The relationship between linearised 3D and 2DH models for tidally dominated shallow waters

Marco P. Rozendaal*, Yoeri M. Dijkstra, Henk M. Schuttelaars

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


The water motion computed using 3D and 2DH models in tidally dominated shallow waters can, in some cases, differ significantly. In 2DH models, bed friction is typically parametrised in terms of the depth-averaged velocity, whereas in 3D models, typically the near-bed velocity is used. This difference causes the bed shear stress in 2DH models to point towards the depth-averaged velocity, whereas in 3D models, it points towards the near-bed velocity, which are not necessarily the same. Focussing on linearised barotropic models, we derive an exact friction parametrisation for 2DH models such that the same depth-averaged dynamics are described as in the corresponding 3D model. The result is a convolutional friction formulation where the instantaneous friction depends on the present and past velocities, thus modifying the traditional 2DH friction formulation that only depends on the present depth-averaged velocity. In the case of harmonic (tidal) waves, this parametrisation has a clear physical interpretation and shows that the near-bed velocity should be parametrised as a rotated, deformed and phase shifted variant of the depth-averaged velocity. We demonstrate that in certain regions of the parameter space, it may be impossible to calibrate a 2DH model that uses a traditional friction law to reproduce the water levels from a 3D model, showing that the 3D friction formulation can be crucial to capture the 3D dynamics within a depth-averaged model. This phenomenon is explored in detail in a narrow well-mixed estuary.

Original languageEnglish
Article number102330
JournalOcean Modelling
Publication statusPublished - 2024

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


This work was supported by Flanders Hydraulics ( WL2021P20_007_1 ). The authors would like to thank the anonymous reviewers for their valuable comments and insights.


  • 2DH model
  • 3D friction formulation
  • 3D model
  • Idealised model


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