dc.contributor.author Akselsen, Andreas Holm dc.contributor.author Ellingsen, Simen Andreas Ådnøy dc.date.accessioned 2019-11-13T13:18:22Z dc.date.available 2019-11-13T13:18:22Z dc.date.created 2019-09-18T15:50:12Z dc.date.issued 2019 dc.identifier.citation Journal of Fluid Mechanics. 2019, 878 740-767. nb_NO dc.identifier.issn 0022-1120 dc.identifier.uri http://hdl.handle.net/11250/2628293 dc.description.abstract When shallow water flows over uneven bathymetry, the water surface is modulated. This type of problem has been revisited numerous times since it was first studied by Lord Kelvin in 1886. Our study analytically examines currents whose unperturbed velocity profile $U(z)$ follows a power-law $z^q$, flowing over a three-dimensional uneven bed. This particular form of $U$, which can model a miscellany of realistic flows, allows explicit analytical solutions. Arbitrary bed shapes can readily be imposed via Fourier's theorem provided their steepness is moderate. Three-dimensional vorticity-bathymetry interaction effects are evident when the flow makes an oblique angle with, a sinusoidally corrugated bed. Streamlines are found to twist and the fluid particle drift is redirected away from the direction of the unperturbed current. Furthermore, a perturbation technique is developed which satisfies the bottom boundary condition to arbitrary order also for large-amplitude obstructions which penetrate well into the current profile. This introduces higher-order harmonics of the bathymetry amplitude. States of resonance for first and higher order harmonics are readily calculated. Although the method is theoretically restricted to bathymetries of moderate inclination, a wide variety of steeper obstructions are satisfactorily represented by the method, even provoking occurrences of recirculation. All expressions are analytically explicit and sequential fast Fourier transformations ensure quick and easy computation for arbitrary three-dimensional bathymetries. A method for separating near and far fields ensures computational convergence under the appropriate radiation condition. nb_NO dc.description.abstract Sheared free-surface flow over three-dimensional obstructions of finite amplitude nb_NO dc.language.iso eng nb_NO dc.publisher Cambridge University Press nb_NO dc.title Sheared free-surface flow over three-dimensional obstructions of finite amplitude nb_NO dc.type Journal article nb_NO dc.type Peer reviewed nb_NO dc.description.version acceptedVersion nb_NO dc.source.pagenumber 740-767 nb_NO dc.source.volume 878 nb_NO dc.source.journal Journal of Fluid Mechanics nb_NO dc.identifier.doi 10.1017/jfm.2019.657 dc.identifier.cristin 1726371 dc.relation.project Norges forskningsråd: 249740 nb_NO dc.description.localcode © 2019. This is the authors' accepted and refereed manuscript to the article. Locked until 10.5.2020 due to copyright restrictions. The final authenticated version is available online at: https://doi.org/10.1017/jfm.2019.657 nb_NO cristin.unitcode 194,64,25,0 cristin.unitname Institutt for energi- og prosessteknikk cristin.ispublished true cristin.fulltext original cristin.fulltext preprint cristin.qualitycode 2
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