Dune convergence/divergence controlled by residual current vortices in the Jade tidal channel, south-eastern North Sea

A field of large to very large subaqueous dunes was investigated in the Jade tidal channel, south-eastern North Sea, between January 2006 and October 2011. A ground-truthed sidescan sonar sediment map shows that the dunes, which are located on top of a consolidated clay surface, are composed of medium to coarse sand. A series of 35 consecutive high-resolution bathymetric surfaces collected by multibeam echosounder revealed a complex migration pattern induced by the reversing tidal currents. Various parts of the dune field are under the influence of either ebb- or flood-dominated currents, as indicated by dune asymmetries. Although some dunes migrate at a pace exceeding 100 m/year, the majority are displaced by 30 m/year in the direction of the locally dominant current. In the deepest part of the channel, however, dunes were observed to converge head-on, resulting in practically zero net transport with minor oscillations of symmetrical dunes at the apex. Applying the numerical UnTRIM model for the simulation of the fair-weather hydrology, a simplified map of residual current vectors over the dune field was generated. The residual flow vectors are found to perfectly match the derived dune migration vectors, suggesting that dune convergence is controlled by two counter-rotating residual current vortices caused by the local shape of the tidal channel. As no sediment build-up is observed, a mechanism of sediment bypassing with potential recirculation must exist, but has not yet been identified.


Introduction
Subaqueous dunes, called also marine sand waves, are one of the most fascinating sediment ary features on continental shelves. They are defined as flow-transverse bedforms with wavelengths exceeding 0.6 m and heights greater than 0.075 m (Ashley1990 ). It is well documented that dune morphologies tend to adjust to changing hydrological conditions until a dynamic equilibrium is reached. Their shapes and dimensions reflect the interaction between critical current velocities, water depth, grain size and sediment availability, the relationships between these parameters ap-plying equally to unidirectional currents (rivers, geostrophic flows) and reversing tidal currents (e.g. Flemming 1988Flemming , 2000Mazumder 2003;Bartholomäetal. 2008;Carle and Hill 2009;Van Landeghem et al. 2012 ). In general the dune asymmetry indi-cates the direction of the prevailing current, but antiasymmetry migration has been also reported (Hanes 2012 ). In the case of periodically reversing flows, the symmetry/ asymmetry of the dunes is, in addition, controlled by the ratio between the local flood and ebb flow velocities which, in simplified form, is also expressed in the residual tidal flow pattern. Moreover, local seabed topography can greatly influence the flow pattern, especially in meandering channels (Hughes 2012).
The combination of complex topography, water level changes and reversing currents produces dune fields which are commonly separated into flood-and ebb-dominated regions (e.g. Belderson et al. 1978 ;Harris 1988 ;Harris et al. 1995 ;Gonzales and Eberli 1997 ;Fenies and Faugères 1998 ;Kubicki, Kösters, Bartholomä: Dune convergence/divergence controlled by residual current vortices in the Jade tidal channel, south-eastern North Sea.
S. 48 Geo-Marine Letters; Vol. 37; Heft 1; Seite 47-58 Bates and Oakley 2004;Carle and Hill 2009;Kubicki and Bartholomä 2011;Van Landeghem et al. 2012). The line separating the ebb-and flood-dominated parts is called the zone of zero net transport, also known as a bedload convergence zone. This line is mostly sharp and only in rare cases accompanied by symmetrical dune bodies (e.g. Le Bot and Trentesaux 2004;Barnard et al. 2006;Gómez et al. 2010;Fraccascia et al. 2016), let alone head-on dune convergence (e.g. Van Landeghem et al. 2012). The flow conditions triggering the head-on convergence has to date not been fully explained, potential control by local residual current vectors having been hypothesized but not verified in the field (Idier et al. 2011).
In the course of the present study, physically converging dunes discovered in the Jade tidal channel (Kubicki and Bartholomä 2011), south-eastern North Sea, presented an ideal opportunity to further investigate the underlying mechanisms of bedload convergence/divergence. The dune field was monitored for 6 years (January 2006-October 2011) by repetitive multibeam echosounding accompanied by sidescan sonar mapping calibrated by grab samples in the closing 12 months. In order to understand the characteristic distribution of residual current vectors, a numerical model was applied to simulate the local hydrology-a method already utilised in the 1970s (e.g. Tee 1976). Numerical modelling of local hydrology allows a physically consistent but spatially larger, synoptic view of residual current vectors than can be achieved by in situ measurements (Li et al. 2008). In the past, such modelling was not only limited because of insufficient computing power but often also tended to fail in reproducing true current magnitudes due to insufficient data on seabed topography (Hanes 2009). This situation changed dramatically as computing power increased and bathymetric data acquisition exploded by the development of multibeam echosounders for seabed mapping as well as LiDAR techniques for mapping the topography of intertidal areas. Nonetheless, in spite of the improvement in computing power and numerical models (e.g. Castro Díaz et al. 2008), there exists no universal modelling approach to reproduce accurately the interaction of fluid flow and sediment transport in dynamic shallow-water environments (Van Rijn et al. 2013). Therefore, numerical hydrological modelling often still acts as an aid in morphodynamic studies, rather than being the base of it (e.g. Fraccascia et al. 2016).
Investigations of seabed dynamics therefore still depend on repetitive in situ measurements of local topography. The monitoring period of subaqueous dunes commonly spans periods ranging from a few months (e.g. Whitmeyer and FitzGerald 2008) to at least 15 years (Zorndt et al. 2011). In view of this, the period covered in the present study can be considered as medium-term. The numerical modelling of the local hydrology was applied for a 2-week period to cover a complete spring-neap tidal cycle. The specific aims of the present study were (1) to document, for the first time, dune head-on convergence in a large tidal channel at high temporal and spatial resolution, and (2) to provide a plausible explanation of the mechanism controlling this phenomenon.

Physical setting
The Jade is a 50-km long, slightly meandering tidal channel located in the south-eastern German Bight. It is a natural waterway to the harbours of Wilhelmshaven, which include the largest German naval base and the easternmost deep-water container terminal in the North Sea, the Jade Weser Port. Due to its economic and military importance, the Jade fairway is monitored at monthly intervals by the German authorities to ensure the required water depth of 17.6 m below SKNLAT (marine chart datum corresponding to the lowest astronomical tide; Götschenberg and Kahlfeld 2008 ). The time span between the surveys is never longer than 1 month. To maintain the design depth, the fairway is regularly dredged, the dredge spoil being subsequently deposed at designated dump sites near the mouth of the Jade in proximity to the study site. The semi-diurnal tides ranging from 2.8 m in the north to 3.8 m in the south (Götschenberg and Kahlfeld 2008 )trigger maximum tidal current velocities exceeding 1.5 m/s (Grabemann et al. 2004 ). The tidal wave is uniformly distributed across the channel width, and no obvious stream core exists during either flood or ebb tide (Kahlfeld and Schüttrumpf 2006).
The area of interest covers ca. 14 km 2 and is situated in the northern part of the Jade between the islands of Minsener Oog and Oldoog in the west and the lighthouse Mellumplate in the east (Fig. 1). It covers a channel width of ca. 3.2 km and includes both channel flanks up to a water depth of 5 m below SKNLAT . The eastern flank in the vicinity of the lighthouse is used as a dump site for the dredge spoil from the navigation channel. Over 11 million m 3 of sediment were disposed of here between 1994and 2001(BfG/WSA 2003. No official reports on dumping volumes are available after this period, although the site continued to be utilised. Kubicki and Bartholomä (2011) calculated that there has been a surplus of ca. 0.13 m/m 2 of sediment in the deepest investigated section of the channel of the Jade fairway between 2005 and 2010. If the value holds true for the entire area of interest, a further 1.8 million m 3 could have been dumped in this period.  Table 1). The survey area was expanded compared to earlier studies in this region (Kubicki and Bartholomä 2011) in order to also investigate the eastern flank of the Jade tidal channel and the vicinity of the Mellum lighthouse up to a water depth of 5 m, which is the vessel's safe under-keel clearance. The Reson SeaBat 8125 multibeam echosounder operating at 455 kHz was interfaced with a Magellan Aquarius 5002 Long Range Kinematic Global Navigation Satellite System. This configuration achieves vertical and lateral accuracies of better than 0.05 m (Ernstsen et al. 2006). The echosounder has a fixed recording swath width of about three times the water depth, which is considerably smaller than that recorded by sidescan sonar.

Materials and methods
The Benthos SIS-1624 sonar, a dual-frequency system scanning at 123 and 382 kHz with along-and across-track resolution of better than 0.1 m, was set to record a 200-m wide swath. Full spatial coverage of the area was therefore achieved only by the sidescan sonar, whereas the bathymetric swaths were separated by regular gaps. This was visible especially in the shallow water, where many more multibeam tracks were needed to achieve full data coverage, but were not measured due to the limited timeframe of the campaigns. After each measuring campaign, the bathymetry and backscatter datasets were spatially matched in ArcGIS in order to manually delineate the crests of dunes higher than 1m, which are here referred to as large dunes sensu Ashley (1990). This dune height limit was arbitrarily chosen to ensure identification of individual dune crests even after time intervals of 6 months. Smaller dunes migrate faster and individual crests can therefore no longer be traced at the chosen time interval. The crests of large dunes were also clearly recognisable on sonographs due to morphology-induced contrasts in backscatter records. This allowed delineating crests even where swath bathymetry lacked coverage.
The monthly bathymetric surveys for fairway monitoring performed by the WSAWilhelmshaven were carried out with an Atlas Fansweep 20-200 multibeam echosounder. This system operates with a frequency of 200 kHz and achieves a vertical accuracy of 0.05 m ±0.2 % of the water depth. These surveys were limited to the actual fairway width of ca. 300 m. In order to also monitor the area adjacent to the fairway, the lateral survey width was increased twice a year. After identifying sites requiring dredging, the bathymetric data were converted to a regularly spaced grid of 2 m and archived. For the purpose of the present study, 32 available datasets collected between January 2006 and October 2010 were used (see Fig. 2a, location A). Based on these data, digital terrain models (DTMs) were generated for time intervals spanning periods of 2 weeks to 7 months between individual surveys. After assigning the same colour scale to the bathymetry values, a 32frame movie was generated which highlighted any changes in the lateral positions of the large to very large dunes in the survey area (see Electronic supplementary material available online for this article).
In addition, a sediment distribution map was compiled after calibrating the sidescan backscatter intensities recorded in October 2010 with 118 Shipek grab samples collected between February 2010 and April 2011 (Table 1). Such a calibration was adequate due to a surprising stability of the sediment distribution map observed in consecutive sonographs (Fig. 3). The sediment samples were analysed in the laboratory after standard desalting by dialysis and separating the volume into gravel, sand and mud fractions. Gravel fractions (grain size >2 mm) were sieved mechanically, whereas the sand fractions (grain sizes between 2mm and 63 μm) were analysed by a settling tube (MacroGranometer; Brezina 1979) and the mud fractions (grain sizes <63 μm) by a Sedigraph III (Micromeritics, Inc.). The results were combined into grain-size distribution plots at quarter-phi intervals. Sediment patches identified on sonographs were classified according to the primary composition of the majority of sediment samples collected within given patch areas following the Udden-Wentworth classification scheme (Wentworth 1922).
Water levels and flow velocities of the Jade-Weser estuary were simulated with the UnTRIM modelling system. UnTRIM (Casulli and Zanolli 2005) uses a finite volume-finite difference method which solves the momentum and transport equations on a horizontally unstructured grid. It was set up threedimensionally with a spatial resolution of about 200 m by 300 m over the study area and a vertically constant resolution of 1 m. Thus, individual dunes are not resolved by the model, which instead simulates the overall flow regime of the Jade. Roughness is taken to be mainly due to spatially uniform small-scale ripples. The overall model topography represents the year 2002 based on echosounding and LiDAR data (data provided by the Federal Waterways and Shipping Administration, BAW, and the Federal Maritime and Hydrographic Agency, BSH) but was updated in the study area with more recent measurements from October 2010. Themodel is set up as a process study with application of realistic forcing. Wind stress at the surface was obtained from the operational German National Meteorological Service (DWD) weather forecast model (COSMO/LM, e.g. Doms et al. 2002). At the lateral open sea boundaries, water levels from a BAW measurement campaign in June 2002 were prescribed. The model was run for 4 weeks of fair-weather conditions (only 2 days with winds reaching 7 Bf at the AlteWeser offshore gauge), and the last 2 weeks were used for analysis of a characteristic spring-neap cycle. Salt transport was taken into account by the model but baroclinic flow is of less importance in the Jade due to very low inflow of fresh water (Reineck and Flemming 1990). In the model, river discharge was only considered for the Weser river. Validation of the model was successfully performed on the basis of the original 2002 setup (BAW 2009) and also included sediment transport (Kösters et al. 2014)which, however, was not analysed for this study. For each computational node in the model, the flood and ebb tides were determined and an average flood and ebb tidal current velocity was calculated. In addition, the current velocity for each node was summed over a full tidal cycle and subsequently averaged for the modelled springneap cycle. The resulting vector field describes the Eulerian residual flow field physically consistent over the model domain.

Bathymetry and sediments
The Jade channel topography was investigated at water depths larger than 5 m (SKNLAT). The crosssection of the channel in the study area shows the trough of a channel orientated NNW-SSE with the deepest point located 35 m below SKNLAT (Fig. 2a). The trough is located closer to the western channel flank off Minsener Oog and Oldoog, resulting in a steeper western flank (ca. 1°) in comparison to the eastern flank (ca. 0.5°), which has more the character of a terrace.
Both flanks of the channel are covered by sandy deposits with a broad grain-size spectrum (Fig. 2b).
The shallowest parts of both flanks are composed of fine sand (2-3 phi), in each case coarsening towards the channel thalweg up to grain sizes ranging between mediumsand and gravel. Bedforms were present in each of the sediment types (Fig. 2c). Largest dunes reaching 9.4 m in height and 300 m in length had grain sizes ranging from fine sand to medium gravel. The primary large to very large dunes were covered by secondary dunes of smaller dimensions, which appeared to be less stable over time. Some of the dune bodies were up to several km in lateral extent, connecting both channel flanks with crests aligned normal to the shore.
Sonographs recorded during the three measuring campaigns in October 2010, April 2011 and October 2011 show little changes in the overall sediment pattern (Fig. 3) but the migration of individual dunes reached several tens of metres (Fig. 2d). Sediment classification uncertainties were mostly associated with large volumes of shell hash passing through the area. Shells trapped in dune troughs are recorded as coarse material on acoustic backscatter images. In addition, grab sampling showed that shells seemed to be easily transported up the stoss side of the dunes, thereby Bcorrupting the groundtruthing of the sonographs at large spatial scales (Fig. 4a). Another characteristic feature of the area is the pres-ence of a consolidated bed beneath the dunes, exposed parts having been identified in dune troughs at several locations (shown as dotted line in Fig. 4a). Successfully recovered samples consist of irregularly shaped cracked fragments of consolidated clay with barnacle shells attached (Fig. 4a). This type of channel bed often outcrops between dune bodies and, due to its rough texture, can also easily be mistaken for a gravelly seabed. It was therefore not always easy to unequivocally identify the material constituting different generations of dunes.
In order to resolve this issue, one of the largest dunes was investigated across its entire length with a series of 31 sediment samples recovered in April 2011 (Fig. 5). In general, a high content of medium to coarse sand was recorded. Sediment coarsening towards the crest of the dune and its lee side is visible in the contents of coarse sand, very coarse sand and gravel. There were also several sites along the stoss slope at which the medium sand content was over 10%higher than at neighbouring sites, thereby replacing the content of coarse sand. The successive samples may have been recovered from either crests or troughs of secondary bedforms superimposed on the large dune. The increase in medium sand content may thus be associated with smaller dunes 6-7 mlong and ca. 0.5 m high (Fig. 5c).

Seabed dynamics
In order to identify probable paths of dune migration, dune asymmetries were analysed even though a study by Hanes (2012) shows that results of such an approach are not always straightforward. Based on the lee-side exposition, flood-and ebb-dominated bedforms had been identified on earlier occasions (Kubicki and Bartholomä 2011). In October 2010 the survey area was expanded, which also allowed a larger coverage of derived migration vectors. The same area was scanned consistently in April 2011 to trace any changes in dune positions and to verify the assumption that asymmetries are induced by modern hydrological conditions. Once the migration paths were verified, it was essential to check whether the migration was perhaps temporarily induced by storm events in the winter of 2010/2011, or whether the observed vectors were the effect of the constantly acting tidal forces. In this manner the October 2011 survey confirmed that the dunes were migrating independently of high-energy events and that the migration rate could be calculated quite reliably (Fig. 4b).
The analysis of crest alignments in the three time steps showed a variety of directions of sediment transport as well as different migration rates throughout the area (Fig. 2d). The longest dunes located in the middle of the survey area weremigrating northwards with a slight bend towards the NNW following the general channel architecture. Some of the dunes were  Among all the bedform migration paths, those facing in opposite direction attracted special attention. The border between flood-and ebb-dominated dunes was delineated by connecting sections of dunes with symmetric stoss and lee angles. Such sections were frequently identified at the centre of dune bodies. As laterally adjacent sections were migrating in opposite directions, the opposing movement resulted in bending of crest lines and occasional calving of dunes. The zone of convergence of opposite migration paths was located exactly below the fairway. Bathymetric data from the fairway monitoring surveys further corroborated these observations. Thus, a series of 32 consecutive DTMs based on data collected between January 2006 and October 2010 confirmed constant movement of dunes in opposite directions, as illustrated in Fig. 6. Datasets from April and October 2011 were excluded from this figure due to insufficient coverage. With the aid of dune crest positions derived from sidescan sonar data, however, it was confirmed that the dunes continued to migrate along their consecutive paths for another year.
The convergence zone is characterised by little change over the 5 years covered by the data. Neither sediment accumulation nor bedform heightening were observed. In one case a section of a dune showed such small spatial oscillations that its position and dimensions could be taken as being stable over the entire 5-year period (Fig. 6).With lateral distance from the centre of convergence, the migration rates of bedforms increased. Within the fairway section the dune migration rate was up to ca. 50 m/year. Even though the latest datasets from 2010 and 2011 cover a larger area, they do not provide any clues as to the fate of the sediment in the convergence area. Due to the fact that the western channel flank was so steep, safe navigation was difficult and the pre-designed survey grid was thus rarely fully accomplished in this part of the Jade channel. Sediment transport on the western channel flank could therefore not be assessed based on bathymetry differences. For this reason the hydrodynamics of this section of the channel was simulated by numerical modelling in order to understand how tidal currents interact over this area, which could give indirect clues on forcing directions.
The modelling results showed that the tidal current exceeds 1 m/s in the middle of the channel during both flood and ebb phases (Fig. 7b, c), and that it progressively slows down towards both channel flanks. In addition, it was revealed that, at any one time, the tidal wave was of uniform height across the entire width of the channel, and that the turn of the tide from ebb to flood was abrupt with only a short slack-water period. The map with the Eulerian residual flow vectors shows that, due to the bending channel of the Jade, flood and ebb velocities are not perfectly symmetrical. Thus, averaging tidal velocities over a full tidal cycle reveals that the resulting residual current vectors show a complicated pattern of secondary circulation (Fig. 7d), which corresponds very well to the spatial pattern of dune migration (Fig. 2d).
The main vector of ebb dominance runs along the S-N axis and coincides with the greatest dune heights in the area. Flanking this vector, three tide-induced residual current vortices are identified, of which a clockwise vortex is located on the eastern flank in the SE of the survey area. The western flank, by contrast, is affected by a clockwise vortex in the north and a counter-clockwise one in the south which, in combination, produce a horizontal circulation pattern in the shape of an "8". Since the two vortices rotate in opposite directions, the current vectors both face westwards at the centre of the "8". This section precisely corresponds to the zone of dune convergence identified in the sedimentological data. The westward-facing vectors thus explain the lack of any dune heightening or sediment accretion in the convergence zone, although the precise mechanism of sediment bypassing and potential recirculation has not yet been identified.

Seabed mobility and implications for dredging management
Without long time series of in situ current measurements, one can only speculate on critical velocities achieved at various tidal phases and under different weather conditions over particular seabed areas. In the present study, however, this shortcoming is compensated by a unique dataset of 35 highresolution bathymetric surveys spanning 6 years. These data show, without any doubt, that bedform migration occurs independently of storm events. The large to very large dunes in the study area migrate at rates of 30-100 m/year. These migration rates are faster than those recorded in similar tidal inlets also comprising medium to coarse sands (32 m/year in Bartholdy et al. 2002;21 m/year in Cuadrado and Gómez 2011).
In addition, smaller bedforms were observed on numerous occasions to completely change direction in response to the reversing tidal currents. This phenomenon was noted when neighbouring echosounding transects crossing the same secondary dunes were scanned at different tidal phases (Fig. 5a). This observation strengthens the notion that the medium sand and finer fractions in the area are mobilised by tidal currents during any weather conditions on a daily basis. The experiment by Svenson et al. (2009) on a large dune located ca. 4 km south of the study area demonstrated that the measured friction velocities were able to mobilise even fine gravel. In that case, the dune responded to the daily tides by an up-crest coarsening trend in sediment sorting-a feature also observed over the largest dunes in the present study area (Fig. 5c). Moreover, bedforms of various sizes were identified in all sediment types ranging in mean diameters from fine sand to gravel. This suggests that the entire channel bed is regularly exposed to tidal currents exceeding critical velocities for sediment mobilisation.
A smooth channel bed composed of consolidated clay, as identified in the study area, would normally be an indication for a prolonged absence of any sediment cover. Instead, the area is covered by fully developed dunes when compared with global data on dune dimensions (Fig. 8;cf. Flemming 1988). This could mean that the observed dunes are a fairly recent phenomenon, being possibly related to the dumping of dredge spoil near the lighthousewhich has provided a newsediment source fromwhere the sediment has been redistributed by the tidal currents. This hypothesis is strengthened by the observation that dunes located south of the lighthouse, up-stream with respect to residual current vectors, are lower and shorter than the ones situated closer to the lighthouse (Fig. 2c). This finding may be useful to authorities striving for an optimisation of dredging and dumping strategies.
When evaluating the bathymetric changes over the past 6 years, it seems that the dunes are merely passing through this section of the channel and that the channel would once again become void of sediment if the source were to be cut off by, for example, closing the dumping site. If the sediment source were indeed the dump site (e.g. Wienberg et al. 2004), then one should be able to precisely calculate the time of natural redistribution of the exogenic material. One could also consider controlling dune dimensions by dumping only certain grain sizes and avoiding others. Thus, the availability of sediments coarser than fine sand would be conducive to forming large to very large dunes in the area. Decreasing the grain size of dumped material would result in the formation of smaller, more rapidly migrating dunes and thereby avoid navigational obstacles in the form of elevated crest heights.

Observed sediment transport pattern in relation to modelled hydrology
Due to the local channel topography, a complicated pattern of residual currents has developed, which was identified even on the relatively coarse grid of the numerical model compared to the dune lengths. It has to be kept in mind here that the simplified bathymetry used in the model does not resolve individual dunes. However, the required assumptions of the numerical model-e.g. averaging the variable topography within individual grid cells-were shown to be insignificant with respect to the advantage of a broader spatial view and the opportunity to analyse the flow field in a physically consistent way using characteristic tidal parameters. A major result of the study is the fact that the transport vectors derived from tracing the crest lines are in ideal agreement with the residual current vectorsmodelled for fair-weather conditions. Thus, the locations of the largest dunes coincide with the highest residual currents, which are locally ebb-dominant. Smaller dunes also clearly migrate in the direction of the residual currents. Because the modelled current velocities lack detailed validation for the 2010 bathymetry, they should in the interim be treated as an approximation. The sedimentological data, on the other hand, provide multiple indicators that critical velocities for mobilising coarse to very coarse sand are exceeded during everyday tidal action. Nevertheless, the model resolution is high enough to reproduce the residual current vortices at exactly the same locations as indicated by the observed dune pathways. Such residual current vortices are a natural phenomenon in environments characterized by reversing tidal currents, but it is a rare experience to be able to observe their effect in dune migration paths on the seabed in such detail.
In the study area, the neighbouring counter-rotating vortices have resulted in dunes converging along one axis. Interestingly, no sediment accretion is observed at the point of convergence in the course of the 6 years of monitoring (Fig. 6). Moreover, even a buffer zone of ca. 200 m radius around the convergence point remained relatively stable, being characterised by symmetrical dune bodies and only minor shifts in the positions of dune crests. In combination with the numerical model results, the westward-directed flow vectors at the centre between the two counter-rotating vortices suggest that the sediment bypasses in that direction, although this could not be verified on the ground by dune migration patterns. Unfortunately, it was not possible to establish the exact nature of the bypassing mechanism because detailed measurements on the western bank were not available to this study. While no evidence of an accreting western bank in the vicinity of the convergence zone is available, a clear depocentre was observed in the north-western corner of the study area (see animation in the Electronic supplementary material). This accumulation is spatially in perfect agreement with the residual current vortex which probably transports the sediment away from the convergence zone towards the north along the shore of the Minsener Oog island, before eventually bending eastwards precisely at the location of the depocentre (see Fig. 7d).
It can thus be hypothesized that the sediment trapped by the opposing residual current vortices over the western channel bank is constantly being recirculated. As this feature could not be confirmed by the available sedimentological data, the hypothesis should be tested by a coupled hydrodynamic-sediment Kubicki, Kösters, Bartholomä: Dune convergence/divergence controlled by residual current vortices in the Jade tidal channel, south-eastern North Sea. S. 57 Geo-Marine Letters; Vol. 37; Heft 1; Seite 47-58 transport simulation using a higher-resolution grid supported by more detailed ground-truthing in the area of interest

Conclusions
The meandering section of the outer Jade tidal channel, which is apparently being supplied with material derived from a nearby dredge-spoil dumping site, was monitored monthly over a 6-year period by means of high-resolution bathymetric mapping to trace dune migration rates and directions. The field investigations were complemented by numerical modelling of the fair-weather hydrology. The main results and implications can be summarized as follows: -The model-derived residual current vectors are in perfect spatial agreement with data collected in situ.
-The main direction and highest velocity of residual ebbcurrent flow is associated with the largest dunes, which are composed of medium to coarse sand.
-Residual current vortices form on both sides of the channel. These are large enough to be traced on the seabed by dune asymmetries.
-Two counter-rotating vortices over the western channel bank result in dune convergence along one axis.
-The convergence zone remained stable over the entire 6-year monitoring period, suggesting equilibrium conditions between hydrology and morphology.
-It is hypothesized that sediment bypasses the convergence zone to be constantly recirculated.