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Idealised flow past an island in a dynamically adaptive finite element model

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Abstract

The problem of flow separation around islands is investigated using a dynamically adaptive finite element model to allow for resolution of the shear layers that form in the advent of separation. The changes in secondary circulation and vertical motion that occur in both attached and separated flows are documented, as is the degree of closure of the wake eddies. In the numerical experiments presented, the strongest motion always takes place at the sides of the idealised island, where flow curvature and shear act together to induce ascent. In contrast, it is the slower motion within the wake eddies that allow streamlines to extend from the bottom to the surface. We find no evidence for closure of the wake eddies. Rather, all of our separated experiments show that streamlines that pass through the eddies originate outside of the shear layers and frictional boundary layers on the upstream side of the idealised island. The numerical experiments demonstrate the potential for dynamically adaptive, unstructured meshes to resolve the separated shear layers that occur downstream of the idealised island, as well as the narrow boundary layers that form on the island itself.

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Notes

  1. Typically, one expects that U ~ WH/L, as a simple scaling of the continuity equation suggests.

  2. All of the model results in Sections 4 and 5 are snapshots taken after 50 nondimensional time-units, when the flow has had more than sufficient time to reach the end of the domain. For the attached flow results of Section 4, this corresponds to a final steady state. For the separated flow results of Section 5, the final state is typically steady at Re L < 1000. When Re L ≥ 1000, the model reaches a quasi-steady state in which small fluctuations in the wake are present far from the idealised island.

  3. At least over the sub-domains shown in Fig. 7. As Fig. 2c, in Section 3, demonstrates, much larger edge lengths occur in the horizontal plane well away from the idealised island.

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Acknowledgements

This work was funded by the UK Natural Environment Research Council under grant number NER/A/S/2003/00595/2. The comments of two anonymous reviewers led to significant improvement in the manuscript as a whole.

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Authors and Affiliations

  1. Atmospheric, Oceanic and Planetary Physics, Department of Physics, University of Oxford, Oxford, OX1 3PU, UK

    David R. Munday & David P. Marshall

  2. Grantham Institute for Climate Change & Applied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College London, London, SW7 2AZ, UK

    Matthew D. Piggott

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  1. David R. Munday
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  2. David P. Marshall
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Correspondence to David R. Munday.

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Munday, D.R., Marshall, D.P. & Piggott, M.D. Idealised flow past an island in a dynamically adaptive finite element model. Ocean Dynamics 60, 835–850 (2010). https://doi.org/10.1007/s10236-010-0291-5

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