onshore in the shoaling zone to 2 cm/min and onshore in the outer surf and no transport in the inner surf. In strong currents, such as feeder currents and rip currents, Sherman et al. (1993) found that lunate megaripples migrated in the same direction as the mean current. In a flow of 0.4 to 0.6 m/s, depth 0.71 m, wave height 0.65 m, wave period 10.6 s and D 50 = 0.33 mm, ripples of length 1.6 m and height 0.16 m migrated at 1.65 cm/min. Ngasuru and Hay (2004) identified that at Duck94, megaripples migrated shoreward under incident wave conditions with orbital velocities in the range 0.5 to 0.8 m/s and with low velocity mean currents but stalled and may have migrated offshore when mean offshore flow exceeded 0.2 m/s.
Field measurements of ripples and megaripples have been made on beaches with different morphological and tidal regimes, including the microtidal beaches at Duck (Gallagher et al. 2003, 2005; Thornton et al. 1998; Ngasuru and Hay 2004), Queensland, Novia Scotia (Crawford and Hay 2001, 2003) and at Scripps (Clarke and Werner 2004), on a mesotidal bar–trough beach at Truc Vert, France (Austin et al. 2007), on coarser sediment macrotidal intermediate beaches, such as Sennen Cove (UK) (Masselink et al. 2007), and in deeper water, such as measurements made on sand ridges in 11 m water depth by Traykovski et al. (1999). In this paper, detailed new field measurements of bedform sizes and migration rates are presented from a macrotidal, sandy, fine grained and dissipative beach. The dataset offers unique new insight into ripple and megaripple dynamics from relatively deep water (∼6 m) through shoaling wave conditions with skewed waves and into the surf zone where incident waves and offshore-directed undertow combine.
2 Field measurements
2.1 Overview of experiment conditions
Oscillatory components of the flow were routinely separated into incident wave (gravity band) and infragravity band oscillations, by applying a frequency domain high/low-pass filter with a cut-off at 0.05 Hz. Orbital velocity was calculated as u m = 2√σ 2 u (where σ 2 u is the total cross-shore velocity variance) following Masselink et al. (2007). Both the incident wave cross-shore velocity variance (not shown) and the orbital velocities (shown) peaked in the shallow water at the start and end of the tide but were modulated by the offshore wave height. Incident wave velocity variance and orbital velocity increased on days when the wave heights were larger and also increased when the water depth over the rig was shallower. A similar pattern was followed by the orbital excursion. Infragravity variance in the cross-shore velocity was generally small at high tide (2 % of the total cross-shore velocity variance) but increased in the shallower water in the surf zone (not shown). The maximum infragravity contribution was 17.6 % of the total cross-shore velocity variance (tide 22, run 224). On other tides, the typical maximum infragravity contribution was 12 %.
Crawford and Hay (2001) found only a small difference in the ability of S u and <u′3> to predict ripple migration rate, but in their data, S u was marginally more skillful. In these data, wave skewness (S u ) increased in a more pronounced manner than the orbital velocity in shallow water and reached a maximum of 1.6 in run 272. The unnormalised skewness parameter <u′3> showed a similar trend to S u .
Wave asymmetry is defined as the time-averaged skewness of the acceleration time series for the incident wave band (Elgar et al. 1998). This parameter quantifies the sawtooth shape of the velocity associated with the wave and is large if there are large accelerations co-incidental with the leading edge of the wave. No clear pattern was evident in asymmetry in these data, and this may have been because the water was not sufficiently shallow for asymmetric bores typical of the inner surf and swash zone to impact on the velocity signal.
Sediment transport by the mean flow <u><c> was generally directed offshore, following the direction of the mean flow <u>. The infragravity component was also directed offshore for the majority of runs. The gravity wave component was variable in direction and was small in magnitude when compared to the combination of mean plus infragravity components. As a result of the combination of these processes, the total suspended sediment transport was: largest in shallow water at the start and/or the end of the tide; was controlled fundamentally by the mean component; and offshore-directed.
The maximum wave ripple steepness was 0.1. For η wr >0.52 cm, the average steepness was 0.03, and for η wr > 1 cm, the average steepness was ∼0.066. The maximum megaripple steepness was 0.18. For η mr > 10 cm, the average steepness was 0.11, and for η mr > 6.58 cm, the average steepness was 0.08.
4 Bedform migration
Bedform migration rates were calculated using a cross-correlation of time-separated bedform scans (Masselink et al. 2007). This was carried out separately for the filtered wave ripple and megaripple bed data. The lag associated with the largest correlation between the time-separated scans was assumed to represent the distance the bed features had migrated within the time period. Where the correlation coefficient was low (<0.2), the migration rate value was discarded. A scan separation of 5 min was found to give results that were consistent with close examination of time-separated scans.
Orbital velocity and both gravity band and infragravity band cross-shore velocity variance generally increased through the shoaling zone towards the surf zone. Skewness also increased towards the surf zone as the waves shoaled. Mean flows were offshore directed in most of the data and increased with H/h, suggesting increasing importance of undertow closer to the shore. Despite considerable scatter in the data, megaripple heights appear to increase from the shoaling zone to just outside the breakpoint and reduce inside the surf zone. Megaripple migration was generally onshore directed. Migration rates increased towards the breakpoint were maximum at approximately the breakpoint and reduced in the surf zone. The distribution of migration appears to be in response to the balanced contributions of orbital velocity facilitating migration, skewness driving onshore migration and mean offshore-directed flow opposing this onshore migration.
Instruments on the rig in this experiment were deployed near the low water mark, and at times, it was possible to see the bedforms at low tide. This gives confidence in the presentation of megaripple data from the SRP and in the approximate magnitudes of the values presented. Ripple alignment and the three-dimensional nature of ripple fields are potential problems in using measurements from ripple profiling sonars. If bedforms crests are not perpendicular to the line of the scan, the wavelength is likely to be overestimated, and in three-dimensional ripple fields, if the ends of crests or troughs pass through the instrument array, bedform heights may be underestimated. Supporting the data here, visual observations by wading and swimming indicated the following: the megaripples persisted as the water depth increased; they were aligned with crests running alongshore; they were approximately perpendicular to the line of the scan and were reasonably alongshore uniform; and they covered an extensive alongshore and cross-shore area in the region of the instruments.
Some features apparent to the eye in Fig. 7 appear to be not well identified by the migration calculation leading to Fig. 14 (e.g. an apparent shoreward migration around run 250). This may be because the correlation was insufficiently large between scans, leading to a return of zero for Mr (e.g. if the shape of the ripple evolves). Differences may also result because the eye is able to give an overall impression of change, by averaging over many different time lags. The results indicate migration rates that are of broadly similar magnitude to previous measurements by Masselink et al. (2007) and are consistent with close examination of the time-separated scans. For the megaripples, filtering out the wave ripples gave a much clearer migration rate than carrying out the cross-correlation approach on an unfiltered bedform trace.
The wave ripples in this data are in the length range indicated by Yalin (1964) for current ripples, with λ = 1,000 D giving a length of 28 cm and a height of η = λ/7 = 4 cm. However, their height reduced as the current and associated shear stress increased (Fig. 11), suggesting that they are unlikely to be current ripples. The height of the wave ripples (1–2 cm) and their length of 20 cm gives them a characteristic steepness of 0.05 to 0.1. They are therefore likely to be ‘post-vortex’ wave ripples, in Bagnold’s (1963) classification.
The megaripples have length scales similar to those expected for current dunes in the shallowest water levels measured. However, their height reduced with increasing current (Fig. 11), and so they are unlikely to be current dunes. They have length scales and heights that tie in with Gallagher et al.'s (1998) classification for ‘megaripples’, and exist in similar mobility number conditions to those observed by Gallagher et al. (2003).
Wave ripples and megaripples were able to occur simultaneously in this experiment in relatively low wave energy conditions (u m < ∼0.65 m/s) (Fig. 11), when mean currents were small (<u> < ∼0.1 m/s), (cf. Blondeaux et al. 2000). This occurred for mobility numbers ψ < 25. In increasingly high energy conditions, it appears that the wave ripples disappear first and that megaripples remain.
The data presented here suggests that the conditions in which the highest wave ripples develop is separated from the conditions for which the highest megaripples develop by an orbital velocity threshold of ∼0.5 m/s (Fig. 12). Hay and Mudge (2005) found a similar delineation, in which the lowest RMS velocities in which megaripples occurred was ∼0.28 m/s, and below this linear transition ripples occurred. They also found overlap between the two regimes. Their RMS velocity is equivalent to a u m value of 0.56 m/s in this analysis. Some scatter in the data across this delineation may exist because the bedforms take time to respond when the hydrodynamic conditions change. Austin et al. (2007) identify that wave ripples respond in time frames of 5–10 min provided the hydrodynamic conditions remain sufficient energetic. In this analysis, the parameters are calculated for 10-min sections of data, and although the depth and orbital velocity changes are assumed to be slow relative to the 5–10 min relaxation time identified by Austin et al. (2007), there may be some lag in bedform response that means they are slightly out of phase.
Although a band of mobility numbers were identifiable in which large megaripple features developed, conditions were not measured in sufficiently high mobility numbers for the bed to flatten. Data were mainly gathered with ψ < 70 (Fig. 11), while Gallagher et al. (2003) indicate bed flattening occurs at ψ ∼ 100. In terms of cross-shore distribution, the largest megaripples occurred just outside the breakpoint, similar to SCUBA observations by Clifton et al. (1971), and reduced in size in the surf zone. However, the bed did not appear to flatten at the breakpoint in this data, possibly because the dissipative nature of wave breaking at this site did not give rise to sufficient turbulence at the bed, or the mobility number was not sufficiently large.
Both megaripples and wave ripples migrated shoreward (Fig. 15) and generally moved in the direction of wave skewness, as observed by Crawford and Hay (2001). Masselink et al. (2007) also documented an onshore migration direction, and a reduction in migration rates in the deeper water in the shoaling zone, compared to the outer surf zone. This supports the observation (Fig. 15) that increases in wave skewness associated with wave shoaling give rise to increased onshore migration rates. Like Masselink et al.’s (2007) data from the inner surf zone, the migration rates reduced in shallow water in this data (Fig. 16), and in this case, this happened when the offshore-directed flow increased. Ngasuru and Hay (2004) also found a reduction in onshore migration when an offshore-directed mean flow was present.
No clear pattern was evident in the wave asymmetry values in this data in relation to ripple migration. Positive (onshore directed) wave asymmetry was identified in the velocity signal for water depths <1 m in the data when the SRP measurements were not possible, and it is therefore possible that wave asymmetry contributes to bedform forcing in shallow water, but the relationship was not measurable in this experiment.
Generally, offshore-directed flows in the surf zone may be due to undertow (e.g. Masselink and Black 1995) or may be part of a rip current circulation (Thorpe et al. 2013). Sherman et al.’s (1993) data indicated that in conditions where the flow strength is strong in a feeder channel of a rip current, the balance may be in favour of the mean flow, and the resulting megaripple migration followed the mean flow direction (offshore) rather than the wave direction (onshore). In the second six tides of data here, the trough may also have experienced occasional rip current conditions when the water was shallow (∼1 m). This would increase the offshore-directed mean flow component in the velocity data and possibly contributes to the offshore-directed migration at the very end of tide 21 (Fig. 14). The specific conditions of sediment transport and bedform migration in rip currents with large offshore-directed mean flows are subject to further study (e.g. Thorpe et al. 2013).
The data here suggest that the suspended sediment transport is directed offshore for the majority of the time (Fig. 17). Offshore sediment transport at incident wave frequencies in the region just seaward of the breakpoint, in conditions likely to have supported a rippled bed, have also been observed by Davidson et al. (1993). A mechanism for this process was identified by Inman and Bagnold (1963), who suggested that the release of a sediment vortex at the start of the offshore-directed stroke of the wave could result in a net offshore suspended transport above a ripple field. Similar observations (i.e. offshore-directed suspended sediment transport above shoreward-migrating ripples) were made by Traykovski et al. (1999), who hypothesized that the onshore migration may be due to an unmeasured bedload transport.
Morphologically, the measurements at Perranporth represent a dissipative macrotidal beach. This is in contrast to the microtidal barred beach at Duck, which has a small tidal range, and a distinct bar–trough morphology. Both have fine sand, and in similar mobility numbers, megaripples develop in the surf zone at both sites (Thornton et al. 1998; Gallagher et al. 2003; Ngasuru and Hay 2004). A key difference is that at Perranporth, the bed has to react to incident wave conditions that vary as a result of water depth change on a tidal time scale, as well as with offshore wave conditions, and this possibly contributes to the variability in the data here. Further contrast is given by comparison with observations at an intermediate macrotidal coarse grained beach with a low tide terrace morphology at Sennen, UK (Austin et al. 2007; Masselink et al. 2007). Masselink et al. (2007) used the change in bedform dynamics at a point location with changing tide height, to identify a similar cross-shore migration pattern relative to surf zone position as found in this data. However, despite similar mobility number conditions, the bedform wavelengths at Sennen were indicative of wave ripples (wavelengths 28 to 38 cm, and heights 4.5 to 5.5 cm), while at Perranporth and Duck, the bedform features are megaripple scale. The most obvious difference to explain this is that Sennen has a more coarse grain size (D 50 = 0.69) compared to Perranporth (D 50 = 0.28 mm) and Duck (D = 0.2 mm). The average beach slope is also steeper at Sennen: tan β = 0.08 on the upper beach and 0.03 on the terrace, compared to 0.0125 at Perranporth and 0.014 over a cross-shore distance of 350 m at Duck. In synthesis, it appears that finer grained, dissipative beaches may be more likely to lead to megaripples and that these features are likely to migrate according to their cross-shore position relative to the surf zone, as driven by the balance of wave skewness, orbital velocity and mean flow.
Wave ripples with heights up to 2 cm and lengths of ∼20 cm were observed to develop on a sandy dissipative beach in low energy conditions (u m < 0.65 m/s), corresponding to mobility numbers <25. Wave ripple heights decreased with increasing orbital velocity and with increased mean current strength. Wave ripples were superimposed on top of small megaripples in these low energy conditions and contributed at most 35 % of the total bed roughness. In higher energy conditions, the wave ripples flattened, and the seafloor was dominated by megaripples. Megaripples had heights 10–30 cm and lengths of 1–1.8 m. Megaripples were largest when orbital velocities were in the range 0.5 to 0.8 m/s and when mean currents were weak (∼0.05 m/s), corresponding to mobility numbers in the range 25–50.
Wave ripple and megaripple migrations were generally onshore, and migration rates reached 1.9 cm/min. Migration rates increased with orbital velocity and +ve (shoreward directed) wave skewness but were reduced by an offshore-directed mean flow. Shoreward migration was halted for offshore flows >0.15 m/s. Measured suspended sediment transport was generally directed offshore; however, no clear link was evident between bedform migration and suspended sediment transport rates. The pattern of migration appeared to be linked to surf zone position. Migration increased shorewards towards the breakpoint with wave shoaling and reduced inside the surf zone due to the effect of undertow.
The fieldwork for this project was funded by a partnership grant from the UK Natural Environment Research Council (NERC) and the UK Royal National Lifeboat Institution (RNLI), ‘Dynamics of Rip Currents and Implications for Beach Safety (DRIBS)’, (NERC ref: NE/H004262/1).
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