Figures 3–10, Table 1, Supplementary Table S2, and Supplementary Video S1 provide a detailed summary of all the field data collected on the tidal flat during the spring–neap cycle between May 21st and June 3rd, 2013. Figure 3 presents time-series of water depth (Figure 3A), wave and current stresses (Figure 3B), bedform types (Figure 3C), bedform length (Figure 3D), bedform height (Figure 3E), and asymmetry index (Figure 3F). The relative importance of currents, waves, and combined flow for the generation of these bedforms is shown in Figures 3G,H shows the percentage equilibrium, relict, and transitional bedform states. The wave–current angles for ladderback ripples, tile-shaped interference ripples, lunate interference ripples, and upper-stage plane beds are plotted in Figure 3I. Figures 4–8 show characteristic 3D–ARP and BASSI data for selected tidal inundations, and Figure 9 displays the main geometric properties of the equilibrium, relict, and transitional bedform types present, as well as the characteristic hydrodynamic conditions at which these bedforms formed. The phase diagram in Figure 10A shows how the various bedform types are related to the wave and current stresses, and Figure 10B shows the equivalent for the wave velocity amplitude, U ₀, and depth-averaged current velocity, ū, as used by Perillo et al. (2014). Whilst both the stresses and velocities are dimensional, the stresses in Figure 10A can more readily be made non-dimensional, e.g., by using Shields parameters (Kleinhans, 2005), since the median size of the sand particles on the bed was constant in the study area.

In tidal inundations 1 (May 21st, pm) and 2 (May 22nd, am), the current stresses were below τ₀ at all times, whereas the wave stresses exceeded τ₀ around high slack water (Figures 3A,B). In both inundations, the currents and waves were co-linear. The 3D–ARP shows small, straight-crested, near-symmetric ripples with bifurcation patterns that are typical of wave ripples (Figures 4A, 9C, 10; Table 1; Allen, 1984; Perron et al., 2018). Since the wave stress was close to zero at the start of inundation 1, these wave ripples are interpreted as relict bedforms generated by waves in an earlier inundation. During flood and ebb, when current stresses reached 0.09–0.18 Nm⁻², the wave ripples migrated slowly in the downstream direction (slightly inclined vertical lines in BASSI data in Figure 4B), possibly because these weak currents helped the combined stresses to exceed τ₀ (Figure 3B). Relatively high, equilibrium wave ripples were present around high slack water on May 22nd, when the wave stress reached 0.5 Nm⁻² (Figures 3B,C,E), which signifies the precursor of the storm that started to affect the field site later that day. The length of the wave ripples in tidal inundations 1 and 2 was 124 mm (Figures 3C,D), whereas the height of these bedforms increased from 10 to 16 mm, reaching a temporary maximum of 18 mm during the period of large wave stresses in tidal inundation 2 (Figures 3B,C,E).

Tidal inundation 3 (May 22nd, pm) experienced a peak current stress of 0.34 Nm⁻² during flood and a peak wave stress of 0.8 Nm⁻² immediately before high slack water (Figures 3A,B), and the currents and waves remained co-linear. Strong combined currents and waves during the flood (τ_max < 0.88 Nm⁻²; Figure 3B) caused the two-dimensional wave ripples of inundation 2 to evolve into larger, more asymmetric bedforms with a moon-shaped plan morphology, classified as lunate interference ripples (Figures 3A–F, 4C,D, 9F, 10; Table 1). Figure 4C shows that this process included an initial period in which both bedform types were present on the sediment bed. The lunate interference ripples were particularly high and long for c. 1 h around high slack water (Figures 3C–E, 4D), Thereafter, when the current stress was small and the wave stress decreased, the lunate interference ripples changed back gradually to smaller wave ripples (Figures 3B–E, 4E). During the ebb, these transitional bedforms formed the nucleus for the formation of incipient current ripples (Baas, 1994; Table 1), which were about half the size of the lunate interference ripples (Figures 3A,C–E, 4F). The current stress was larger than the wave stress at the end of inundation 3 (Figure 3B), which supports the presence of these non-equilibrium current ripples.

Tidal inundation 4 (May 23rd, am) reveals complex and rapidly changing hydrodynamics, which caused rapidly changing bed morphology. The wave stress was 0–0.50 Nm⁻² during the flood, it decreased around high slack water, and waves were absent during the ebb (Figures 3A,B). The tidal currents rotated clockwise from south-southeast to north-west and the wave direction varied between east and south-east. The 3D–ARP recordings start with small, asymmetric, two-dimensional bedforms formed by the flood current (Figures 3A–F, 5A). These bedforms resemble straight-crested current ripples (Figures 9A, 10; Table 1), which probably evolved around low slack water from the incipient current ripples in inundation 3. The bed then changed to lunate interference ripples, similar to those in inundation 3 under large co-linear wave and current stresses. Thereafter, the wave stresses fluctuated between 0.06 Nm⁻² and 0.34 Nm⁻² (Figure 3B), the tidal current waned, and the wave–current angle increased to 65°. This resulted in the formation of tile-shaped bedforms that were clearly asymmetric in cross-section on the 3D–ARP and BASSI profiles, with two crest-line orientations that corresponded to the current and wave directions (Figures 5B, 9E; Table 1). These tile-shaped interference ripples became relict towards the end of the flood (Figures 3A–C), but waves continued to reshape the bed during high slack water by forming small wave ripples in the troughs of the tile-shaped interference ripples, classified as ladderback ripples (Figures 5C, 9D, 10; Table 1; Klein, 1970). Near the end of high slack water, the ladderback ripples had evolved into wave ripples. Local remnants of the tile-shaped interference ripples caused the wave ripples to have straight but discontinuous crestlines (Figure 5D) and possibly also an uncharacteristically large asymmetry (Figures 3C,F). The ebb current, in the absence of waves, was strong enough to form small, quickly migrating, incipient to locally straight-crested current ripples (Figures 3A–E).

A storm passed the field site during tidal inundations 5 (May 23rd, pm) and 6 (May 24th, am). The current stresses were generally close to or well above τ₀, with a peak stress of c. 0.6 Nm⁻² during flood, more than twice the peak stress in inundation 4 (Figure 3B). The wave stresses were also larger than in inundation 4, particularly around high slack water (Figures 3A,B). Upper-stage plane beds (Figures 6A,B, 10; Table 1) prevailed during most of the flood tide when the combined stress was in the sheet flow regime (Figures 3A–C). The 3D–ARP recorded ribbon-like features (McLean, 1981), oriented parallel to the wave direction (Figure 6A), on these plane beds. In inundation 5, the upper-stage plane bed was preceded during the flood tide by a bed covered in asymmetric, equilibrium linguoid current ripples (cf., Baas, 1994; Figures 9B, 10; Table 1), formed when strong currents acted in the same direction as weak waves in relatively shallow water. In inundation 6, however, the plane beds were preceded by washed-out, lunate interference ripples (Table 1) during somewhat weaker combined flow. The 3D–ARP recorded smaller straight-crested to slightly three-dimensional current ripples, when the hydrodynamics were current-dominated, half an hour before the bed was covered with the washed-out ripples (Figures 3B,C). After the flood in both inundations, when the current stresses were small, but the wave stresses caused τ_max >> τ₀, washed-out ripples (Table 1) and then more pronounced ripples with straight but discontinuous crestlines appeared on the flat bed. Based on the dominance of wave action and the large wave–current angle, these bedforms are interpreted as wave ripples in which the weak tidal current disrupted the two-dimensional plan morphology. The wave-free ebb current (Figures 3A,B) may have been just powerful enough to move the wave ripples in a downstream direction (Figure 6C), given their low migration rate (Figure 6D), and initiate a change to current ripples at the end of the inundation.

At the start of tidal inundation 7 (May 24th, pm), the storm had peaked and the tide was midway between neap and spring. The current stresses dominated the combined stresses during the flood and ebb, reaching 0.48 Nm⁻² and 0.25 Nm⁻², respectively, and the wave stresses pushed the combined stresses above τ₀ around high slack water (Figures 3A,B). Current ripples and wave ripples dominated this inundation. Downstream-migrating equilibrium linguoid current ripples (Baas, 1994) formed during the flood (Figures 3A–C, 7A,C). At high slack water, moderate waves slowly modified these current ripples into wave ripples by slightly decreasing the asymmetry and forming more continuous crestlines. Upon the decrease in wave stress during ebb, these wave ripples became relict and then changed gradually to more asymmetric equilibrium linguoid current ripples (Figures 3A–C,F, 7B,D).

Except for tidal inundation 12 (May 27th, am), the wave stresses were small or absent in tidal inundation 8 (May 25th, am) to inundation 16 (May 29th, pm) (Figure 3B). Current-generated bedforms therefore dominated these inundations. Equilibrium linguoid current ripples formed during the flood and ebb tides (Figures 3A–C, 8A). These bedforms were stationary and thus relict during high slack water, even when the bed was exposed to weak waves in inundations 10, 11, 15, and 16. The BASSI data show that the migration rate of these ripples increased, as the current stresses increased (cf., Lichtman et al., 2018). Spring tidal current stresses peaked at 0.6–0.7 Nm⁻² in the final recording of the ebb in inundations 10 and 11 (Figures 3A,B), resulting in the formation of washed-out ripples (Figures 3C, 8B). On either side of these peak spring inundations, the ebb current formed merely linguoid current ripples.

Spring tide inundation 12 was different in that it captured large maximum current stresses in combination with moderate wave stresses during high slack water that caused the combined stresses to be above τ₀ throughout the inundation (Figures 3A,B). These conditions led to a dominance of two types of combined-flow bedforms, both of which formed at large wave–current angles of between 40° and 85°. Tile-shaped interference ripples were recorded during the last hour of the flood tide (Figures 3A–C, 8C). These bedforms replaced equilibrium linguoid current ripples that formed earlier, when the current stress was at its peak and waves were absent. The second type of combined-flow bedforms were ladderback ripples (Figure 8D). These bedforms formed during high slack water and the ebb, mostly when the wave stresses were larger than the current stresses, and they were roughly 50% lower and shorter than the tile-shaped interference ripples (Figures 3A–E). The height and length of the subordinate bedforms in the trough of the ladderback ripples gradually decreased in time in parallel with a gradual change from wave-dominated to current-dominated flow. The final recording during the ebb, when the flow depth had reduced to 1.72 m and waves were absent, revealed asymmetric, non-equilibrium current ripples that were partly straight-crested and in the process of replacing the ladderback ripples (Figures 3A–C).

The wave stress had a significant influence on the bedform dynamics during tidal inundation 17 (May 30th, am). Wave stress dominated the combined stress around high slack water, whereas the current stress was dominant during the flood and ebb (Figures 3A,B). Consequently, the 3D–ARP data show a bed occupied by equilibrium linguoid current ripples during most of the flood. The waves gradually changed these current ripples into wave ripples over high slack water and then into ladderback ripples at the start of the ebb. The final recording shows bedforms in which the wave-generated “steps” of the ladderback patterns had almost disappeared and the current-generated crests had become more pronounced; these bedforms thus started to resemble non-equilibrium straight-crested current ripples. All the bedforms in inundation 17 migrated in the direction of the flood and ebb current, helped by the waves when the current stress was small. The current ripples were more asymmetric than the wave ripples and the ladderback ripples (Figures 3C,F).

Tidal inundations 18 (May 30th, pm) to 21 (June 1st, am) experienced small wave stresses and peak current stresses that progressively decreased, in line with the change from spring to neap tide, but were above τ₀ (Figures 3A,B). This current dominance resulted in the formation of asymmetric equilibrium current ripples (Figures 3C, 8E) that were stationary, and therefore classified as relict, when the current stress was below c. 0.18 Nm⁻². These current ripples migrated during part of the flood in inundation 18, but this swapped to migration during the ebb in inundations 20 and 21. In the intermediate inundation 19, the current ripples migrated during both the flood and ebb tides (Figure 3A). The bed morphologies can be followed across the low slack water between the tidal inundations, as the current ripples migrated over a short distance without radically changing their plan morphology. When waves were present, the wave stress was largest during high slack water, but this did not significantly modify the current ripples.

During the neap tide inundations 22–25, the linguoid current ripples that were actively migrating earlier became stationary and therefore relict (Figure 8F). Waves were entirely absent, and all flood and ebb current stresses were below 0.12 Nm⁻² and thus too weak to move the current ripples (Figures 3A,B), even at shallow depths around low slack water.

As expected, equilibrium current ripples (Figure 9B) formed when the combined stress was above τ₀ = 0.18 Nm⁻² for 0.227 mm sand and current-dominated (Figure 10A). The equilibrium current ripples formed at stresses below c. 0.65 Nm⁻². Likewise, equilibrium wave ripples (Figure 9C) formed at wave-dominant combined stresses between 0.18 Nm⁻² and 0.65 Nm⁻². The grey dashed lines near to the axes in Figure 10A delimit the stability regimes of equilibrium wave ripples and equilibrium current ripples, based, on the following equations:

Eq. 3, regime boundaries for equilibrium wave ripples: τ c < 0.2   τ w ,   0.18 < ( τ c + τ w ) < 0.65 (3)

Eq. 4, regime boundaries for equilibrium current ripples: τ c > 3.3   τ w ,   0.18 < ( τ c + τ w ) < 0.65 (4)

Using Eq. 2 to calculate τ₀ for single and combined currents and waves, the black dashed quarter circle in Figure 10A, based on φ = 90°, accurately delimits a no-motion regime with stationary, and therefore relict current ripples and wave ripples. The black dashed straight line, based on φ = 0°, is shown for comparison. Non-equilibrium, incipient and straight-crested current ripples (Figure 9A) plot mostly within the current ripple stability regime, but these bedforms are characterised by combined stresses between 0.18 Nm⁻² and 0.44 Nm⁻² (Figure 10A). Such small current stresses explain the transitional state of these bedforms, as non-equilibrium current ripples need more time to reach linguoid equilibrium morphology as the current stress is reduced (Baas, 1994, 1999; Oost and Baas, 1994) and therefore are more likely to be recorded at small than at large current stresses. For a similar reason, bedforms that were transitional from current ripples to wave ripples plot at small, combined stresses, where the wave stresses dominate (Figure 10A).

With few exceptions, the combined-flow bedforms plot well outside the stability regimes for current ripples, wave ripples, and no motion in Figure 10. Lunate interference ripples (Figure 9F) have combined wave–current stresses between 0.8 Nm⁻² and 0.9 Nm⁻², when the wave direction was almost parallel to the current direction (Figure 3I) and the wave stresses were larger than the current stresses (Figure 10A). The lunate interference ripples may correspond to the lunate megaripples and the oriented hummocks in the combined-flow phase diagram of Kleinhans (2005). The ladderback ripples (Figure 9D) and tile-shaped interference ripples (Figure 9E) were stable at smaller combined stresses than the lunate interference ripples. The ladderback ripples formed at combined stresses of 0.26 ± 0.04 Nm⁻². The tile-shaped interference ripples formed at a slightly larger combined stress of 0.33 ± 0.08 Nm⁻², but there is a substantial overlap in the combined stresses for these two bedform types. The angles between the wave and current directions for the ladderback and tile-shaped interference ripples were mostly above 45° (Figure 3I). The ladderback and tile-shaped interference ripples may correspond to the mixed wave–current ripples and the three-dimensional asymmetrical ripples in the combined-flow phase diagrams of Kleinhans (2005) and Perillo et al. (2014), respectively. These phase diagrams also include symmetric and asymmetric dunes between ripples and upper-stage plane beds for a similar grain size, but these large bedforms were not present at the study site. This may be because the flow conditions changed too quickly for dunes to develop, causing wave ripples and current ripples to change directly to and from washed-out ripples and upper-stage plane bed.

Washed-out ripples formed mainly at large shear stresses in current-dominant and wave-dominated flow, averaging 0.69 Nm⁻² (Figure 10A). In contrast, upper-stage plane beds mostly required strong combined stresses between 0.81 Nm⁻² and 1.20 Nm⁻². The formation of upper-stage plane beds appears independent of the wave–current angle, because it covers a wide range of angles from 0° to 70° (Figure 3I) whereas the lunate interference ripples are confined to angles less than 25°. Combined stresses of 0.78 Nm⁻² and 0.89 Nm⁻² can be used to separate the stability regime of the lunate interference ripples from that of washed-out ripples and upper-stage plane bed under strong wave-dominated conditions (Figure 10). Lunate interference ripples do not appear to form under current-dominated conditions, approximated by a gradual tapering of the phase boundary between lunate interference ripples and upper-stage plane bed in Figure 10A, according to the following equation:

Eq. 5, regime boundaries for lunate interference ripples: τ c < − 0.593   τ w + 0.621 ,   0.39 < τ w < 0.66 (5)

Comparing the field-based bedform phase diagrams in Figure 10 with laboratory-based phase diagrams (e.g., Arnott and Southard, 1990; Yokokawa et al., 1995; Dumas et al., 2005; Kleinhans, 2005; Tinterri, 2011; Perillo et al., 2014) is complicated by the large number of physical variables that bedform dynamics are controlled by under natural wave–current conditions. Phase diagrams of the principal form presented in Figure 1 do not incorporate the effects of, for example, grain diameter, water depth, wave–current angle, wave period, bed clay content, and tide-induced shear-stress variations. Although Dumas et al. (2005) and Perillo et al. (2014) proposed phase diagrams for different wave periods and grain diameters, no diagram covers a full range of controlling parameters yet. Another difference is that the field data were collected in an intertidal environment, where the hydrodynamic forcing changed on the scale of tens of minutes, whereas the laboratory-based phase diagrams used constant wave and current forcing, thus essentially simulating subtidal conditions in which bedforms are more likely to be in equilibrium with the hydrodynamic forcing and water depth plays a smaller role than in intertidal environments. For example, storm waves were found to have only a small effect on bedform dynamics during shallow water at the field site.

Despite these complications, some of the bedforms found at the field site can be matched to those recognised in experimental flumes. The linguoid current ripples and wave ripples in Figure 10 correspond to the 3D current ripples and 2D/3D symmetric ripples of Perillo et al. (2014), respectively. These bedforms also appear in the phase diagrams of Arnott and Southard (1990), Yokokawa et al. (1995), and Dumas et al. (2005), but a comparison of forcing parameters is hampered by the small current velocities simulated in these experiments. The stability regime of the tile-shaped interference ripples overlaps with the 3D quasi-asymmetrical and asymmetrical ripples of Perillo et al. (2014), although the plan morphology of the tile-shaped interference ripples in this study is more regular. This difference might be explained by the fact that the tile-shaped interference ripples were formed at large wave–current angles and Perillo et al. (2014)’s 3D quasi-asymmetric and asymmetric ripples were associated with co-linear waves and currents. Subaqueous dunes were not found at the field site. Instead, the stability fields of 3D symmetric and asymmetric dunes and current dunes of Perillo et al. (2014) are occupied by washed-out ripples, lunate interference ripples, and upper-stage plane beds in Figure 10. This may be a key characteristic of intertidal environments, where water depths are generally shallow and rapidly changing, thus hindering the development of dunes, which need greater water depths and more time to form than ripple-sized bedforms. Dunes were seen on intertidal flats adjacent to the field site, but these dunes were poorly defined, with large form indices—the ratio between length and height. The 3D-ARP data did not show any hummocks, which have been considered to form in combined flow (Duke, 1985; Arnott and Southard, 1990; Dumas et al., 2005; Dumas and Arnott, 2006; Tinterri, 2011). The washed-out ripples at the field site are probably nearest to small-scale hummocks (Tinterri, 2011), because these share a similar size and large form index, but their shape is closer to flattened current ripples and lunate interferences ripples. The lack of conventional hummocks at the field site agrees with the facts that: 1) hummocks have not been described in estuarine sedimentary sequences (Tinterri, 2011, his Table 2); 2) hummocky cross-stratification serves “as a useful indicator of deposition in unrestricted, open-water conditions” (Dumas et al., 2005) instead of semi-enclosed esturaries, and; 3) hummocks form by wave-dominated combined flows with wave periods of 8–10 s (Dumas et al., 2005), whereas the measured wave periods at the field site were c. 6–8 s for the lunate interference ripples, washed-out ripples, and upper-stage plane beds and c. 3–6 s for the wave ripples. Hence, a dominance of ladderback ripples and tile-shaped and lunate interference ripples over hummocks and dunes might be diagnostic in sedimentary successions of estuarine mixed sand–mud tidal flats.

The time-series in Figures 3A–F reveal that equilibrium current ripples dominated the flood and ebb during spring tides; these bedforms were relict for a short period around high slack water. Some of the highest-energy ebb currents during the spring tide, at current stresses of 0.6 Nm⁻² – 0.7 Nm⁻² (inundations 10 and 11), were able to form washed-out ripples from these equilibrium current ripples. The flood currents during spring tide did not form washed-out ripples within the measurement period, even though the shear stress was occasionally as large as in the ebb currents (e.g., tidal inundation 11). The relict current ripples became progressively less frequent in the runup to spring tide and more frequent during the transition from spring to neap tide. Around neap tide, the current ripples stopped moving altogether and near-identical bed morphologies could be traced across areal exposure in tidal inundations 22–25 (Figures 8E,F).

Water surface waves modified or replaced the current-generated bedforms during nine tidal inundations. The wave stresses were largest just before and at high slack water, suggesting that during ebb and most of the flood, when water depths were up to 3 m lower than during high slack water, waves largely dissipated before reaching the study site. This resulted in 23% of the bedforms showing wave-dominance or combined-flow properties (Figure 3G). The storm waves between May 22nd and 24th (inundations 3–6) had the largest influence on the bed morphology. The relict wave ripples at the start of inundation 2 evolved into equilibrium wave ripples when the waves were strong enough to move sediment around high slack water. Combined flow was dominant at the peak of storm intensity, resulting in the development of tile-shaped interference ripples and ladderback ripples at relatively weak current stresses, and lunate interference ripples, washed-out ripples and upper-stage plane beds at relatively large current stresses. The bedform evolution closely followed temporal changes in wave stress, best exemplified in inundations 4 and 6. In inundation 4, non-equilibrium current ripples existed when waves were absent. These current ripples then rapidly evolved into lunate interference ripples as the wave stress quickly increased, followed by tile-shaped interference ripples, ladderback ripples and wave ripples during decreasing current and wave stresses, and ending with non-equilibrium current ripples in the wave-free ebb current. Inundation 6 also started and ended with non-equilibrium current ripples. In between these, washed-out ripples followed by upper-stage plane beds formed around peak wave stress. Eventually, wave ripples and then current ripples formed during decreasing wave stress and small current stresses. The wave stress during tidal inundation 7 was just large enough to form wave ripples from relict current ripples during high slack water. These wave ripples became relict and then evolved into current ripples during the ebb. In inundation 17, ladderback ripples formed as an intermediate stage between the wave ripples and the current ripples. Finally, relatively weak waves affected the bed during the spring tide of inundation 12, forming a temporal sequence of tile-shaped interference ripples to ladderback ripples over high slack water and the ensuing ebb tide.

In summary, the field data show that strong waves lead to the formation of predominately lunate interference ripples, washed-out ripples and upper-stage plane beds, whereas weaker waves generate merely tile-shaped interference and ladderback ripples. Spring tides promote the development of upper-stage plane beds. In this dynamic environment, only 50% of the bedforms were found to be in equilibrium with the flow conditions (Figure 3H).

Figures 3D,E show that the bedforms found in the study area are remarkably similar in height and length, even though the sediment bed was exposed to substantial variations in current stresses during the neap–spring cycle and to several periods of large wave and combined stresses. Except for the upper-stage plane beds, bedform height and length ranged from 11 to 17 mm (average: 14 ± 2 mm) and from 122 to 192 mm (average: 149 ± 23 mm), respectively. However, within this small range of bedform dimensions, which will be covered in more detail in the following sections, distinct differences in the asymmetry index and form index were distinguished, when grouped based on bedform type (Figure 11).

Although fully symmetric ripples, i.e., with an asymmetry index of 0.5, did not form, the wave ripples were more symmetric than the current ripples and the interference ripples, with the lunate interference ripples, tile-shaped interference ripples, and washed-out ripples showing the highest asymmetry (Figure 11). Based on their phase space positions in Figure 10, a set of wave-dominated bedforms can be grouped together, including the transitional current–to–wave, lunate interference, transitional lunate–to–wave, and wave ripples. The ladderback and tile-shaped interference ripples are wave-influenced, but these bedforms are grouped with the remaining current-dominated ripples, because the near orthogonal waves and currents resulted in two distinct sets of bedforms where those associated with the waves were subordinate. Except for the transitional current–to–wave and lunate interference ripples, the asymmetry index for the wave-dominated bedforms was below 0.61, the significance of which will be explained in the next section, and this provides a way of distinguishing wave- and current-dominated bedforms. The wave ripples had the lowest form index of all the bedform types encountered at the study site, and indeed a form index of below 10 distinguishes all but the lunate interference ripples in the wave-dominated set. The tile-shaped interference ripples had relatively high asymmetry and form indices whereas the ladderback ripples had indices much more in keeping with current ripples. Although being considerably smaller, the subordinate bedforms in the trough of the ladderback ripples had similar form and asymmetry indices to the main bedforms. As expected, the washed-out ripples had the highest form and asymmetry indices (Baas and De Koning, 1995; Figure 11). The size and shape of the transitional lunate–to–wave and current–to–wave ripples were in between their end members. For the transitional current–to–wave ripples, the form index already represented that of the wave ripples, but the asymmetry was still closer to that of the current ripples (Figure 11).

The bedforms that were affected by waves in the field area include equilibrium and relict wave ripples, ladderback ripples, tile-shaped and lunate interference ripples, and transitional current–to–wave and lunate–to–wave ripples. The widely used wave bedform size predictor of Wiberg and Harris (1994) is chosen to verify if it is sufficiently accurate to generalise the relationships between wave-generated and combined-flow bedform size, and flow and sediment parameters found in this study. The non-iterative version of Wiberg and Harris’ (1994) predictor (Malarkey and Davies, 2003; Appendix Equation A2) depends only on the ratio of the wave orbital diameter, d ₀, (= TU ₀/π, where T is the wave period and U ₀ is the wave velocity amplitude; Lichtman et al., 2018) and the median grain diameter, D ₅₀. The predictor distinguishes between orbital ripples (d ₀/D ₅₀ < 1754), where the bedform dimensions depend on the orbital diameter, anorbital ripples (d ₀/D ₅₀ > 5,587), where the bedform dimensions depend on the grain diameter, and suborbital ripples (1754 < d ₀/D ₅₀ < 5,587) where the bedform dimensions depend on both the orbital and grain diameters. Soulsby and Whitehouse (2005) produced a similar wave ripple predictor, whereas some researchers have done away with the intermediate suborbital range (e.g., Traykovski, 2007). The presence of a small current is accounted for with an enhanced orbital diameter, d _wc , following the approach of Lacy et al. (2007):

Eq. 6, Enhanced orbital diameter: d w c = d 0 2 + 0.25 ( T u δ ) 2 + d 0 T u δ ⁡ cos ⁡ φ (6) where u _δ = 0.65ū is the current velocity at c. 20 mm above the bed in terms of ū, the depth-averaged current velocity. In the absence of a current, ū = 0, the enhanced orbital diameter returns to its wave-only value, d _wc = d ₀. As in the wave-only case, Eq. 6 determines the distance a particle is advected in half a wave cycle. This definition is only meaningful if the magnitude of the freestream velocity has two minima in the wave cycle, corresponding to (u _δ/U ₀)cosφ < 1. Therefore, Eq. 6 was applied only when this condition was met. The comparison for the measured bedform heights and lengths is shown in Figures 12A,B.

The subordinate bedforms in the ladderback and tile-shaped interference ripples are of interest here, since the crest of these bedforms tend to be oriented perpendicular to the wave propagation direction. It is therefore anticipated that these subordinate bedforms are dependent on the wave-only orbital diameter d ₀, rather than d _wc . The subordinate dimensions of the ladderback and tile-shaped interference ripples tend to be lower than the dimensions of the wave ripples. Their lengths are in the orbital range, but their heights are lower than expected for orbital ripples (Figures 12A,B). This may be because the subordinate bedforms are topographically constrained by their superimposition on the main bedforms in the ladderback and tile-shaped interference ripples.

Figure 12A shows that the relict wave ripples fall to the left of the grey shading associated with the original experimental scatter of Wiberg and Harris’ (1994) predictor, because the orbital diameters of the waves were too weak to influence the bedforms. Moreover, most equilibrium wave ripples and transitional current–to–wave ripples fall within the original laboratory and field data scatter and have lengths that are close to Wiberg and Harris’ (1994) anorbital value of 535D ₅₀. Most of these ripple types can be considered as suborbital, but their dimensions correspond to anorbital ripples. This agrees with a laboratory study by Lacy et al. (2007), who found that wave-dominated ripples in combined wave–current flow fall in a similar suborbital region of the Wiberg and Harris (1994) plot. Anorbital ripples are analogous to current ripples in that their size depends only on the grain diameter. This may explain why there were only modest changes in the ripple dimensions during the field campaign when evolving from wave-dominated to current-dominated conditions. Indeed, since several wave ripples developed from current ripples at the beginning of the flood and weak currents commonly accompanied the wave ripples (Figures 3A–C), we infer that these currents may have forced the wave ripples towards becoming anorbital.

Because of their formation under wave-dominated conditions (Figure 10), it is reasonable to test the lunate interference ripples against the Wiberg and Harris (1994) predictor. These bedforms tend towards the anorbital range, but their length is larger than the predicted value for anorbital bedforms. Various researchers have found that the dimensions of anorbital ripples can have wave-period dependence (Mogridge et al., 1994; O’Donoghue et al., 2006), which is reflected in the scatter in the original Wiberg and Harris (1994) data in Figure 12A. This wave-period dependence may thus also apply to the lunate interference ripples.

For practical purposes, the length of the equilibrium and relict wave ripples and the transitional current–to–wave ripples can be considered constant, hence independent of the orbital diameter, at Wiberg and Harris’ (1994) anorbital value of 535D ₅₀. However, the length of the lunate interference ripples, which is distinct from the wave ripples, is better described by 806D ₅₀. Hence, L = 535D ₅₀, for d _wc /D ₅₀ < 5,320 and L = 806D ₅₀, for d _wc /D ₅₀ ≥ 5,320 (Figure 12A). Assuming that the bedform height can also be represented by a constant value, the mean of all the heights, other than for the lunate interference ripples, gives H = 68D ₅₀ (Figure 12B). Since the lunate interference ripples represent wave-dominated bedforms with the highest combined stress before upper-stage plane beds develop and are well described by Wiberg and Harris’ (1994) predicted heights for anorbital ripples, a better predictor in this case would be H = 68D ₅₀ for d _wc /D ₅₀ < 5,320 and H = H _WH , for d _wc /D ₅₀ ≥ 5,320, where H _WH is the height from the Wiberg and Harris (1994) predictor. This yields a representative form index of c. 7.7 for the wave ripples and transitional current–to–wave ripples and 12.5 for the lunate interference ripples. These predicted form indices are close to those shown in Figure 11B.

Since it is anticipated that wave ripples are more symmetric than current ripples and perhaps combined-flow bedforms, it is worth comparing the asymmetry indices of the wave ripples, lunate interference ripples and transitional current–to–wave ripples with the asymmetry indices found in literature. Sato and Horikawa (1986) determined that the asymmetry of wave ripples formed in the laboratory has an upper limit of 0.61, based on the steepest part of the upstream slope reaching the angle of repose. The ripple asymmetry increased up to this limit with increasing wave asymmetry (skewness), as determined by U _max/U ₀, where U _max is the maximum near-bed velocity in the wave cycle, U _max/U ₀ is calculated by Stokes 2^nd order (U _max/U ₀ = 1+3kH/8sinh³ kh, where H and k are the surface wave height and number and h is the water depth, Soulsby, 1997), and U _max/U ₀ = 1 corresponds to a symmetric wave. Sato and Horikawa’s (1986) prediction is shown in Figure 12C together with all the bedforms shown in Figures 12A,B. The accompanying Figure 12D shows τ _c /τ _w versus U _max/U ₀. Figure 12C reveals that the asymmetry is generally in the correct range for the wave ripples and the transitional lunate–to–wave ripples, even though Sato and Horikawa’s (1986) expression tends to underpredict the ripple asymmetry as a function of wave asymmetry. Figure 12D shows that there is an inverse relationship between the relative current stress and the wave asymmetry, and Figure 12C shows that the weaker the wave asymmetry is the more substantial the ripple asymmetry underprediction, thus strongly suggesting that the presence of the current causes additional ripple asymmetry. This is valid in particular for the transitional current–to–wave ripples, which have ripple asymmetries that are completely independent of wave asymmetry and generally greater than 0.61. The lunate interference ripples, although fitting the general predicted trend in wave asymmetry (Figures 12C,D), show a slightly larger asymmetry (Figure 11A), possibly because their larger form index (Figure 11B) means they are not constrained by Sato and Horikawa’s (1986) angle-of-repose limit.

Most of the bedforms in the field area were either wholly or partially influenced by currents. These include the equilibrium, non-equilibrium, and relict current ripples; the dominant bedforms in the ladderback ripples and tile-shaped interference ripples; washed-out ripples; and upper-stage plane beds. These bedforms can be used to test the accuracy of the Soulsby and Whitehouse (2005) equilibrium current ripple predictor (Appendix Equation A3) and possibly extend its use to combined wave–current flows under natural conditions. Appendix Equation A3 has a grain size dependence but also predicts a linear decrease in ripple height with increasing stress for washed-out ripples, with the height becoming zero for sheet flows on upper-stage plane beds. Because waves and currents were both present at the field site, it is the maximum shear stress, τ_max, rather than the current stress, that controls the ripple height. Also, we optimised the Soulsby and Whitehouse (2005) descriptor for this dataset by forcing H _max = 67D ₅₀ and L = 655D ₅₀, based on the mean height and length of the equilibrium current ripples, and τ _wo = 0.65 Nm⁻² and τ _sf = 0.78 Nm⁻², based on the lower and upper boundaries of washed-out ripples in Figure 10A (according to Appendix Equation A3, H _max = 84D ₅₀ and L = 674D ₅₀, τ _wo = 0.76 Nm⁻² and τ _sf = 1.08 Nm⁻²).

The heights and lengths of all the current-dominated ripples are plotted against τ _max in Figures 13A,B, respectively. These figures also show the predicted values according to Soulsby and Whitehouse (2005). The range in the dimensions of the current ripples appears to increase, as the maximum stress increases, with the largest mean heights and lengths at τ _max > 0.5 Nm⁻². This increase in current ripple size agrees with the presence of relatively large ripples at high shear stresses in laboratory experiments with 0.238 mm sand, interpreted as bedforms transitional to subaqueous dunes (Baas, 1999).

The dominant bedforms in the ladderback and tile-shaped interference ripples are also well described by the Soulsby and Whitehouse (2005) predictor. However, the non-equilibrium current ripples have lower heights and lengths, and some relict current ripples have lower heights (c. 10 mm instead of 15 mm), but not lower lengths, than predicted. The non-equilibrium current ripples were clearly not fully developed, and therefore plot below the equilibrium heights and lengths predicted by Soulsby and Whitehouse (2005) in Figures 13A,B. Moreover, these non-equilibrium ripples were most common during ebb, near the end or directly after periods of declining wave stress. The low-amplitude relict current ripples were present during neap tides with increased bed clay and EPS content (inundations 16–24). The greater reduction in height than in length of these relict ripples is consistent with increased bed clay and EPS content in the experiments of Baas et al. (2013) and Malarkey et al. (2015), respectively. The gradual reduction in ripple height during inundations 15, 16, and 17 is inferred to relate to the increase in bed clay and EPS content measured by Lichtman et al. (2018, their Figure 4) by drawing cohesive clay into the bed through hyporheic processes (Dallmann et al., 2020; Wu et al., 2021).

The large variety of sedimentary bedforms in the study area underlines the complex interactions between hydrodynamics and sediment dynamics on intertidal flats (e.g., Deloffre et al., 2007; Gao, 2009). However, this large variety does not necessarily mean that each bedform type has a preservation potential in sedimentary successions of intertidal flats that matches its frequency of occurrence on modern intertidal flats. The present study shows that bedform type is often related in a predictable way to tidal phase and bed shear stress, the presence or absence of waves, and large (near orthogonal) or small (near co-linear) wave–current angles (Table 1). Since previous studies have shown at which conditions intertidal sediment is most likely to be preserved (e.g., Deloffre et al., 2007; Gao, 2009), it should also be possible to predict which intertidal bedform types have the highest preservation potential in the sedimentary record.

Using a combination of numerical modelling and field validation, Gao (2009) found that supratidal, high intertidal, and subtidal environments have a higher preservation potential than low intertidal environments, such as the study area. This reflects the notion that salt marshes and tidal channels usually have more space to accommodate net sediment accumulation than intertidal flats. Intertidal flat sediment can be preserved when the rate of bed aggradation is higher than the rate of bed erosion, but such aggradation rates are often too low to preserve entire bedforms, as exemplified by a comparative study of three estuaries by Deloffre et al. (2007). Even in the highly dynamic Seine estuary, NW France, the aggradation rates did not exceed 6 mm per semi-diurnal tidal cycle (Deloffre et al., 2007). Specific conditions are therefore required to preserve diagnostic sets of cross-stratification or entire bedform profiles in vertical cross-section. These include: 1) rapid aggradation after a sudden large influx of sediment by decelerating current-dominated or combined flow; 2) deposition of a protective layer of cohesive, ‘sticky’ clay during high slack water; 3) formation of a biofilm, i.e. a protective surface layer of extracellular polymeric substances (EPS) produced by benthic micro-organisms, during low slack water (Hope et al., 2020); and 4) a prolonged period of small stress and absence of strong bed erosion after these events, most likely around neap tide after the largest spring tides (Deloffre et al., 2007), and in the absence of strong waves over periods of at least weeks to months. Examples of large influxes of sediment are river floods, strong flood tides combined with strong onshore wind, and upstream breaching of, for example, the cut bank of a meandering tidal channel (e.g., Van den Berg et al., 2002). The formation of a protective layer of cohesive clay is most effective during long high slack water periods, i.e. at spring tide, in the estuarine turbidity maximum and in estuaries with strong ebb–flood asymmetry (Deloffre et al., 2007; Friedrichs, 2011; Kirwan and Guntenspergen, 2012; Lichtman et al., 2018). Protection from erosion by biofilm growth is most common during spring and summer, when storm events are less frequent along most coastlines, and during neap tides, when the period of bed strengthening by drying owing to atmospheric exposure is longest (Amos et al., 1988; Lichtman et al., 2018).

Although the sediment bed in the Dee estuary was not exposed to significant periods of deposition or erosion during the field study, the above-mentioned conditions for bedform preservation can be used to predict the preservation potential of the various types of bedform in the sedimentary record (Figure 3). In the absence of wave stresses, the tidal stresses almost exclusively formed current ripples. Upper-stage plane beds and washed-out ripples were found only for maximum ebb stresses during spring tides, although their generation during flood tides at depths below the minimum measurement depth of the instruments on the SEDbed frame cannot be ruled out. The upper-stage plane beds and the washed-out ripples have a low preservation potential, because these bedforms transform rapidly into current ripples, as the flow decelerates to slack water. Their preservation is probably limited to periods of rapid bed aggradation, thus forming sequences of plane-parallel lamination or climbing washed-out ripples. Migrating equilibrium current ripples were most common during flood and ebb in between neap and spring, whereas relict equilibrium current ripples were characteristic of high, and possibly also low, slack water periods and neap tides in the study area. In the absence of waves, these equilibrium ripples have a high preservation potential, not only because of their abundance, but also because these bedforms are stationary under the small current stresses around neap and become covered by increasing amounts of cohesive clay and EPS in the transition from spring to neap (Lichtman et al., 2018). The preservation potential of current ripples is expected to be even higher under weaker hydrodynamic forcing than at the study site, e.g. towards salt marshes or in estuaries with a lower tidal range, where the stresses are weaker and bed strengthening by cohesive clay and EPS is enhanced. However, such conditions are more likely to lead to the preservation of non-equilibrium than equilibrium current ripples, because the bedform development rate decreases exponentially with decreasing current stress (Baas, 1993, 1999). Even though upper-stage plane beds and washed-out ripples will be more common under stronger hydrodynamic forcing than at the study site, e.g. towards tidal channels, where tidal stresses are larger and cohesive clay and EPS are less abundant, the sediment bed is still subjected to rapid current ripple development when entering the current ripple stability regime during flow deceleration. An exception is fast runoff on steep local slopes during late ebb by sheet flow, which is prone to preserving upper stage plane beds (e.g., Collinson and Mountney, 2019). Hence, equilibrium current ripples are expected to remain the dominant bedform type in sedimentary successions of such dynamic intertidal environments, provided that τ_w << τ_c.

Weak waves (τ _w < τ ₀) had little effect on the bedforms in the study area, even for large combined stresses. Moderate waves (τ _w > τ ₀), such as in inundations 2, 7, 12, and 17, were able to modify the currents and thus change the bedform type. During neap tides, equilibrium wave ripples formed around high slack water and these bedforms became relict during the flood and ebb. This suggests that wave ripples can replace current ripples and persist as relict bedforms on the bed during neap tides, when currents are not strong enough to move bed sediment, as exemplified by tidal inundation 1. However, moderate waves are unlikely to be accompanied by a large influx of sediment during neap when τ _c < τ ₀. Hence, the high aggradation rates required to preserve wave ripples in this way are inferred to be rare. This leaves the potential to preserve wave ripples by the bed strengthening effect of clay and EPS, as discussed above. The clay would be preserved as a drape over the wave ripples in the sedimentary record.

During spring tides and the transitions between spring and neap, moderate waves modified the flow field to form tile-shaped interference ripples, wave ripples, and ladderback ripples at the study site. The ladderback ripples evolved rapidly from wave ripples or tile-shaped interference ripples around high slack water and then into current ripples in late ebb (e.g., tidal inundations 12 and 17). Because of these rapid changes in bed morphology, we anticipate the tile-shaped interference ripples, wave ripples, and ladderback ripples to be preserved only in exceptional circumstances, also because the formation of the tile-shaped interference ripples and ladderback ripples requires large wave–current angles, and the moderate waves prevent the tide from reaching zero stress at high slack water (e.g., tidal inundation 12 in Figures 3A,B) needed for bed strengthening by clay deposition. This leaves rapid sediment delivery and bed aggradation—here, during a period of up to 3 h (tidal inundation 12; Figure 3C)—combined with rapid waning of the waves, as the only scenario at which the tile-shaped interference ripples and ladderback ripples might be preserved. This rapid aggradation without clay deposition would be reflected in the sedimentary record as co-sets of climbing bedforms, but the lack of descriptions of such co-sets in the geological literature might be indicative of their scarcity. Instead of exhibiting a clay drape, the tops of these rare co-sets may be reworked into current ripples and cross-lamination, since τ _w < τ ₀ in the late ebb, presumably because the moderate waves are dissipated before reaching the study site. In fact, these non-equilibrium and equilibrium current ripples have a higher preservation potential than the tile-shaped interference ripples, wave ripples, and ladderback ripples, because they may be stabilised by EPS and clay around low slack water (Lichtman et al., 2018; Hope et al., 2020). In contrast, the equilibrium current ripples formed in the early flood (Figures 3A–C) have a low preservation potential, because these bedforms are rapidly replaced by wave ripples or tile-shaped interference ripples during late flood.

Although it is reasonable to assume that the preservation potential of wave ripples and combined-flow ripples increases as moderate waves recur more often, it is more difficult to predict their preservation potential under conditions of weaker and stronger current stresses than at the study site. Smaller current stresses during neap may lead to an increased preservation potential of wave ripples (cf., inundation 2; Figures 3A–C). Larger current stresses during neap may cause tile-shaped interference ripples and ladderback ripples to become more common, with their preservation potential requiring the same specific conditions as those mentioned above. Smaller current stresses during spring may induce a shift in preservation from tile-shaped interference ripples and ladderback ripples to wave ripples (cf., inundation 7; Figures 3A–C), whereas larger current stresses during spring may cause a change to washed-out ripples, upper-stage plane beds, and possibly lunate interference ripples. However, it should be mentioned that the present dataset lacks a clear picture of stable bedform types at moderate wave stresses and large current stresses (Figure 10A).

During the transition from neap to spring in tidal inundations 3–6, storm waves (τ _w >> τ ₀), with wave stresses up to 0.84 N m⁻², formed upper-stage plane beds, washed-out ripples, lunate interference ripples, tile-shaped interference ripples, and ladderback ripples under the rapidly changing contributions of waves and currents to the combined stresses. For reasons similar to those discussed for moderate waves above, we anticipate these bedforms to be preserved only in exceptional circumstances, limiting the preservation to sets of plane-parallel lamination and co-sets of climbing current ripples without clay drapes, but possibly with the tops reworked into non-climbing current ripples during the late ebb. Again, these current ripples have a higher preservation potential than the storm-wave induced bedforms, because the current ripples may be stabilised by EPS and clay around low slack water (Hope et al., 2020), if the storm wanes rapidly. The relatively high preservation potential of these late-ebb current ripples is remarkable because it may conceal evidence of waves, including storm waves, in the sedimentary record.

No recordings of storm waves during neap, spring, and the transition from spring to neap are available from the study site. Predicting bedform types and their preservation potential is therefore more challenging. Storm waves affecting the bed during neap are hypothesised to induce a dominance of wave ripples and wave-induced upper-stage plane beds around high slack water. The upper-stage plane beds are unlikely to be preserved because they change into wave ripples as water levels drop during the ebb, and rapid bed aggradation and clay drape formation are unlikely to take place during large wave stresses combined with small current stresses. The wave ripples may be larger than those formed by moderate waves during neap, discussed earlier, but their preservation potential is similar. Storm waves occurring during spring (τ _max >> τ ₀) are expected to promote the formation of bedforms typical of large combined stresses, i.e., upper-stage plane beds, washed-out ripples and lunate interference ripples (Figure 10A). Upper-stage plane beds and washed-out ripples may also dominate shallow-water flood and ebb tides, when the wave stresses are small and the current stresses are in or just below the sheet flow regime. The preservation potential of these bedforms is probably similar to that of the bedforms formed by storm waves during the transition from neap to spring and by tidal currents in the absence of waves during spring at the field site, as discussed earlier. However, the highly dynamic conditions induced by storm waves during spring tides may cause bed scouring that removes bedforms preserved in earlier tidal inundations. Finally, it seems reasonable to assume that bedforms forming in the transition from spring to neap are similar to those forming in the transition from neap to spring. However, their preservation potential may be somewhat higher because current stresses progressively decrease from spring to neap, thus the potential for bed reworking also decreases.

Figure 14 summarises the preservation potential of bedforms on intertidal flats using a relative scale, as quantification of the preservation potential is not possible yet. The schematic drawings of sedimentary deposits in Figure 14 are based on the most likely scenarios at which each bedform type can be preserved. Current ripples generated under wave-free conditions have the highest preservation potential, as individual ripple trains or climbing ripple co-sets covered by clay drapes and further stabilised by EPS. Wave ripples formed by moderate or strong oscillatory flow combined with relatively weak currents, for example during neap, have a moderate preservation potential, as individual wave ripple trains stabilised by clay and EPS, but not as climbing ripple co-sets. These deposits comprised of current ripples or wave ripples resemble flaser and lenticular bedding (Reineck and Singh, 1980). In contrast, combined-flow ripples, upper-stage plane beds, and washed-out ripples have a low to very low preservation potential, limited to conditions of rapid aggradation. These bedforms are unlikely to form part of flaser and lenticular bedding, but the plane-parallel laminated sets and climbing-ripple co-sets they generate may be covered by current ripples and their cross-lamination that form during ebb and around low slack water. So even under storm conditions, current ripples are more likely to be preserved than upper-stage plane beds, wave ripples and combined-flow ripples. Figure 14 is primarily based on the synthesis of the data collected in the Dee Estuary, so further work is needed to test the concepts presented. This should include combined hydrodynamic and sediment dynamic data acquisition on microtidal, mesotidal, and other macrotidal sand and mixed sand–mud flats in different wave climates, as well as targeted studies of bedforms and primary current lamination in sedimentary successions of intertidal flats.