Historical and future development of the tidally averaged transport of sandy sediments in the Scheldt estuary: a 2D exploratory model

Abstract

To investigate the historical development of the tidally averaged transport of sandy sediments in the main branch of the Scheldt estuary over the last decades (1950–2013), a 2D exploratory model has been developed. This model comprises the depth-averaged (2DH) shallow water equations, driven by an asymmetric tidal forcing at the seaward side, as well as an advection-diffusion equation to describe the depth-integrated dynamics of the suspended sediment concentration. The tidally averaged sand transport results from a subtle balance between the various contributions; advective contributions due to internally generated and externally prescribed overtides and the diffusive and topographically induced contributions. A seaward tidally averaged sand transport is found near the open boundary, whose magnitude has increased since ca. 1950. Moving upstream, the magnitude of the seaward transport decreases and changes into a smaller landward transport with a local maximum near the landward boundary. This maximum has increased over the years. Varying parameters that capture changes in the environment, e.g. historical changes in the bathymetry, future mean sea-level rise or changes in tidal forcing, results in changes in the tidally averaged sand transport that are systematically analysed and related to changes in the various contributions. Our model shows that there is a competition, in terms of determining the magnitude and the direction of the tidally averaged sand transport, between the effects of historical bathymetric changes, changes in tidal forcing and (projected) SLR. Even small changes in the tidal forcing at the seaward boundary can have a large impact on the magnitude and the direction of the tidally averaged sand transport. This hampers accurate predictions of sediment transport and morphodynamic changes in tidal systems, due to the uncertainty in the response of the tidal dynamics to the projected sea-level rise.

Appendices

Appendix

A Tidal asymmetry

The tidal asymmetry affects the sediment transport by means of the advective terms. So, if we consider only the advective contributions to the sediment transport, we get

$$ q_{u} \sim \left\langle uC\right\rangle $$

(A.1)

Looking at the dimensionless equation for the sediment concentration Eq. 2.10 and considering an approximate balance between erosion and deposition, assuming $\beta \sim 1$, we find that

$$ C \approx |\mathbf{u}|^{2}. $$

(A.2)

In this case, the four contributions to the sediment transport $q_{u,\text {adv}}^{M_{2},\text {int}}$, $q_{u,\text {adv}}^{M_{4},\text {int}}$, $q_{u,\text {adv}}^{M_{2},\text {ext}}$ and $q_{u,\text {adv}}^{M_{4},\text {ext}}$ are simplified to the following two terms, as was explained in Boelens et al. (2018),

$$ \begin{array}{@{}rcl@{}} q_{u,\text{adv}}^{\text{int}} & \sim& U_{M_{2}}^{2}U_{M_{4}}^{\text{int}}\cos(2\phi_{M_{2}}-\phi_{M_{4}}^{\text{int}})\\ &=& U_{M_{2}}^{3}\frac{U_{M_{4}}^{\text{int}}}{U_{M_{2}}}\cos(2\phi_{M_{2}}-\phi_{M_{4}}^{\text{int}}) \end{array} $$

(A.3)

$$ \begin{array}{@{}rcl@{}} q_{u,\text{adv}}^{\text{ext}} & \sim& U_{M_{2}}^{2}U_{M_{4}}^{\text{ext}}\cos(2\phi_{M_{2}}-\phi_{M_{4}}^{\text{ext}})\\ &=& U_{M_{2}}^{3}\frac{U_{M_{4}}^{\text{ext}}}{U_{M_{2}}}\cos(2\phi_{M_{2}}-\phi_{M_{4}}^{\text{ext}}). \end{array} $$

(A.4)

These simplifications illustrate that only taking amplitude asymmetry into account would imply that the system is flood dominant, according to the definition of Friedrichs and Aubrey (1988) (as can be seen in Fig. 12a and b), and sediment would be transported in the landward direction throughout the channel. However, our model, which also includes other effects, such as temporal and spatial settling lag (de Swart and Zimmerman 2009), shows sediment transport in the seaward direction in the seaward part of the channel. Therefore, other transport mechanisms, included in Eq. 2.10, are essential to consider. This also shows that the widely used proxy from Friedrichs and Aubrey (1988), who only consider short channels (L < 15km), is not valid for long systems, such as the Scheldt estuary.

Fig. 12

Amplitude ratio and phase difference of the M₂ and M₄ tidal constituent of the longitudinal velocity. The parameters are shown for the internally generated (int, orange line) and the externally prescribed (ext, green line) M₄ component, as well as for the combined (full, blue lines) M₄ component