An investigation into the numerical and physical behaviour of a hybrid finite-volume finite-difference Boussinesq-type model, using a rotational surface roller approach in the surf-zone is presented. The relevant theory for the required development of a numerical model implementing this technique is outlined. The proposed method looks to achieve a more physically realistic description of the hydrodynamics by considering the rotational nature of the highly turbulent flow found during wave breaking. This involves a semi-analytical solution to the vorticity transport equation and provides a mechanism by which energy is dissipated. Resolving vorticity within the flow also allows vertical profiles of the horizontal velocity to be constructed, offering valuable detail that is otherwise unavailable when using equivalent irrotational Boussinesq-type models. By obtaining additional information about the structure of the flow, other quantities can be determined, such as the undertow, which has a key role in morphodynamic processes occurring in this region. These benefits are combined with a finite-volume finite-difference scheme, which yields improvements in stability and possesses inherent shock-capturing capabilities. The ability of the model to replicate laboratory observations is verified, and identified shortcomings are explained in the context of the numerical procedure and the assumptions made during the derivation of the governing equations. Although the weak nonlinearity of the Boussinesq-type equations means the shoaling characteristics of the model do not accurately reflect those found experimentally, the adopted formulation of the finite-volume scheme is shown to prevent the inclusion of the necessary higher-order derivatives which exist in a fully-nonlinear formulation. In order to establish a realistic dissipation mechanism, it is vital that the extent of any misleading numerical artefacts are recognised and their effects alleviated. This study explores a range of physical attributes predicted by the present model and discusses the numerical features of the scheme, evaluating how these influence the results.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:682653 |
| Date | January 2015 |
| Creators | Tatlock, Benjamin |
| Publisher | University of Nottingham |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://eprints.nottingham.ac.uk/30443/ |
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