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Numerical simulation of intertidal areas

Jone Liekens; Tom De Mulder; Henk Schuttelaars; Yoeri Dijkstra

Abstract

Our research is focused on the numerical simulation of water motion and morphodynamics in tidal systems. Morphodynamics, the study of how the bed changes over time due to erosion and deposition, is important for several reasons: the bedform geometry can influence flood risks, is important for vegetation and wildlife and affects which ships can pass. Using numerical models allows for proper ecological and economic management of these systems. As preliminary step in my research, the detailed tide-induced water motion in an intertidal area is investigated for a schematized tidal inlet system with a rectangular plan view and a linearly sloped bed, forced by a semi-diurnal lunar tide at the seaward boundary. The flow is governed by the 1D Shallow Water Equations. For the considered configuration, velocity peaks occur in the intertidal area during both flood and ebb. We compare the coordinate transformation method with other wetting-drying approaches, such as the removal/addition of grid cells used in Delft3D, the Defina approach with partially dry cells and perturbation methods. As a next step, we will focus more on idealized modelling: the use of simplified models based on first principles, where on the basis of scaling analysis the most dominant mechanisms can be selected and a perturbation method and harmonic analysis can be applied. The main advantage of these idealized models is their fast execution time, so that it is possible to thoroughly investigate the sensitivity for a range of parameters and identify equilibria and their stability.

Full text

NUMERICAL SIMULATION OF INTERTIDAL AREAS *HYDRAULICS LABORATORY, DEPARTMENT OF CIVIL ENGINEERING, GHENT UNIVERSITY ** DELFT INSTITUTE OF APPLIED MATHEMATICS, DELFT UNIVERSITY OF TECHNOLOGY Jone Liekens*, Tom De Mulder*, Henk Schuttelaars**, Yoeri Dijkstra** Contact: [email protected] Bottom friction 𝜏𝑏: quadratic vs. linear (with Lorentz linearization) in velocity Fixed grid - Cell removal/addition algorithm (e.g. Delft3D) [1] Fixed grid –Defina approach [2] Fixed grid - Perturbation from mean water level [3] Variable grid - Coordinate transformation [4] Y(x) Different wetting-drying approaches Preliminary results: coordinate transformation vs. Delft3D Next steps: idealized modelling ▪Simplified models based on (physical) first principles ▪Scaling analysis to identify a small parameter 𝜀in governing equations (e.g. ratio at entrance of tidal amplitude and mean depth) allows to apply a perturbation method and find solutions at O(1) and O(𝜀) in harmonic domain ▪Main advantage: short runtime ▪Enables thorough sensitivity analysis, e.g. - increasing mean sea levels , - varying bed roughness (sediment grain size), - varying length of tidal systems, etc. ▪Research objective: which wetting-drying approach is best suited for idealized modelling (i.e. yields good results without jeopardizing short runtimes) Solution: 1D shallow water equations High water Low water Intertidal area Problem ▪Bed in tidal systems (e.g. estuaries, tidal rivers, back-barrier tidal inlet basins) may change in time due to natural or human-induced changes in flow velocities or sediment transport ▪Prediction of changes important for: - Ecology: wildlife (breeding ground for birds and fish), vegetation - Safety: damping of tide and flood waves - Economy: ship access to port (e.g. Western Scheldt) ▪Accurate modelling crucial for management of tidal systems ▪Modelling water motion in shallow or intertidal area is difficult: several wetting-drying approaches are possible ▪Goal: compare the different approaches, when solving tide-induced water motion governed by 1D shallow water equations References: Image Eastern Scheldt: “Roggenplaat-Eastern-Scheldt-Zeeland-2020-Luka-Peternel.jpg” by Luka Peternel, licensed under CC BY-SA 4.0 [1] Deltares. (2025). Delft3D-FLOW, user manual (Version 4.05) [Draft]. https://content.oss.deltares.nl/delft3d4/Delft3D-FLOW_User_Manual.pdf [2] Defina, A. (2000). Two‐dimensional shallow flow equations for partially dry areas. Water Resources Research , 36 (11), 3251-3264. [3] Dijkstra, Y. M., Brouwer, R. L., Schuttelaars, H. M., & Schramkowski, G. P. (2017). The iFlow modelling framework v2. 4: A modular idealized process-based model for flow and transport in estuaries. Geoscientific Model Development, 10(7), 2691-2713. [4] Hermans, C. (2024). Exploring the (boundaries) of the moving boundary problem. Bachelor thesis, Appl. Math. and Appl. Phys., Delft University of Technology. ▪The velocity profile (in space) at different moments in the tidal cycle (yellow: ωt = 0, dark blue ωt ≈ 2π) ▪With coordinate transformation method: intertidal velocity peaks ; in Delft3D: peaked, but wiggly results a) Coordinate transformation method b) Delft3D: cell removal/addition approach