# Capturing the residence time boundary layer—application to the Scheldt Estuary

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## Abstract

At high Peclet number, the residence time exhibits a boundary layer adjacent to incoming open boundaries. In a Eulerian model, not resolving this boundary layer can generate spurious oscillations that can propagate into the area of interest. However, resolving this boundary layer would require an unacceptably high spatial resolution. Therefore, alternative methods are needed in which no grid refinement is required to capture the key aspects of the physics of the residence time boundary layer. An extended finite element method representation and a boundary layer parameterisation are presented and tested herein. It is also explained how to preserve local consistency in reversed time simulations so as to avoid the generation of spurious residence time extrema. Finally, the boundary layer parameterisation is applied to the computation of the residence time in the Scheldt Estuary (Belgium/The Netherlands). This timescale is simulated by means of a depth-integrated, finite element, unstructured mesh model, with a high space–time resolution. It is seen that the residence time temporal variations are mainly affected by the semi-diurnal tides. However, the spring–neap variability also impacts the residence time, particularly in the sandbank and shallow areas. Seasonal variability is also observed, which is induced by the fluctuations over the year of the upstream flows. In general, the residence time is an increasing function of the distance to the mouth of the estuary. However, smaller-scale fluctuations are also present: they are caused by local bathymetric features and their impact on the hydrodynamics.

## Keywords

Residence time Boundary layer Parameterisation X-FEM Finite elements Diagnostic Adjoint modelling Local consistency## Notes

### Acknowledgements

Sébastien Blaise is a Research fellow with the Belgian Fund for Research in Industry and Agriculture (FRIA). Richard Comblen and Eric Deleersnijder are, respectively, a Research fellow and a Research associate with the Belgian National Fund for Scientific Research (FNRS). Eric Delhez is an honorary Research Associate with the Belgian National Fund for Scientific Research. Anouk de Brauwere is a postdoctoral researcher at the Research Foundation Flanders (FWO-Vlaanderen). The present study was carried out within the scope of the project “A second-generation model of the ocean system”, which is funded by the *Communauté Francaise de Belgique*, as *Actions de Recherche Concertées*, under contract ARC 04/09-316, and the project “Tracing and Integrated Modelling of Natural and Anthropogenic Effects on Hydrosystems” (TIMOTHY), an *Interuniversity Attraction Pole* (IAP6.13) funded by the *Belgian Federal Science Policy Office* (BELSPO). This work is a contribution to the development of SLIM, the Second-generation Louvain-la-Neuve Ice-ocean Model (http://www.climate.be/SLIM). The authors are indebted to Emmanuel Hanert and Olivier Gourgue for their useful comments.

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