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

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

Rozendaal, M.C. (TU Delft Human Information Communication Design)
Dijkstra, Y.M. (TU Delft Mathematical Physics)
Schuttelaars, H.M. (TU Delft Mathematical Physics)

2024

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.

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

http://resolver.tudelft.nl/uuid:d6f6758f-b484-4373-92d3-4b37b32ebee7

https://doi.org/10.1016/j.ocemod.2024.102330

2024-08-05

1463-5003

Ocean Modelling, 188

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care 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.

Institutional Repository

journal article

© 2024 M.C. Rozendaal, Y.M. Dijkstra, H.M. Schuttelaars