Insaf Draoui

This study presents a model for simulating the interaction of river influxes with tidal propagation in region of varying complexity for the Scheldt basin (river, tributaries and estuary) and the European continental shelf. While the domain for inland rivers is one-dimensional and extends until the limit of tidal influence, the estuary and shelf region are dealt by means of two-dimensional equations. Within this region, there exists a hydraulic structure in one of the Scheldt tributaries (Dyle River), that is implemented to simulate the bidirectional flow of the tide. In this model a tidal forcing at the shelf break, metrological forcing at the free water surface and hourly discharges for the rivers and tributaries at the upstream boundaries are applied. Using this, the coupled model was firstly calibrated for the Manning coefficient for a relatively quiet period. Then it is extensively validated using available measurements for simulations in the month of January (2021), which is generally marked by strong tides. Moreover, the shelf region of the model was evaluated with the existing literature for the harmonic analysis of the dominant M2 tide. The simulated results show good agreement with a RMSE under 0.3 meters for the measured water levels.

Compared to deltas, lakes and estuaries, rivers generally are characterized by their natural downstream flow that can often be dealt with adequately by having recourse to 1D models. The cross-section integrated Saint-Venant equations are widely used in river modeling and engineering applications. In order to ensure the mass conservation the conservative form of the equations is preferred. In this case, the flux and source terms may be formulated in several ways. It is seen, however, that not all of them lead to stable and accurate numerical results. The choice of the convenient unknown and intermediate variables allows getting an optimal stability with fewer numerical adjustments. Furthermore, in a realistic domain, two different issues should be carefully dealt with, namely the relative paucity of geometric data points and the connection to larger water bodies ( delta, lakes ...). Regarding the data interpolation, the reference level for data definition and interpolation is generalized along the river instead of associating a local reference frame to each cross-section, allowing to obtain a smooth, stable source term. As for the connection to a 2D model, a boundary-connected coupling based on flux continuity is adopted. The aforementioned modules are implemented in the framework of a discontinuous Galerkin finite-element model, i.e., the Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM, www.slim-ocean.be). Validation is performed by running the model in idealized configurations. Then, the river-lakes-delta continuum of the Mahakam River (Borneo, Indonesia) is modeled and validation is based on measured water level.

Age can be evaluated at any time and position to understand transport processes taking place in the aquatic environment, including for reactive tracers. In the framework of the Constituent-oriented Age and Residence time Theory (CART), the age of a constituent or an aggregate of constituents, including the water itself, is usually defined as the time elapsed since leaving the boundary where the age is set or reset to zero. The age is evaluated as the ratio of the age concentration to the concentration, which are the solution of partial differential equations. The boundary conditions for the concentration and age concentration cannot be prescribed independently of each other. Instead, they must be derived from boundary conditions designed beforehand for the age distribution function (the histogram of the ages, the age theory core variable), even when this variable is not calculated explicitly. Consistent boundary conditions are established for insulating, departure and arrival boundaries. Gas exchanges through the water–air interface are also considered. Age fields ensuing from consistent boundary conditions and, occasionally, non-consistent ones are discussed, suggesting that the methodology advocated herein can be utilized by most age calculations, be they used for diagnosing the results of idealised models or realistic ones.