"2D or not 2D?" Three-dimensional effects in two-dimensional modelling of oscillatory flow in shelf seas and estuaries

"2D or not 2D?" Three-dimensional effects in two-dimensional modelling of oscillatory flow in shelf seas and estuaries

Doorn, F.A.

Uijttewaal, W.S.J. (mentor)
Labeur, R.J. (mentor)
De Wit, L. (mentor)
Les, B.A.J. (mentor)

Civil Engineering and Geosciences

Hydraulic Engineering

2014-03-14

This study develops a theoretical framework to judge in which particular instances a two-dimensional depth-averaged model is sufficient to simulate flow processes in continental shelf seas or when a fully three-dimensional model is required for accurate results. A depth-averaged model does not give any vertical information, which is unfortunate when the model user is interested in it. Moreover, the model output, i.e. the surface elevation and the depth-averaged velocity components, may be affected by omitting the vertical dimension. In a frictionless case, two-dimensional and three-dimensional model results are expected to be similar. First, it is examined whether the reduction from 3D to 2DH has a significant effect on model output by comparing mathematical models with (2DV) and without (1D) vertical information. Localized analytical solutions are derived for the propagation of a single (predominant) tidal constituent in a shallow well-mixed continental shelf sea or estuary. The advective and Coriolis terms are neglected, the eddy viscosity is assumed constant and the bottom friction term is linearised. Special attention is paid to the latter, since both 1D and 2DV responses appear to depend substantially on the way the bottom friction coefficients are defined. The analytical method developed in this study indicates that certain combinations of the higher flow velocities (U > 1 m/s) and water depths (d > 50 m) may cause extensive differences between the results from a depth-averaged model and from a model that contains vertical information. However, it should be kept in mind that those two parameters interact and hence conclusions in general sense are hard to quantify. The resulting findings are tested by conceptual numerical simulations of steady and unsteady, periodic flows in a schematized rectangular basin. The results obtained from a three-dimensional simulation are compared to those from a two-dimensional depth-averaged simulation. Both simulations show good correspondence with the analytical solutions. As the development of the study is motivated by practical problems in the North Sea, its implementation is tested using the European Continental Shelf Model in both two-dimensional and three-dimensional version. A simple iteration procedure is performed to investigate what regions in the flow domain may be important. After an orienting 2D calculation a reasonably simple post-processing step reveals interesting locations where 2D and 3D results are expected to deviate strongly. For these specific locations the performance of the numerical models is analysed and compared. The case study confirms that the modeller needs to be careful when it comes to two-dimensional depth-averaged hydrodynamic modelling of large-scale domains like the European Continental Shelf Sea. For tidal propagation through large parts of the Central North Sea the flow velocities are rather low (U = 0.2 m/s) and hence two-dimensional (depth-averaged) models are adequate to calculate flow velocities. For several other regions though, being the English Channel, the Irish Sea and around the Orkney Islands, it is shown that it is required to be prudent with interpreting the two-dimensional results.

two-dimensional
depth-averaged
numerical model
continental shelf sea
analytical solution
three-dimensional
tidal propagation

http://resolver.tudelft.nl/uuid:0707e594-c4da-4db8-bd5d-92832475f5f7

Student theses

master thesis

(c) 2014 Doorn, F.A.