Back‐flow ripples in troughs downstream of unit bars: Formation, preservation and value for interpreting flow conditions

Back‐flow ripples are bedforms created within the lee‐side eddy of a larger bedform with migration directions opposed or oblique to that of the host bedform. In the flume experiments described in this article, back‐flow ripples formed in the trough downstream of a unit bar and changed with mean flow velocity; varying from small incipient back‐flow ripples at low velocities, to well‐formed back‐flow ripples with greater velocity, to rapidly migrating transient back‐flow ripples formed at the greatest velocities tested. In these experiments back‐flow ripples formed at much lower mean back‐flow velocities than predicted from previously published descriptions. This lower threshold mean back‐flow velocity is attributed to the pattern of velocity variation within the lee‐side eddy of the host bedform. The back‐flow velocity variations are attributed to vortex shedding from the separation zone, wake flapping and increases in the size of, and turbulent intensity within, the flow separation eddy controlled by the passage of superimposed bedforms approaching the crest of the bar. Short duration high velocity packets, whatever their cause, may form back‐flow ripples if they exceed the minimum bed shear stress for ripple generation for long enough or, if much faster, may wash them out. Variation in back‐flow ripple cross‐lamination has been observed in the rock record and, by comparison with flume observations, the preserved back‐flow ripple morphology may be useful for interpreting formative flow and sediment transport dynamics.


INTRODUCTION
Water flowing over non-cohesive sediments can form regular bed morphologies such as ripples, dunes and bars. Bedforms are controlled by parameters of the flow including velocity, shear stress and flow depth as well as the sediment characteristics. Bedforms modify the flow with flow separation generating lee-side eddies. Within lee-side eddies, the flow close to the bed travels in the opposite direction to the main flow ( Fig. 1) or obliquely to it. In the lee of dunes or bars the upstream current may be able to rework sediment on the bed to form back-flow which are identifiable on the scale of cores and can act as laterally extensive partial barriers to interstitial flow.
Back-flow ripples have been identified in the lee of large ripples (e.g. Baas et al., 2011), dunes (e.g. Kirk, 1983;Martinius & Van den Berg, 2011) and unit bars (e.g. Reesink & Bridge, 2011). The factors that control back-flow ripple formation depend in part on the host bedform type. Dunes form in a relatively narrow range of conditions and, if in equilibrium with the flow, their crest height is related to the water flow depth (Yalin, 1964;Allen, 1982a). Martinius & Van den Berg (2011) suggest that back-flow ripples do not form downstream of all dunes, they form in association with constructive dunes where the flow conditions allow relatively fine sediment to be deposited within the lee-side eddy; this holds true unless the flow conditions over the dunes change substantially (for example, during the falling stage of a flood). Dune three-dimensionality is also important; this influences the flow within the dune trough (Maddux et al., 2003;Best, 2005;Venditti, 2007;Omidyeganeh & Piomelli, 2013) altering the characteristics of any back-flow ripples formed. Allen (1968Allen ( , 1982b noted that back-flow ripples created in the lee of long crested dunes can consist of a number of ripple fans, often bounded by spurs which extend out from the dune lee. In contrast, bars form in a wide range of conditions, may persist through varying flow conditions and their height is not directly related to flow depth. Back-flow ripples can form in a wider range of conditions (for example, velocity and flow depth above bedform) in the lee of bars than dunes. Flows along bar troughs may be more common in association with bars than dunes (Reesink & Bridge, 2011) which influences the formation and orientation of back-flow ripples. Jopling (1961) documented back-flow ripples, created in the lee of a migrating 'delta front', during flume experiments. The maximum backflow velocity within the lee-side eddy ranged from 16 to 33% of the mean flow velocity measured upstream of the 'delta front'. This author suggested that back-flow ripples would not form at free stream velocities <0Á61 m s À1 . Saunderson & Jopling (1980) recorded back-flow ripples in the Brampton Esker, Ontario, Canada. Based on previous flume research by Jopling these authors assumed that the back-flow must have had a mean velocity >0Á12 m s À1 to generate back-flow ripples in 'fine silty sand'. Using the Jopling (1961) relationship between the backflow velocity and mean down-channel flow velocity, along with other methods, Saunderson & Jopling (1980) estimated a palaeocurrent velocity of 0Á65 m s À1 . Allen (1965) observed back-flow ripples in the lee of a migrating 'sand wave' within a flume and noted that, at relatively low stream velocities, ripples were generated by grain movement driven by sporadic turbulence that attained instantaneous back-flow velocities >0Á2 m s À1 . This author described ripples as subdued and 'scalelike', becoming more developed close to the 'sand wave'. Allen (1965) provided simple two-dimensional interpretations of this threedimensional phenomena, suggesting that the sediment flux reaching the trough of the host bedform can alter the structure of the back-flow ripples. At low flow velocities a large proportion of the sediment is deposited on the upper lee face of the host bedform and the sediment flux to the trough is small; this results in the lee face prograding discordantly over a 'pavement' of ripples ( Fig. 1). At higher flow velocities more sediment can be deposited directly in the trough, resulting in a thicker bottomset layer containing ripple cross-lamination (Allen, 1965). More recent studies have linked flow deceleration to bottomset development (Reesink & Bridge, 2009, with larger decelerations over a bedform enhancing suspended sediment deposition. Bottomset deposits are also influenced by the sediment and host bedform characteristics. Different grain sizes will alter the sediment transport dynamics over the host bedform, influencing the proportion of sediment reaching the bottomset derived from different transport mechanisms (for example, suspension and saltation). With a relatively small host bedform the bottomset could contain a significant proportion of grains saltated over the host bedform brink. As the host bedform height increases the chance of saltated grains reaching the bottomset decreases. If the host bedform features a relatively high climb angle, downstream directed co-flow ripples can be preserved within the bottomset (Boersma, 1967;Martinius & Van den Berg, 2011). In some instances the contact between the bottomset and the slip face becomes transitional with back-flow ripples interfingering with the grain flows of the host bedform lee face or becoming preserved between or at the base of the host bedform foresets.
With a very large host bedform back-flow dunes could potentially form. For example, Collinson (1968) found medium-scale cross-bedding in the lower 2 m of a 12 m thick cross-bed set with opposing palaeoflow direction in the Namurian Kinderscout Grit of Northern England. Allen (1980) suggested that back-flow dunes may explain up-slope directed cross-stratification observed in some marine deposits whilst Dasgupta & Bandyopadhyay (2008) proposed that back-flow dunes could have formed during aeolian deposition of the Late Pleistocene to Early Holocene granular carbonates of Saurashtra, India. However, these dunes could have been formed by recirculation in the horizontal plane.
Bedforms with a similar structure to back-flow ripples but a different formation mechanism have been found in tidal settings. These ripples ascend reactivation surfaces; unlike back-flow ripples, these are not created within a lee-side eddy but are formed by a transition to the subordinate-current in a bidirectional flow environment (Boersma, 1967;De Mowbray & Visser, 1984). In this article, the term subordinate-current ripples (cf. De Mowbray & Visser, 1984) is used to differentiate these from back-flow ripples; however, other terms also exist such as set climbers (Van den Berg et al., 2007). Terms used for back-flow ripples have also been used to describe subordinate-current ripples formed by tidal activity (e.g. George, 2000;Kostic & Aigner, 2004;Zhang et al., 2008) leading to possible confusion between ripples formed within leeside eddies and those formed by tidal current reversal. Boersma (1967) suggested that supposed back-flow ripples found in the Folkestone Beds by Allen & Narayan (1964) were misinterpreted and were actually formed by a subordinate current. Conversely, structures attributed to tidal subordinate-current may be back-flow ripples (e.g. Abouessa et al., 2012). Care should be taken when distinguishing back-flow and subordinate-current ripples formed in tidal environments. Interfingering of foreset and bottomset is characteristic of unidirectional currents (such as in rivers), whereas subordinate-current ripples may climb high up reactivation surfaces and may contain other indicators of tidal origin such as mud drapes and periodicity (Martinius & Van den Berg, 2011, fig 3.5.1). In extreme cases sets can be constructed entirely by subordinate-current ripples (Van den Berg et al., 2007).
This article aims to improve the understanding of back-flow ripples and thus the usefulness of the resulting structures for palaeoenvironmental reconstruction by answering two key questions: 1 What are the conditions required for the formation of back-flow ripples on a well-sorted sand bed? 2 Can ripple cross-lamination formed by backflow ripples in conjunction with related crossstrata be used to improve the interpretation of palaeoenvironments?
To address these questions the formation of back-flow ripples in the lee of a large bedform (herein called a unit bar) over a range of flow conditions was examined in the University of East Anglia recirculating flume ( Fig. 2A) and the resulting deposits are compared with structures found in Carboniferous sandstones at Pittenweem, Scotland.

METHODOLOGY
The flume used in these experiments has a 10 9 1 9 1 m glass-walled test channel and recirculates sand and water in a closed loop, with no settling tank. In this study, the channel was horizontal and the bed consisted of well-sorted sand (D 50 = 230 lm; Fig. 2B). Positions (x, y and z) within the channel are recorded with reference to the upstream most left-hand side of the channel floor ( Fig. 2A). A unit bar was formed from a mound of sand that was modified into an asymmetrical bedform by running the flume, first at 0Á06 m 3 s À1 for 1200 sec and then at 0Á10 m 3 s À1 for 5400 sec, following a procedure similar to that used by Reesink & Bridge (2007).
Data are presented from 19 Runs (Table 1) in which back-flow ripple formation and evolution were observed directly, photographed and measured. Unit bars were formed before the start of Runs 1, 9, 17 and 19. The other runs used the bars that had been modified by the preceding run. Runs 1 to 16 were of 1800 sec duration and, at the end of each, pumping stopped and all ripples in the lee of the bar were flattened before the start of the next run. In Runs 17 and 18 three velocity profiles were measured (two at y = 0Á5 m and one at y = 0Á2 m) within the leeside eddy at a constant discharge known to form back-flow ripples using a Nortek acoustic Doppler velocimeter (ADV; Nortek AS, Rud, Norway) with a sampling volume of 1 mm and a sampling frequency of 20 Hz. The ADV probe was positioned at 0Á05 m intervals above the bed and velocity was measured for 300 sec at each height. The streamwise location of the probe, x, was adjusted at each height to maintain its position relative to the lee face of the bar. Ripples in the lee of the bar were not artificially flattened between the two runs. Run 19 ran for 21 600 sec continuously at a constant discharge. The data were recorded in six individual 3600 sec intervals (denoted by subscript letters a to f; Table 1) with no artificial flattening of the bed between intervals.
The highest point of the bar (the bar crest) changed position and height rapidly as superimposed bedforms moved up to the top of the stoss side of the bar. Sometimes the crest of the bar coincided with the brink of the avalanche slip face, but at other times, when a superimposed bedform was a short distance upstream of the bar brink (as in Fig. 1), the bar crest was also some distance upstream of the bar brink. Because the crest position changed quickly but the lee face brink position changed relatively slowly, flow conditions were assessed in relation to the position of the brink. The mean flow velocity above the unit bar brink (U b ) was estimated by dividing the discharge measured electromagnetically within the flume recirculation pipes by the cross-sectional area of the flow at the unit bar brink. For this calculation it was assumed that the brink was perpendicular to the flow and that there was no flow through the sediment bed. Table 1. Experimental conditions in which back-flow ripples were observed. Run 19 consisted of one continuous 21 600 sec flume experiment which was split into six 3600 sec recording windows (denoted by subscript letter). Mean flow velocity above the unit bar brink (U b ) was calculated by dividing the discharge (which was measured using electromagnetic flow meters in the recirculation pipes) by the cross-sectional area above the brink.

Run
Duration (

RESULTS OF THE FLUME RUNS
During the runs the unit bars migrated downstream. Back-flow ripples preferentially formed near the sidewalls of the flume. The ripple crests varied from being constrained close to the side walls to extending ca 0Á2 m out from them. Ripples that formed in the centre of the flume (away from the side wall) were smaller than those near the sides and had more variable migration directions, with their crests varying from parallel to highly oblique to the bar front (Fig. 3A). The ripple pattern generated in the trough points to the formation of multiple flow cells ( Fig. 3B; cf. Allen, 1968). In the runs where back-flow ripples occurred, the number formed varied from one to trains of up to eleven and they were always present at the toe of the lee face of the unit bar. The ripple trains extended downstream <0Á7 m from the lee face toe. Back-flow ripples formed at U b between 0Á27 m and 0Á78 m s À1 , the upper end of this range was the highest velocity tested. The height of the back-flow ripples, measured from the ripple trough to the ripple crest, increased with increasing U b and also showed a very weak dependence on unit bar height within the range investigated ( Fig. 4A and B). The variation in the height of individual back-flow ripples generally increased with increasing U b ( Fig. 4A; Tables 1 and 2).
The difference in depth between the brink and trough is an important control on flow separa-tion. The height of unit bars relative to flow depth varies from very small (low bars in deep flow) to near unity (bar height approaching the full flow depth) resulting in significant differences in flow deceleration over bars. The ratio between the water depth over the brink and trough averaged over each run varied from 0Á42 to 0Á74 and showed no relationship (R 2 = 0Á02) to back-flow ripple height under the tested conditions. However, ripple height had a relatively strong dependence on flow deceleration over the bar, with greater deceleration associated with larger ripples (Fig. 4C). Ripple height was also related to the Van den Berg & Van Gelder (1993) modified mobility parameter h' (Fig. 4D). Over Runs 1 to 19 back-flow ripples were observed forming mostly outside the conditions suggested for dune-related bottomset development (

Incipient back-flow ripples
Incipient back-flow ripples formed in the trough at U b ranging from 0Á27 to 0Á34 m s À1 and 0Á35 to 0Á38 m s À1 in runs with a water surface 0Á69 m and 0Á60 m above the flume base, respectively (Tables 1 and 2). In Runs 4 and 11 some of the incipient back-flow ripples grew into conventional back-flow ripples by the end of the run. Incipient back-flow ripples ranged in height from 1 to 4 mm, featured straight to sinuous crests and formed in the fine sand deposited in the trough. Incipient back-flow ripples featured a long shallow-dipping stoss and a short high-angle lee slope (Fig. 6A). Height : length ratios of these ripples were low (0Á01 to 0Á05). The ripples were easily removed by grain flows on the unit bar lee slope and no evidence of them was  , 1993). Bars denote the data range. To calculate h' it was assumed that the density of the quartz rich sand was 2650 kg m À3 . This calculation also required depth averaged flow velocity to be determined in relation to the mean water depth between the bar brink and trough. Side wall effects were corrected for by multiplying this velocity by an average correction factor. This correction factor was calculated from velocity profiles collected with an ultrasonic Doppler velocity profiler over twelve additional flume runs. Over these runs the average correction factor was 1Á06 (minimum: 1Á04, maximum: 1Á07) and showed no dependence to the width to depth ratio.
observed in the preserved deposits. Occasionally at higher U b incipient back-flow ripples formed on the unit bar lee slope while conventional back-flow ripples formed in the trough (Fig. 6B).

Conventional back-flow ripples
Conventional back-flow ripples (so called because they look like those described by Jopling, 1961;Johansson, 1963;Basumallick, 1966) formed in the unit bar trough at U b of 0Á32 to 0Á7 m s À1 (Tables 1 and 2). Their height ranged from 3 to 20 mm and their height : length ratios (0Á05 to 0Á25) were greater than incipient back-flow ripples. These ripples had straight to sinuous crests, moved towards the lee face of the bar (Fig. 7A) and occasionally travelled tens of millimetres up it. As the unit bar advanced, the ripples were buried beneath grain flows (Fig. 7B), creating structures like those observed in the rock record ( Fig. 7C to E). Runs 17 and 18 resulted in the preservation of conventional back-flow ripples within the unit bar deposits. Their preserved structure was predominantly controlled by the height that migrating ripples reached up the lee slope prior to being buried by grain flows. If no migration occurred prior to burial the ripples were confined to the bottomset, sometimes showing a symmetrical structure due to deformation caused by sand avalanching down from the lee of the unit bar (Fig. 7B). When back-flow ripples migrated up the unit bar lee slope, a wedge shaped ripple was preserved and the back-flow ripples would sometimes interfinger with the Table 2. Minimum, maximum and mean heights for up to ten back-flow ripples (five from each side of the flume closest to the unit bar toe) recorded at the end of each run. In some runs less than ten ripples were present, in these cases the mean is calculated from the number of ripples present. Only an approximate height is given for transient back-flow ripples as their short existence period made them difficult to measure. Runs 15 and 16 featured conventional back-flow ripples at the start of the run transitioning to no ripples and transient back-flow ripples, respectively, by the end. For Run 15 these changes resulted from the breakdown of the lee-side eddy induced by a large superimposed bedform.

Transient back-flow ripples
Transient back-flow ripples sporadically formed in the trough and on the lee slope of the unit bar when U b > 0Á65 m s À1 (Tables 1 and 2; Fig. 8A and B). Due to the turbid nature of the flow, observations of these ripples were limited towards the side walls; they formed rapidly, taking only a few seconds to reach heights of ca 4 to 10 mm, but within a few seconds were washed out by a change in near-bed flow or through entrainment into grain flows on the bar lee face. During their brief existence these ripples rapidly migrated hundreds of millimetres towards the bar lee slope; their occurrence coincided with the transition from angular to tangential lee face laminae downlap. The migration of transient back-flow ripples up the bar lee face contributed to an observed decrease in grain size in the unit bar foresets; this was due to the remobilization of relatively finer sand, deposited from suspension in the bar trough, up the bar lee face. This effect, combined with ripple scouring, also caused increased grain-size heterogeneity within cross-stratum but decreased the grain-size variation between cross-strata. Transient back-flow ripples were often incorporated into grain flows on the unit bar lee face or were destabilized by a change in the lee-side eddy flow conditions and generated grain flows. Because of their rapid washing out, these ripples were infrequently preserved within the deposit as slight undulations on bar foreset cross-stratum (Fig. 8C).

Velocity profiles in the lee of the bar
Velocity data within and above the lee-side eddy were collected in Runs 17 and 18, while conventional back-flow ripples formed in the lee of the unit bar. The unit bar prograded 0Á44 m in Run 17 and 0Á29 m in Run 18. The ripples were progressively buried under grain flows as the bar moved downstream. Three velocity profiles were constructed; two at the bar toe at y = 0Á5 m and y = 0Á2 m and one 0Á1 m downstream of the toe at y = 0Á5 m ( Fig. 9A to C). At all three locations time averaged downchannel velocities ( u) near the water surface were ca 0Á4 m s À1 , further down the water column much lower velocities or reversed flow was recorded. Within the lee-side eddy the magnitude of the back-flow velocity was higher closer to the sidewall (Fig. 9B). At y = 0Á5 m u near the unit bar toe was close to 0 m s À1 (Fig. 9A) but, despite this, small ripples still formed.
Within the lee-side eddy 0Á1 m above the bed the downchannel velocity component (u) ranged from À0Á49 to 0Á54 m s À1 [standard deviations (r) 0Á075 m s À1 to 0Á103 m s À1 ; Fig. 10A lateral component and above the toe there was also a considerable vertical component towards the bed (Fig. 10A and E). Variation in u was greater at y = 0Á5 m ( Fig. 10A and E) and decreased close to the side walls (Fig. 10C). At the flume centreline (y = 0Á5 m) u was positive for short periods ( Fig. 10A and E) suggesting periodic weakening or breakdown of the flow separation cell. Wavelet analysis of the time series data has been applied using the method described in Torrence & Compo (1998) and Liu et al. (2007). This technique allows for the decomposition of the velocity time series identifying periodicity and how this periodicity varies with time (Fig. 11). Peaks can be seen between periods of 4 to 32 sec (Fig. 11A, C and E). Smaller peaks are also present at periods of >32 sec; however, for these longer period velocity fluctuations the recording window was too short to adequately quantify them using wavelet analysis.
Over the lee-side eddy 0Á5 m above the bed u ranged from À0Á15 to 0Á75 m s À1 (r 0Á065 m s À1 to 0Á077 m s À1 ; Fig. 10B, D and F). Relative to u the flow had minimal lateral and vertical velo-city components and lacked the long period velocity fluctuations found close to the bed (Figs 10 and 11). Instead higher frequency turbulence with periods between 0Á5 to 4 sec was more predominant (Fig. 11). The magnitude of u fluctuations were significantly lower than in recordings taken at y = 0Á5 m close to the bed. Yalin (1985) stated that ripple geometry is controlled by five characteristic parameters: fluid density, kinematic viscosity, shear velocity, grain size and specific weight of the grains in the fluid. Back-flow ripples are controlled by sediment availability and the flow within the separation eddy in the lee of the host bedform. The lee-side eddy length is controlled by the host bedform height and the brink angle (Schatz & Herrmann, 2006;Paarlberg et al., 2007). Host bedform height also influences the velocity gradient within the lee-side eddy, and thus shear velocity. The velocity above the crest of the host bedform (U b herein) controls the velocity within the separation eddy and thus influences backflow ripple size and morphology. Jopling (1961) suggested that a minimum stream velocity of 0Á61 m s À1 was required to form back-flow ripples, but did not indicate how this would vary with changes in the host bedform or sediment characteristics. In Runs 1 to 19 back-flow ripples formed when U b >0Á27 m s À1 , and conventional back-flow ripples formed at U b of 0Á32 to 0Á7 m s À1 . Allowing for some dissimilarity in the way velocities were assessed, this demonstrates that back-flow ripples can form at much lower velocities than Jopling (1961) stated and suggests that some published estimates of palaeocurrent velocity deduced from back-flow ripples (e.g. Saunderson & Jopling, 1980) could be overestimated.

Controls of back-flow ripple formation
If the entrainment velocity for 230 lm sand is 0Á274 m s À1 (Miller et al., 1977), and the flume sand D 50 = 230 lm, it might be a surprise that back-flow ripples form at velocities significantly lower than this. Part of the explanation is the dynamic size sorting that operates over the barform such that the sand deposited in the trough and reworked by the return flow, has a finer grain size than the bulk sand in the flume.
Mean flow direction within lee-side eddies was found to be oblique to the bar lee face, with this being more pronounced at the flume centreline (Fig. 10); this explains the more oblique orientation of some back-flow ripple crest lines close to the flume centreline (Fig. 3). In the Normalized power flume, secondary currents are generated by turbulence anisotropy induced by its non-circular cross-sectional morphology (Nezu & Nakagawa, 1993) with the width to depth ratio of the flow being an important control. In these experiments width to depth ratios varied from 4Á2 to 2Á8 above the brink and 2Á0 to 1Á5 above the trough. At width to depth ratios of <5 secondary currents generated at the side walls can influence the flow (Nezu & Nakagawa, 1993) and at greater width to depth ratios secondary currents can be induced in the centre of the flow by sediment ridges on the bed (Nezu et al., 1985). Secondary currents induced by the width to depth ratio could influence the orientation of back-flow ripples generated in the bar trough. This effect may be less pronounced when the bar shows significant three dimensionality (Allen, 1968(Allen, , 1982b. Secondary currents induced by both the width to depth ratio and bar three dimensionality probably influenced the distribution of ripples in these flume experiments (Fig. 3). Back-flow ripples were generally larger within 0Á2 m of the flume side wall, which was not observed in previous flume studies by Reesink & Bridge (2007) and Johansson (1963); this is due to differences in the secondary circulation patterns probably induced by different width to depth ratios. Unit bar experiments by Reesink & Bridge (2007) generally featured higher width to depth ratios, ranging from 10 to 4 above the brink and 3Á0 to 1Á7 above the trough. This finding raises questions on how applicable the relationships between back-flow ripples, flow and sediment characteristics found in flume experiments are to natural environments where no side wall would be influencing the flow. However, secondary flow cells exist in river systems and are an intrinsic part of the flow. Flow patterns within troughs downstream of bars are likely to be equally if not more three-dimensional, influenced by channel bends, tributaries, channel banks and obstacles, as well as obliquely orientated and three-dimensional bar fronts. Reesink et al. (2014) suggested that oblique flows are important for the formation of backflow ripples that climb onto the lee slope of the host bedform; Fig. 3 somewhat supports this theory with back-flow ripples that are oblique to the bar front migrating further up the lee slope. Incipient back-flow ripples forming directly on the bar lee face had variable crest line orientations often oblique to the bar front. However, climbing conventional back-flow ripples were observed forming close to the sidewalls where flow featured less obliquity (Fig. 10C). Back-flow ripple crest line orientations near the side walls were often nearly parallel to the bar front, suggesting little influence from oblique flow. This may suggest that, while the lack of oblique flow does not preclude the formation of climbing back-flow ripples, oblique currents may increase the chances of climbing back-flow bedforms.
Previous experiments suggested that back-flow velocity must exceed 0Á12 m s À1 before backflow ripples will form in 'fine silty sand' (Saunderson & Jopling, 1980, and references therein). However, in Runs 17 and 18 the magnitude of u recorded above conventional back-flow ripples within the lee-side eddy was often less than 0Á12 m s À1 (Figs 9, 10A, 10C and 10E). Backflow ripple development can be explained by u measured at the flume centreline only being a component of an oblique flow, and also the variable velocity within the unit bar lee resulting from wake flapping and vortex shedding from the separation zone. Wavelet analysis of the u time series close to the bed in Runs 17 and 18 identifies a number of strong peaks spread across a wide range of periods (Fig. 11). Turbulence periodicities have been estimated (Table 3) using scale relations proposed by Simpson (1989). Wavelet analysis identifies large peaks in normalized power between 4 and 8 sec for both Run 17 (Fig. 11E) and Run 18 ( Fig. 11A and C), this is close to the estimated vortex shedding periods (Table 3). Slightly smaller peaks in normalized power can be seen at 32 to 64 sec in Fig. 11. Wavelet power spectrum (using the Morlet wavelet) of the velocity time series recorded at (A) at y = 0Á5 m, 0Á09 m above the unit bar toe; (B) at y = 0Á5 m, 0Á49 m above the unit bar toe; (C) at y = 0Á2 m, 0Á08 m above the unit bar toe; (D) at y = 0Á2 m, 0Á48 m above the unit bar toe; (E) at y = 0Á5 m, 0Á07 m above the bed, 0Á1 m downstream of the unit bar toe; (F) at y = 0Á5 m, 0Á5 m above the bed, 0Á1 m downstream of the unit bar toe. Contours are normalized power (normalized by variance) in logarithm (base 2) and have been rectified for bias (cf. Liu et al., 2007). A solid black line encloses regions of greater than 95% confidence for a red-noise process. The curved dashed line indicates the cone of influence. Below this, edge effects can influence the power distribution. Due to this, additional measurements beyond the 300 sec recording window were also used when available. A detailed explanation of the method used can be found in Torrence & Compo (1998) and Liu et al. (2007).
Run 17 (Fig. 11E) and 16 to 32 sec in Run 18 ( Fig. 11A and C) which is close to the estimates of wake flapping periodicity (Table 3). Kostaschuk (2000) observed similar velocity patterns in data collected downstream of a dune in Canoe Pass, Canada.
In addition to wake flapping and vortex shedding, the lee-side eddy changes with the arrival of superimposed bedforms at the bar crest. This causes velocity fluctuations with a period influenced by the migration rate of the superimposed bedforms and explains some of the long period peaks (>64 sec) recorded close to the bed (Fig. 11). Vortex shedding, wake flapping and superimposed bedforms all result in packets of flow near the bed in the bar lee with much greater velocity magnitude than u. In settings where the mean return flow is not fast enough to generate ripples, fast flow packets from any of the three mechanisms described above may induce back-flow ripple formation if the minimum velocity required for ripple generation is exceeded for long enough. Within the lee-side eddy the mean back-flow velocity (labelled V 1 on Fig. 12A) may not be fast enough to initiate grain movement, but high velocity packets from eddies may allow sporadic grain movement and incipient back-flow ripple development (Fig. 12A). With an increase in the size of the lee-side eddy induced by wake flapping the mean back-flow velocity (labelled V 2 on Fig. 12B) is strengthened compared to its previous state (V 2 >V 1 ; cf. Allen, 1968;Simpson, 1989). With more frequent or longer duration high velocity packets more grain movement on the bed results in the development of conventional back-flow ripples (Fig. 12B). In settings where the mean back-flow velocity (labelled V 3 on Fig. 12C) is fast enough for transient backflow ripple formation, slower flow packages may generate transient back-flow ripples that are periodically washed out by faster flow packages (Fig. 12C). With an increase in the size of the lee-side eddy induced by wake flapping the mean back-flow velocity increases (labelled V 4 on Fig. 12D, V 4 >V 3 ). Conditions may no longer favour the generation of back-flow ripples (Fig. 12D).
Superimposed bedforms can alter flow separation, turbulence and geometry. Fernandez et al. (2006) observed higher levels of turbulence intensity, Reynolds stresses and turbulent kinetic energy downstream of a fixed bedform when a fixed superimposed ripple was located 0Á03 m (33% of the wavelength of the superimposed ripple) from the host bedform crest. These authors found that the lee-side flow structure was altered by the interaction of the shear layers produced from the adjacent flow separation zones of the host and superimposed bedform both of which periodically merged forming a larger unified flow separation zone leading to increased turbulence production. However, it is unlikely that the large effect observed in these experiments would be found in natural fluvial systems because the large superimposed bedform (66% of the host bedform height) would generate a reactivation surface (McCabe & Jones, 1977). Although a similar effect, albeit probably lower magnitude, is possible if the superimposed bedform height is <25% of the host bedform height precluding reactivation surface formation (Reesink & Bridge, 2009). Relatively small superimposed bedforms could lead to more rapid conventional back-flow ripple development during periodic merging of the flow Table 3. Predicted turbulence periodicities based on a range of estimated mean flow separation lengths. Estimates of periodicities are derived from the scale relations proposed by Simpson (1989). For vortex shedding P v % x r /0Á7U b where P v is the periodicity of vortex shedding and x r is the flow separation length. In this case U b is multiplied by 0Á7. Simpson (1989) suggests a range for this value from 0Á6 to 0Á8, for this equation Kostaschuk (2000) and Shugar et al. (2010) use 0Á8 whilst Hardy et al. (2009) use 0Á6. For wake flapping P w >x r /0Á1U b where P w is the periodicity of wake flapping. The estimates are derived using a bar height of 0Á327 m and 0Á257 m and U b of 0Á47 m s À1 and 0Á41 m s À1 in Runs 17 and 18, respectively.
Paarlberg et al. separation zones ( Fig. 12E and F) by allowing more grain movement induced by either longer duration, more frequent or higher magnitude velocity packets (represented on Fig. 12E and F by the root mean square back-flow velocity, V rms , where V rms2 >V rms1 ). Best et al. (2013) found that for relatively large superimposed bedforms which generate reactivation surfaces, the migration of the superimposed bedform to the brink decreases the size of the lee-side eddy of the host bedform. This decrease in lee-side eddy size could also occur with a relatively small superimposed bedform if its lee-side eddy erodes the brink point of the host bedform, as the angle between the brink and crest (which could potentially be the crest of the superimposed bedform) can control the size of the flow separation zone (Paarlberg et al., 2007). This suggests that the time-averaged back-flow velo-city is not the critical factor in the formation of back-flow ripples. A measure of the frequency and duration of high magnitude velocity packets must also be considered. Whilst little correlation was observed between bar and ripple height in these experiments, host bedform height is likely to influence ripple development under certain conditions. Because flow separation length is influenced by host bedform height, larger host bedforms will often provide a longer zone in which back-flow ripples can develop, this could be particularly important under low flow velocity conditions where ripple development is relatively slow. It is also likely that there exists a minimum host bedform height beyond which back-flow ripple formation is precluded by the small size and length of the flow separation zone which was not reached in these experiments.

Relatively low mean flow velocity in separation eddy
Relatively high mean flow velocity in separation eddy Implications of superimposed bedforms to flow separation and back-flow ripple formation Deceleration over bars is an important factor in bottomset development (Reesink & Bridge, 2009. Larger deceleration over a bar leads to enhanced suspended sediment deposition. Thus, little bottomset development is expected with low height bars relative to water depth. With a relatively weak back-flow, finer sand deposited from suspension would more easily develop back-flow ripples by allowing sediment movement by lower magnitude velocity packets. With a relatively strong back-flow, finer sand is more likely to be washed out by higher magnitude velocity packets. Where suspension fallout in the trough is minimal but a strong back-flow develops, back-flow ripples could form by reworking coarser sand already present on the bed.

Ripple types and preservation
Ripple heights varied from 1 to 20 mm; a greater range than the 3 to 10 mm found by Allen (1965) related to the difference in grain size. Ripple heights were often less than the 15 to 20 mm recorded by Johansson (1963).
Conventional back-flow ripples were either straight or sinuous crested, as observed also by Johansson (1963) and Allen (1965); they tended to be preserved in the deposits and this high preservation potential explains the prevalence of conventional back-flow ripple descriptions in the literature (e.g. Jopling, 1961;Johansson, 1963;Basumallick, 1966;Boersma et al., 1968). Jopling (1961) suggested that the geometry of back-flow ripples was usually well-preserved during burial, but occasional distortions were induced by avalanching sands from the lee face of the host bedform.
As with ripples formed under steady unidirectional flow, flow sheltering (cf. Baas, 1994) can occur with back-flow ripples when a large number form. This is where individual back-flow ripples are sheltered from the flow by a ripple, which in this case is located further down-channel due to the back-flow within the lee-side eddy. This creates a ripple train with alternating ripple sizes (Fig. 7A).
Incipient back-flow ripples feature similar dimensions to incipient ripples at the early stages of ripple development in a steady unidirectional flow (Harms et al., 1975;Baas, 1994Baas, , 1999 and are similar to the 'scalelike' ripples described by Allen (1965). Given enough time it is likely that they would grow into conventional back-flow ripples, but the time available is limited by the migration rate of the host bedform and the size of the lee-side eddy. The time needed for ripples to reach equilibrium with the flow is inversely related to flow velocity (Baas, 1994). Given the duration of the flume runs, and more importantly the speed of bar migration, it is unlikely that any of the ripples reached true equilibrium with the flow; this is supported by the predominance of straight and sinuous crest lines. The size of these non-equilibrium ripples may be partly related to the duration of ripple formation.
The formation of transient back-flow ripples coincided with the transition from angular to tangential cross-strata. A number of controls have been suggested which contribute to this transition, including increased deposition from suspension on the lower lee slope, the ratio of flow depth above the brink to flow depth above the trough, and turbulent eddies accelerating grain flows (Jopling, 1965;Reesink & Bridge, 2009). Transient back-flow ripple formation promotes the transition to tangential cross-strata. Transient back-flow ripples rapidly migrate from the trough up the lee slope, driving a decrease in grain size and changes in the heterogeneity of the unit bar.
Occasionally slight undulations on unit bar laminae were observed after the transition to tangential foresets (Fig. 8C). Transient back-flow ripples on unit bar foreset lamina are either completely washed out or significantly modified by grain flows and have a low preservation potential, but undulations on foreset laminea may be preserved in the deposits. Under certain flow or sediment conditions these undulations may be better preserved. Cross-stratification that may have been influenced by transient back-flow ripples has been identified in fluvial deposits (type 3 cross-strata in fig. 10, as well as fig. 13 in Boersma, 1967) and in flume studies ( fig. 12A in Reesink & Bridge, 2009). These deposits often featured abundant foresets that appeared wavy or curvilinear. Boersma (1967) noted that these foresets contained finer or more poorly sorted sediment in comparison to the rectilinear foresets, as also observed in the present study. Similar structures have been found in the rock record (Fig. 8D).

Palaeoenvironmental interpretations from back-flow ripples
This research indicates that bottomsets in crossbedded sand can form in conditions other than those proposed by Martinius & Van den Berg (2011) for dune-related bottomset development (Fig. 5) when they form in association with unit bars or in settings where the flow over dunes changes faster than the dunes can adjust. Although these runs have examined back-flow ripples formed in the lee of unit bars, some observations may be applicable to back-flow ripples formed in dune troughs (e.g. Kirk, 1983;Martinius & Van den Berg, 2011). Dunes out of equilibrium with the flow migrating under unsteady flow conditions, such as a decreasing h' (cf. Van den Berg & Van Gelder, 1993), could generate back-flow ripples outside the conditions suggested in Fig. 5.
When conventional back-flow ripples are restricted to the bottomset, they tend to be wellpreserved and the dimensions of the preserved forms are close to those of the back-flow ripples during their formation. However, when backflow ripples migrate rapidly or the host bedform migrates very slowly, preserved ripples become wedge shaped and extend up the host bedform foreset laminae creating fine-grained periodic climbing ripple cross-lamination (Fig. 7F).
Back-flow ripples can form over a wide range of flow velocities, contrary to earlier suggestions that they are either evidence of low flow velocities (Boersma, 1967;Nio et al., 1980) or of stream velocities >0Á61 m s À1 (Jopling, 1961). The variation in ripple structure with flow velocity make back-flow ripples potentially viable palaeovelocity indicators, although it is important to remember that these results do not precisely model riverine conditions because velocity increases were not associated with a water depth increase. At low flow velocities (<0Á3 m s À1 in this study) incipient back-flow ripples can form and preservation depends on the transition to conventional back-flow ripples. If back-flow ripples are preserved their height is likely to be much less than a ripple of the same grain size at equilibrium with the flow due to both the limited ripple development time prior to burial and sediment transport in the trough being driven only by turbulent events. Host bedform height may influence back-flow ripple development at low flow velocities because larger bedforms will often provide a larger flow separation zone, lengthening ripple development time. At moderate flow velocities (0Á3 to 0Á7 m s À1 in this study) conventional back-flow ripples can develop. Depending on the backflow velocity and variability, the length of the flow separation zone and the host bedform migration rate conventional back-flow ripples may or may not approach equilibrium height. At high flow velocities (>0Á65 m s À1 in this study), the remnants of migrating transient back-flow ripples may be present as occasional undulations anywhere along the host bedform foresets.
Deducing the original height of back-flow ripples that have interfingered with the foreset lamination of the host bedform may be difficult, hindering palaeovelocity interpretation. However, interfingering suggests that the host bedform migration rate was slow relative to the migration rate of the back-flow ripples. Flow unsteadiness can lead to significant variations in bar trough deposits, particularly in shallower parts of a channel (Reesink & Bridge, 2011) and it is likely that back-flow ripple preservation in rivers may be intermittent because of flow variability. When present, structural variation in back-flow ripples preserved along the base of a cross-stratified set could be used as an indicator of flow variability during deposition. For example, during changing flow conditions conventional back-flow ripples may be preserved at the base of a cross-bed set formed by a unit bar; these may change in height as the flow conditions change (Fig. 4). Past a threshold velocity (0Á65 to 0Á7 m s À1 in these experiments) conventional back-flow ripples no longer form, instead transient back-flow ripples make undulations on unit bar cross-stratum (Fig. 8C) and there is a transition to tangential foreset laminae.
Back-flow ripple development is influenced by the flow in the trough downstream of the host bedform. Strongly three-dimensional flow, which can be induced by host bedform threedimensionality, can lead to the creation of ripple fans or a number of ripple fan cells (Allen, 1968(Allen, , 1982b. Where there is a considerable lateral component to the flow (for example, a bar front oblique to mean flow direction, close to a channel bend or tributary) back-flow ripples are likely to form oblique to the bar front (e.g. Boersma et al., 1968). If lateral flow predominates and there is negligible flow separation normal current ripples may develop. These ripples can appear like back-flow ripples in cross-section of deposits (e.g. Collinson, 1970). For any palaeoenvironmental reconstruction, the orientation of ripples in relation to the mean flow direction should be assessed. Many factors including the characteristics of the sediment, host bedform height and shape, lee-side eddy and discharge variation probably alter the structure of preserved back-flow ripples, and at present most remain unquantified. Examples of this are found in bottomsets influenced by tidal processes that can contain back-flow and co-flow ripples (Nio et al., 1980;Van den Berg et al., 2007), as well as parallel lamination (Van den Berg et al., 2007) and climbing ripple cross-lamination (Nio et al., 1980). This variation in bottomset structure has been attributed to flow reversals controlled by flood and ebb currents (Nio et al., 1980;Van den Berg et al., 2007) as well as wave action (Nio et al., 1980). Due to the number of unquantified parameters that can influence back-flow ripple formation and structure, currently many assumptions must be made for palaeocurrent reconstructions using them. Further flume research is required to determine the effects of bar height, water depth and bottomset grain size on back-flow ripple development and geometry.

The role of unsteady flows in bedform development
As with back-flow ripple development, unsteady flow could be an important control in the development of larger bedforms. Flow conditions in rivers are often variable leading to changes in bedform geometry over time; however, bedform geometry change generally lags changes in flow conditions (Allen, 1973). If flow variation is slow, bedforms may adjust to the changing conditions so that bedform dimensions remain close to equilibrium values (Gabel, 1993). However, in rivers dominated by unsteady flows, such as arid ephemeral and semi-arid flashy rivers (e.g. Karcz, 1972;Amos et al., 2004) or rivers with dam releases (e.g. Reesink & Bridge, 2011), large bedforms (for example, unit bars) will be the product of rapidly changing flow resulting in composite bed features formed and progressively modified under a wide range of discharges, never reaching equilibrium with the changing flow. Shortduration high discharge events could cause bedform growth and migration or could wash out pre-existing bedforms fully or in part, in a comparable way to high velocity packages forming or washing out back-flow ripples in the experiments described above. During low discharge conditions bedforms present on the bed could differ significantly to what would be generated under steady flow conditions. With both back-flow ripples and larger bedforms in flashy settings the relative duration of different flow conditions (high and low velocity packages in a bar lee, or flash flood and low discharge conditions in a semi-arid river) will be as or more important than mean flow conditions.

CONCLUSIONS
Back-flow ripples formed in the lee-side eddy of a unit bar over a wide range of flow velocities. Millimetre high incipient back-flow ripples formed at low velocities. Well-developed conventional back-flow ripples formed at moderate velocities and transient back-flow ripples formed and migrated up the unit bar lee slope at higher velocities. Although no record of incipient back-flow ripples was preserved in the deposits, conventional back-flow ripples had a high preservation potential and formed characteristic structures within the bar deposits. Evidence of transient back-flow ripples was occasionally preserved as undulations on foreset laminae. These ripples influenced the grain size and sorting within the host bedform by transporting sediment from the trough up the lee face.
The very variable flow velocity near the bed in the lee of the bar allowed back-flow ripples to form at lower mean back-flow velocities than anticipated. The velocity variation was caused by vortex shedding, wake flapping and changes in the size of and turbulence within the flow separation zone resulting from superimposed bedforms on the bar approaching the bar crest. In this context mean back-flow velocity may be less important for back-flow ripple formation than the magnitude and duration of high velocity packages. These packets cause the transience of the back-flow ripples at higher flow velocities.
Burial of back-flow ripples by the advancing host bedform limits the time available for the bedforms to develop; this as well as the limited length of the lee-side eddy and the velocity variability within it means that back-flow ripples will rarely reach equilibrium and their size and shape may be an indicator of depositional conditions (unlike equilibrium ripples where size is related more strongly to sediment grain size). The shape of back-flow ripples in these experiments changed with flow velocity, suggesting that it may be possible to use the morphology of back-flow ripples preserved within ancient deposits as an indicator of palaeoflow velocity in cases where ripples had migration directions parallel but opposed to the mean flow direction. Changes in back-flow ripple morphology within h' Modified mobility parameter (cf. Van den Berg & Van Gelder, 1993)