This study presents an investigation into the non‐linear hydrodynamics in the Scheldt River estuary using the two‐dimensional vertical (2DV) idealised iFlow model. It extends the earlier study by Brouwer et al. (2017) on weakly non‐linear hydrodynamics by including higher‐order non‐linear physical mechanisms and non‐linear parametrisations of turbulent mixing. The goals of this study are to a) simplify the calibration of the model, by reducing the number of calibration parameters from two to one, (b) improve the performance of the idealised iFlow model in the Upper Sea Scheldt and (c) understand the essential physical mechanisms required for such improved performance. The k − ε turbulence closure model was used to derive linear and non‐linear parametrisations of turbulence that depend only on one calibration parameter. The calibration yields a clear best fit for the M2 tide, while no single best value for the M4 tide could be found. The result of the calibration on the M2 tide yields a good description of this tidal component, though the amplitude is overestimated in the Upper Sea Scheldt when using the linear model. The M4 tidal amplitude is typically overestimated by the model in the whole estuary. The relative phase of both the M2 and M4 tidal components are well described. The higher‐order non‐linear mechanisms are insignificant for the Western Scheldt and Lower Sea Scheldt, but are important in the Upper Sea Scheldt. The model shows a further set‐up of the M2 tide in the Upper Sea Scheldt as a consequence of these mechanisms. This set‐up increases the discrepancy between modelled and measured water levels. Damping of the M2 tide is achieved by including a non‐linear description of turbulent mixing. This description relates turbulent mixing to the local velocity magnitude. The relatively high tidal velocity in the Upper Sea Scheldt then produces additional mixing and therefore damping of the tide. An additional source of damping is found by including time variations of turbulent mixing on the tidal time‐scale. This also improves the correspondence between the modelled and measured M4 tide. Nevertheless, the error in the modelled M4 tidal amplitude remains large, with values up to 100%. The total effect of all non‐linear terms and turbulent mixing improve the result compared to that of Brouwer et al. (2017), but do nevertheless not produce a sufficient degree of damping of the tide in the Upper Sea Scheldt. It is therefore concluded that a change in the roughness value or the representative depth of the system is required to further improve the model result. The additional physical mechanisms studied in this report do not lead to a qualitative change in measures of tidal asymmetry. Although these measures provide an indication for the direction of the net sediment transport, the effect of non‐linear terms on the net sediment transport remains to be investigated.
Januari 2023
Scheepvaart, waterwegen en zeewezen
Dijkstra, Y.M.
FHR reports 15_039_1