Non-Hydrostatic Modelling of Waves in Layered Fluids

Non-Hydrostatic Modelling of Waves in Layered Fluids

Balkema, S.H.

Civil Engineering and Geosciences

Fluid mechanics

2009-04-02

In this thesis a non-hydrostatic two-layer 2DV model, based on the scheme presented by Stelling and Zijlema (2003), is developed. The model is non-hydrostatic; the velocities are corrected with a pressure gradient following from the requirement of a divergence free flow field per computational cell. The model is a two-layer model; only layered systems with two layers of different but constant density are considered and the mixing is left out of consideration. The divide between the between upper and lower layer is considered a sharp interface. The density is discontinuous at the interface and the fluids are completely separated by the interface. To guarantee an exact representation of the interface, a boundary following grid is used in the vertical. In several test cases the model has been validated. In a closed basin test the dispersion relation is shown to follow the linear dispersion relation for internal and external waves almost exactly when two layers are used. The model is also tested against analytical models with regard to dissipation of the waves by a viscous lower layer (mud) and showed comparable results. The model however performed less well for highly advective processes with large gradients such as the sex-change test. Considering differences in flow velocity between the layers, the stability of the model was substantially lower than according to linear theory. The limit for this new model has been found to depend on the thickness of one layer only in stead of the total depth. Finally the model was used to reproduce results of laboratory experiments found in literature. The steepening of internal waves and generation of solitons was reasonable well represented. The result of this study is a non-hydrostatic 2DV two-layer model, which has the same attractive properties as the model by Stelling and Zijlema regarding wave dispersion of both internal and ex-ternal waves.

non-hydrostatic two-layer internal wave numerical model

http://resolver.tudelft.nl/uuid:8f12ee2d-4a59-42b8-b2eb-9cb610e213e9

Student theses

master thesis

(c) 2009 Balkema, S.H.