Bokhove, O and Cotter, C (2010) Variational water-wave model with accurate dispersion and vertical vorticity. Journal of Engineering Mathematics, 67 (1-2). 33 - 54 (22). ISSN 0022-0833
Abstract
A new water wave model has been derived which is based on variational techniques and combines a depth-averaged vertical (component of) vorticity with depth-dependent potential flow. The model facilitates the further restriction of the vertical profile of the velocity potential to n-th order polynomials or a finite element profile with a small number of elements (say), leading to a framework for efficient modelling of the interaction of steepening and breaking waves near the shore with a large-scale horizontal flow. The equations are derived from a constrained variational formulation which leads to conservation laws for energy, mass, momentum and vertical vorticity. It is shown that the potential flow water wave equations and the shallow-water equations are recovered in the relevant limits. Approximate shock relations are provided, which can be used in numerical schemes to model breaking waves.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2010, Springer Netherlands. This is an author produced version of a paper published in the Journal of Engineering Mathematics. Uploaded in accordance with the publisher's self-archiving policy. The final publication is available at Springer via http://dx.doi.org/10.1007/s10665-009-9346-3 |
Keywords: | New water wave model, variational principle, hydraulic jump relations; New water wave model; variational principle; hydraulic jump relations; bores; coastal engineering; wave-current interactions |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 16 Feb 2015 12:30 |
Last Modified: | 17 Jan 2018 02:38 |
Published Version: | http://dx.doi.org/10.1007/s10665-009-9346-3 |
Status: | Published |
Publisher: | Springer Netherlands |
Identification Number: | 10.1007/s10665-009-9346-3 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:83391 |