Complex Flow Patterns in the Scheldt Estuary: Field Measurements and Validation of a Hydrodynamic Model

The Scheldt estuary is a 180-km-long macrotidal estuary in Belgium and SW Netherlands (Fig. 1). A shallow mouth, the Vlakte van de Raan (KM -20 to KM 0), connects the estuary with the North Sea and has several deeper channels (Elias et al. 2017). The Western Scheldt (KM 0 to KM 60) consists of a multiple channel system, with ebb and flood channels divided by intertidal sandbars. Further up-estuary, near the Dutch-Belgian border at Prosperpolder, the morphological system changes into a single channel system, the Lower and Upper Sea Scheldt (KM 60 to KM 160). Tributaries and side-branches include the Durme and Rupel rivers. The estuary is characterized by macrotidal semidiurnal tides, creating ebb and flood currents that carry both cohesive (mud) and noncohesive (sand) sediment loads (Baeyens et al. 1998). While cohesive sediment transport is most important in the up-estuarine part (Lower and Upper Sea Scheldt), sediment transport in the Western Scheldt is dominated by sand transport. To guarantee the accessibility towards the port of Antwerp, Europe’s second largest port, maintenance dredging works have to be performed almost continuously. Specific temporal valid licenses have to be granted to execute the necessary dredging works, which, since the last enlargement of the navigation channel in 2010 (De Wit et al. 2007), vary between 10 and $15{\mathrm{Mm}}^3$ annually.

The Belgian-Dutch research program, “Agenda for the Future,” addresses system management challenges for the Scheldt estuary in the near future (e.g., tidal amplification, risk of regime shift towards a hyperturbid system, sediment management, improvement of ecological value). Furthermore, within the MONEOS monitoring program (Plancke et al. 2012), continuous water level measurements are performed at more than 20 locations along the estuary, as well as measurements of both flow velocities and physicochemical parameters at different point locations. Besides these continuous measurements, annual 13-h flow and discharge measurements across several transects in the estuary are done as well as annual topo-bathymetric sounding using single beam and multibeam echo soundings and LIDAR. On top of that, additional measurements are performed at specific areas of interest (e.g., sills and intertidal areas) to improve system understanding and to collect datasets for model validation. For example, velocity measurements are performed to validate the numerical models that are used on the one hand to derive flow characteristics (e.g., peak velocity, duration that flow velocity exceeds a certain threshold) for the classification of distinct ecological regions or ecotopes (van der Wal et al. 2017) within the scope of the NATURA 2000 European Directives. Furthermore, flow fields from numerical models are also used as basic information in ship simulators, where the feasibility is investigated of new generation container vessels using the navigation channel (e.g., Eloot and Verwilligen 2010).

For this study, the area of interest concerns the sill of Hansweert and adjacent tidal flats and channels (Fig. 1). The present-day tidal range at Hansweert varies between 3.70 and 5.05 m for neap and spring tide respectively, resulting in strong tidal ebb and flood currents (up to $2\mathrm{m}/\mathrm{s}$). Near Hansweert, the navigational channel makes a sharp bend of almost 180°, causing strong secondary flows. At the inner bend of the navigation channel, the $4\text{-}{\mathrm{km}}^2$ intertidal flat of Ossenisse is located. Between the eastern edge of the Ossenisse sandflat and the sill of Hansweert in the navigation channel, lies a shallow subtidal area (plateau) of approximately $2{\mathrm{km}}^2$ with a bed level at about $-6\mathrm{m}$ TAW (i.e., TAW is the Belgian ordnance level, about 2.33 m below mean sea level), where the velocity measurements that are presented in this study were performed. The adjacent navigation channel has a depth of $-15.2\mathrm{m}$ TAW. Annual maintenance dredging volumes are high at the sill of Hansweert (i.e., approximately $2–3{\mathrm{Mm}}^3{\mathrm{y}}^{-1}$ from 2010 onwards according to Vos et al. 2017), while flow patterns are known to be complex due to the formation of large scale (i.e., $\sim 2\mathrm{km}$ in diameter) eddies during spring tide high waters (Decrop et al. 2010). In particular, the tidal propagation over the Ossenisse sandflat during the flood phase of higher high waters is slow relative to the tidal propagation in the estuarine channel itself due to differences in bottom friction, resulting in a water level depression above the shoal. The subsequent water level gradients induce a return flow from the southeast towards the shallow plateau, which has an opposite direction than the regular flood tidal flow in the main channel. As the opposing flows enclose the water level depression above the shallow plateau, the flow field starts to curve due to water level gradients in the depression and an eddy is formed. The presence of these large scale eddies may cause cross-currents in the navigation channel, which can be dangerous for shipping traffic, e.g., the grounding of the Fowairet in 2005, and also more recently ships were confronted with the hazardous cross-currents at this location. Previous research suggested that the presence of the shallow plateau between the Ossenisse shoal and the Hansweert sill is of major importance for the development of a large horizontal eddy and associated cross-currents in the study area (Decrop et al. 2010). However, the extent of this shallow plateau increased since their study, while the Hansweert sill deepened due to capital dredging of the navigation channel (Plancke et al. 2015), potentially changing the presence and frequency of occurrence of these eddies and accompanying cross-currents.

In this study, a velocity measurement campaign near the intensively dredged Hansweert sill in the main navigation channel of the Scheldt estuary is presented, as well as the validation of existing numerical models of the estuary based on these measurements. This study aims at: (1) identifying and improving insight into the present-day complex flow patterns around the sill of Hansweert using field measurements and numerical modeling; and (2) validating, comparing, and preferably also improving the model performance of two existing hydrodynamic models of the Scheldt estuary with regard to the representation of these flow patterns. Ultimately, beyond this first phase of the research, it is intended that these numerical models are used for sediment transport and morphological modeling in order to optimize dredging strategies.

In 2016, a hydrodynamic measurement campaign was executed by Rijkswaterstaat near the sill of Hansweert in the Western Scheldt. At four locations (Fig. 1 and Table 1), up-looking ADCPs (i.e., RD Instruments Workhorse Monitor 1,200 kHz) were deployed for two spring-neap cycles (April 28, 2016 until May 26, 2016). These devices provide directional velocity data which is processed with an output interval of 10 min. Two devices were placed on a shallow plateau between the sill of Hansweert and the Ossenisse shoal (i.e., H1 and H2) and two devices were placed at the other side of the sill near the Walsoorden shoal (i.e., H3 and H4), aiming at picturing the currents near the sill. During the measurement period, different ADCP’s got buried under deposited sediment at different moments (Table 1), leading to incomplete time series over the full period. At location H3, the ADCP got buried after 5 days, causing the spring tide velocity data to be missing at that location.

Field measurements are analyzed focusing on water level (height of high water, gradients, rising velocity) and flow velocity parameters (maximum current, cross-current). Cross-currents are derived calculating the component perpendicular to the mean ebb and flood direction (as mean of absolute value of sinus of current direction) and are related to the formation of large eddies at the location H1 and H2.

Two existing numerical models are compared in this study: a two-dimensional (2D) Delft3D model (Deltares 2016) and a three-dimensional (3D) Telemac-3D model (Hervouet 2007). Both models are extensively used to provide managers with answers within the scope of several projects in the Scheldt-estuary [e.g., sediment strategy (Ides et al. 2010) and Integrated plan of the Upper Sea Scheldt (Adams et al. 2016)]. A description of both models is given below. Model simulations are performed for the period of the field measurements after which modeled flow velocities are compared with the observations. Special focus is laid on the presence of velocity peaks related to the presence of large scale eddies (i.e., circular flow). Additionally, the modeled velocity fields in the study area around high water are analyzed for the spatial development and frequency of occurrence of large-scale eddies.

The first numerical model used in this study is the existing NeVla 2D numerical model of the Scheldt estuary, which was set up in the SIMONA software package and later on exported to Delft3D (Maximova et al. 2014; Verheyen et al. 2013). The NeVla model grid comprises the Scheldt estuary from the mouth area between Cadzand and Westkapelle up until the upstream tributaries (Fig. 1). The model has a structured grid with a resolution in the zone of interest of 150 m (length) by 100 m (width). The implemented bathymetry consists of bathymetrical data of the year 2015 for the Western Scheldt, resulting form single beam echo soundings of equidistant ($\sim 100\mathrm{m}$) spaced transects, interpolated onto a $20\times 20\text{-}\mathrm{m}$ grid, and $5\times 5\text{-}\mathrm{m}$ data from the year 2011 for the Sea Scheldt, generated from multibeam echo soundings with spatial resolution of $1\times 1\mathrm{m}$. For the study area near the Hansweert sill, bathymetrical data obtained during the measurement period (i.e., April 2016) is used. These local multibeam echo soundings (resolution $1\times 1\mathrm{m}$) are more frequently (i.e., every 2–4 weeks) measured on the sills to ensure safe navigation and an extra multibeam echo sounding of a larger area near the Ossenisse sandbar was available within the scope of a disposal test. For this study, the downstream boundary of the model is forced with time series of observed water levels in the mouth area (i.e., data from the Westkapelle and Cadzand tidal stations from April 26, 2016 until May 31, 2016). According to findings from Vanlede et al. (2009) and Maximova et al. (2009), a $+10\min$ phase shift is applied to the Cadzand water level series to correct for a 5,200-m difference between the model boundary and the actual Cadzand tidal station. The upstream boundaries are forced by yearly averaged discharges from Cornet and Mostaert (2010). Besides, discharge influences are expected to be negligible as the study area is situated in the downstream part of the estuary where the total river-induced flow of approximately $80{\mathrm{m}}^3{\mathrm{s}}^{-1}$ only accounts for $<1\%$ of the tidally induced flow in the Western Scheldt (e.g., Stark et al. 2017a).

In Delft3D, the effect of turbulence is included by means of the spatially constant horizontal eddy viscosity parameter (${\nu }_{hor}$), which represents a scale for the lateral momentum diffusion. The horizontal eddy-viscosity is mostly associated with the contribution of horizontal turbulent motions and forcing that are not resolved (i.e., subgrid scale turbulence) either by the horizontal grid or a priori removed by solving the Reynolds-averaged shallow-water equations (Gerritsen et al. 2007). The optimal value of the eddy viscosity parameter is determined by the water depth and grid resolution, and it is suggested to use a value between 0.1 and $0.5{\mathrm{m}}^2{\mathrm{s}}^{-1}$. In Decrop et al. (2009) it was shown that a higher value results in a damping of lateral velocity gradients and reduces the formation of the eddy. In accordance with previous modeling work by Decrop et al. (2010), this user-specified eddy viscosity is set at ${\nu }_{hor}=0.1{\mathrm{m}}^2{\mathrm{s}}^{-1}$ in the present study.

Initially, a uniform Manning bed roughness was applied ($0.025{\mathrm{m}}^{1/3}{\mathrm{s}}^{-1}$) in the subtidal channels, while a height-dependent value was chosen for intertidal areas, leading to a larger bed friction for vegetated salt marshes. These values were copied from the base model, which was calibrated on water levels throughout the estuary, as well as flow velocities on intertidal shoals (Ides and Plancke 2008). In this study, the bed roughness coefficients in the study area are changed to improve the representation of the measured flow velocities and the observed circular flow pattern in particular. More specifically, bottom friction coefficients are lowered on the shallow plateau and Ossenisse sandbar using the following algorithm [Fig. 2(b)]where $z_b$ represents the bottom elevation of each grid cell; and $n$ = Manning coefficient. Physically, bed roughness can be related to grain size, e.g., Strickler (1923), on the one hand and bedforms, e.g., van Rijn (1984), on the other hand. However, due to large spatial variation in both grain size (100–300 μm) and bedforms (ranging from ripples to large dunes) within the study area, the theoretical approach was not applicable for our case. Alternatively, the final settings of the bottom friction coefficients were obtained in the calibration procedure, which aimed an optimal representation of the observed flow patterns. According to Chow (1959) these values are representative for dredged channels with no vegetation, which is applicable for our study area.

A second numerical model was developed using the open source TELEMAC software. TELEMAC-3D is a finite-element hydrodynamic model with an unstructured grid that solves the Navier-Stokes equations in three dimensions. All parameter settings of the Telemac model used in this study are adopted from a previously validated TELEMAC model of the Scheldt Estuary “Scaldis” and can be found in that model’s validation report (Smolders et al. 2016). The only significant differences between the settings of the existing Scaldis model and of the TELEMAC model presented in this study are the extent and resolution of the model mesh. Comparison between the present model and the Scaldis model shows that the performance of both models is equally good in the Western Scheldt. The mesh resolution in the model domain varies from $\sim 500\mathrm{m}$ in the offshore zone, $\sim 150\mathrm{m}$ in the Western Scheldt, 50 m in the study area around Hansweert to 25–100 m in the Sea Scheldt and upstream tributaries. Hence, the TELEMAC model is locally refined and therefore has a finer resolution in the study area compared to the NeVla model (i.e., 50 m versus 100–150 m). The 3D model consists of five sigma-layers with the following distribution: $z*(1)=0.0·h$ (i.e., bottom); $z*(2)=0.12·h$; $z*(3)=0.3·h$; $z*(4)=0.6·h$; and $z*(5)=1.0·h$ (i.e., surface), with $z(i)$ the elevation of each layer and $h$ the water depth.

Based on the Scaldis model calibration (higher high waters betweenVanlede et al. 2015), a spatially varying (streamwise along the estuary) Manning bed roughness coefficient is initially applied in the TELEMAC model (i.e., $\sim 0.022{\mathrm{m}}^{1/3}{\mathrm{s}}^{-1}$ in the Western Scheldt from where roughness coefficients generally stepwise decrease upstream). As for the NeVla model, the model is calibrated by altering the friction coefficients on the shoal of Ossenisse and on the shallow plateau between the Ossenisse shoal and the sill of Hansweert. More specifically, the bottom friction coefficient is lowered using the same procedure as described above for the NeVla model. Hence, bottom friction coefficients are lowered to a minimum value of $0.015{\mathrm{m}}^{1/3}{\mathrm{s}}^{-1}$ depending on the bottom elevation. However, the bottom friction coefficient in deeper subtidal parts and on the higher parts of the Ossenisse shoal is maximized to the surrounding value of $0.022{\mathrm{m}}^{1/3}{\mathrm{s}}^{-1}$. Hence, the bottom roughness in the TELEMAC models slightly differs from the roughness fields that are shown in Fig. 2.

The settings for turbulence modeling are also adopted from the validated Scaldis model (Smolders et al. 2016). Horizontal turbulence is included by the Smagorinsky subgrid turbulence model, which is particularly recommended in the presence of a highly nonlinear flow (EDF R&D 2017; Hervouet 2007). The turbulent viscosity calculated with the Smagorinsky scheme (${\nu }_t$) is added to the user-specified laminar viscosity (i.e., set at ${\nu }_l={10}^{-2}{\mathrm{m}}^2{\mathrm{s}}^{-1}$) to calculate the total viscosity (${\nu }_{tot}={\nu }_t+{\nu }_l$). The bathymetrical data that is interpolated to the mesh is identical to the data used for the NeVla model, as is the upstream forcing. However, the downstream forcing differs between both models. While the NeVla model is cut off at the estuary mouth, the TELEMAC model used in this study extents further offshore into the North Sea (Fig. 1). This also implies that the offshore boundary conditions differ between the two models. In particular, the TELEMAC model is nested in a larger-scale continental shelf model, which is on its turn forced by harmonic components only and does not include surge effects, whereas the NeVla model was forced by measured water level series.

Numerical models allow better insight into physical processes by running specific scenarios. Over the past decades, the morphology and geometry of sandbars in the Scheldt estuary have changed significantly (de Vet et al. 2017). Accordingly, two scenarios were defined in order to evaluate the influence of the height of the Ossenisse sandbar on the development of the large eddies in the study area. These scenarios are only investigated with the NeVla model as this model is better able to reproduce the large eddy than the Scaldis model (see results section). In a first scenario, the intertidal part of the Ossenisse sandbar was lowered with 50% relative to mean low water level (i.e., multiply level above low water with factor 0.5)., which is an approximation of the situation in the past. In a second scenario, the intertidal part of the Ossenisse sandbar was heightened with 50% relative to the low water level (i.e., multiply level above low water with factor 1.5), which may not be a realistic future evolution, but allows to gain an insight in the role of the sandbar if part of it is not inundated or would become supratidal. Both scenarios are simulated with the roughness field of the calibrated NeVla model shown in Fig. 2(b).

Fig. 3 shows the measured flow velocities and directions during the measurement campaign from April 28, 2016 until May 13, 2016. At location H1 on the shallow plateau (Fig. 1), ebb velocities exceed flood velocities during lower tides, while flood velocities are higher during higher tides. During spring tide, flood velocities at location H1 are almost as high as $2\mathrm{m}/\mathrm{s}$, while peak ebb velocities range between 0.8 and $1.5\mathrm{m}/\mathrm{s}$ during the spring-neap cycle. At location H2, flood velocities are relatively low for all tides (i.e., $\sim 0.5\mathrm{m}/\mathrm{s}$) and ebb velocities exceed flood velocities by up to more than a factor two during spring tide (i.e., ebb velocities are up to $\sim 1.2\mathrm{m}/\mathrm{s}$). At locations H3 and H4, at the southeastern side of the Hansweert sill (near the Walsoorden shoal), maximum flood velocities exceed maximum ebb velocities for all tides. It must, however, be stated that spring tides were not measured at location H3. Peak flood velocities at location H4 are up to $1.9\mathrm{m}/\mathrm{s}$ for spring tide and $1.2\mathrm{m}/\mathrm{s}$ for neap tide, while peak ebb velocities range between 0.6 and $1.2\mathrm{m}/\mathrm{s}$.

At locations H1 and H2, on the shallow plateau between the Ossenisse shoal and the Hansweert sill, additional velocity peaks are observed during higher high waters between May 7, 2016 and May 11, 2016. These additional velocity peaks can be attributed to circular flow patterns or eddies that develop over the Ossenisse shoal and the shallow plateau where the measurements were carried out. In particular, the flow direction during regular or lower tides have a flow direction that gradually shifts from flood direction (i.e., $\sim 150°$ at locations H1 and H2) over westerly directions towards ebb direction (i.e., $\sim 330°$ at locations H1 and H2). If additional eddy-induced velocity peaks during high water are present, the flow direction also shifts from flood direction to ebb direction (i.e., from $\sim 150°$ to $\sim 330°–360°$), after which the flow direction rapidly changes to about 270°–300° and back to about 330°–360°.

An ensemble analysis was performed at location H1 for tides resulting in strong and weak cross-currents, using a threshold magnitude of the cross-current of $0.4\mathrm{m}/\mathrm{s}$, which corresponds with the mean value of the calculated cross-currents during the measurement campaign. Cross-currents are defined as the flow portion perpendicular to the mean flow direction. Zimmermann (1990) reports maximum cross-currents of $0.3\mathrm{m}/\mathrm{s}$ for canals, without endangering safe navigation. Although the navigation channel in the Scheldt-estuary should not be seen as a canal, this value is comparable to the chosen threshold of $0.4\mathrm{m}/\mathrm{s}$.

It can be seen (Fig. 4) that strong cross-currents occur during stronger tides (i.e., tides with a large tidal range), resulting in larger water level gradients between the Hansweert and Walsoorden tidal stations (not shown) and also leading to higher flow velocities in the area of interest. The strongest cross-currents occur between the moment of high water and 60 min after high water, and can reach values up to $0.85\mathrm{m}/\mathrm{s}$. Over the total measurement campaign (54 tides), the cross-currents were larger than $0.4\mathrm{m}/\mathrm{s}$ during 25 tidal cycles (i.e., corresponding to 46% of the tides), larger than $0.6\mathrm{m}/\mathrm{s}$ during 10 tidal cycles (19%), and larger than $0.8\mathrm{m}/\mathrm{s}$ during 2 tidal cycles (4%).

Fig. 5 shows a comparison between the observed and modelled flow velocities at locations H1-H4 during a typical spring tide for the NeVla and TELEMAC models (i.e., base runs and calibrated runs), while Fig. 6 shows the results for a typical neap tide. The representation of the measured flow velocities during spring tide can only be assessed for locations H1, H2, and H4 because there is no data for location H3.

The measured flow velocities during neap tide are mostly well captured by both models at all four locations, although the TELEMAC base run and especially the NeVla base run underestimate the flood peak velocities at H1 by up to $0.5\mathrm{m}/\mathrm{s}$. Furthermore, both of the TELEMAC runs overestimate ebb velocities at location H4 during neap tide.

At location H4, situated at the opposite (i.e., southeastern) side of the Hansweert sill, the maximum spring tide velocities during flood are best represented by the NeVla models and somewhat more underestimated by the TELEMAC models. Contrastingly, the spring tide ebb velocities are well-captured by both TELEMAC models and underestimated by the NeVla models. Differences between the base runs and calibrated runs are small at location H4, which can be explained by the fact that the bottom friction field in this area remains similar for all model runs [Fig. 2(b)].

At location H1, the strong $\sim 2\mathrm{m}/\mathrm{s}$ flood peak is only represented as such by the calibrated NeVla model, while the calibrated TELEMAC model and both base models still underestimate the maximum flood velocities at H1. The second velocity peak during high-water spring tide, associated with circular flows, is also best represented by the calibrated NeVla model. This additional velocity peak at H1 is not present in the other three model simulations. At location H2, however, the weaker second velocity peak during high water is to a certain extent represented in all four simulations. The spring flood peak itself at H2 is also well-represented in all simulations, although the calibrated models slightly overestimate the maximum flood velocities [i.e., up to $+0.2\mathrm{m}/\mathrm{s}$ for the calibrated NeVla model, which categorizes as “excellent” to “good” according to Sutherland et al. (2004)]. The ebb velocities at locations H1 and H2 on the shallow plateau are well captured by all models. Besides, differences in ebb velocities between the base runs and the calibrated models are remarkably small.

Over the same period as the measurement campaign (54 tides), the cross-currents in the calibrated NeVla model at location H1 were larger than $0.4\mathrm{m}/\mathrm{s}$ during 39 tidal cycles (corresponding to 83% of the tides), larger than $0.6\mathrm{m}/\mathrm{s}$ during 25 tidal cycles (46%), and were never larger than $0.8\mathrm{m}/\mathrm{s}$ (0%). In comparison with the measurements, medium cross-currents (0.4 and $0.6\mathrm{m}/\mathrm{s}$) are modeled in almost twice the amount of tidal cycles as they were observed for. This implies that the calibrated NeVla model overestimates the frequency of occurrence of eddy formation in the study area. This methodology could not be applied to the calibrated TELEMAC run because there are no distinct additional velocity peaks present at location H1 in this run.

In addition, Figs. 7 and 8 show the modelled velocity fields around spring-tide high water for the Delft3D-NeVla and TELEMAC models respectively. It is noted that the plotted velocity fields are more clear for the Delft3D model results, because this model has a structured grid, whereas the TELEMAC model consists of an unstructured grid.

The base runs of both models do not show strong circular flow patterns over the Ossenisse sandbar and shallow plateau around spring tide high water. In the base run of the NeVla model, however, a small cross-directional flow develops at the northern part of the shallow plateau just before high water, but it doesn’t develop into a large scale eddy. The TELEMAC base run has the opposite directed flows in the channel and on the shallow plateau existing next to each other, without any clear cross-directional flows between them.

In contrast to the base runs, the calibrated NeVla and TELEMAC runs (i.e., with lowered bottom friction values on the shallow plateau) do produce circular flow patterns above the shallow plateau and adjacent channel. Based on the results of the calibrated NeVla model (Fig. 7), which captures the observed flow velocities and directions very well, the eddy forms around 30 min before high water above the shallow plateau between the sandbar and the sill of Hansweert. Near Hansweert, the flood current makes a turn of almost 180°, causing inertial effects that force the strong flood flow away from the eastern side of the sandbar, resulting in lower water levels at the plateau [Fig. 9(a)]. On the other hand, the flood flow simultaneously penetrates through the smaller connecting channel “Schaar van Ossenisse” south of the Ossenisse sandbar, resulting in higher water levels south of the plateau. The spatial water level variation shown in Fig. 9(a) shows a distinct water level depression of up to about 0.15 m over a distance of less than one kilometer between this connecting channel and the center of the depression. The water level depression on the plateau attracts water from this connecting channel in the south as well as from the navigation channel in the north. The local topo-bathymetry of the sandbar, which is lower at the south-eastern side, allows water to flow more easily from the south, over the south-eastern tip of the sandbar, to fill the depression. The corresponding strong currents flowing towards the north, in combination with the strong flood currents in the navigation channel towards the south, then initiate the eddy as both flows start to curve around the center of the depression. Shortly after high water, the eddy has moved towards the channel where it increases in size, but decreases in strength and fades away shortly after. Nevertheless, eddy-induced cross-currents are simulated in the navigation channel with the calibrated NeVla model.

The calibrated TELEMAC model also produces a circular flow pattern, but the location and size of the eddy, as well as the flow speed and directions, correspond less good with the observed velocity vectors (Fig. 8). In particular, the cross-directional velocities (i.e., perpendicular to the ebb-flood-direction) are lower than the observed velocities and the large eddy itself is situated too far to the north on the shallow plateau. Eddy-induced cross-currents in the navigation channel are limited in the calibrated TELEMAC run as the eddy itself seems to be too weak to alter flow directions in the deep subtidal channel itself.

Analysis of the driving mechanisms behind the cross-currents shows differences between the measurements and the calibrated NeVla model, both for high water levels in Hansweert and maximum flow velocities on the shallow plateau (Fig. 11). In both cases, the model overestimates cross-currents. This also translates into a different occurrence frequency of the cross-currents during the measurement period (46% instead of 19% of the tidal cycles within the measurement period for which the modelled cross-current was larger than $0.6\mathrm{m}/\mathrm{s}$).

Both scenarios with altered elevation of the Ossenisse sandbar result in the formation of a large eddy at the eastern edge of the Ossenisse sandbar (Fig. 10). However, both the location of the center of the eddy and the cross-currents generated by the eddy are different. Due to the shift in the location of the center of the eddy, it is difficult to analyze cross-currents at one fixed point as was done for the model validation. Instead, it is opted to analyze the spatial flow patterns during the period of 30 min before to 30 min after high water.

In the scenario with the lowered sandbar, currents over the sandbar are stronger 30 min before high water, while the eddy is not as strong as in the reference run (i.e., the calibrated NeVla model run) at this time of the tidal cycle. At the moment of high water and 30 min after high water, the eddy remains weaker compared to the reference and the position of the center of the eddy is situated more to the south. The spatial water level differences of approximately 0.10 m are also smaller in this eddy. Besides, currents over the sandbar at the start of the ebb phase ($\mathrm{HW}+{30}^{\prime }$) are stronger in this scenario compared to the reference run.

In the scenario with the heightened sandbar, a large part of the sandbar remains dry during the simulated spring tide. Consequently, more water is forced around this dry part of the sandbar (i.e., through the small channel south of the Ossenisse shoal). At the three visualized moments of the tidal cycle (i.e., before, at, and after high water) a strong eddy is formed in this scenario, resulting in similar cross-currents as in the reference run. Both 30 min before and at high water, the center of the eddy is situated more to the west (closer to the eastern edge of the sandbar) compared to the reference, while 30 min after high water the center has moved to the north. The maximum water level depression in the eddy is slightly larger than in the calibrated NeVla reference run (i.e., up to $\sim 0.17\mathrm{m}$ between the connecting channel and the center of the eddy).