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Numerical simulation of internal solitary wave—induced reverse flow and associated vortices in a shallow, two-layer fluid benthic boundary layer

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Abstract

The wave-induced velocity and pressure fields beneath a large amplitude internal solitary wave of depression propagating over a smooth, flat, horizontal, and rigid boundary in a shallow two-layer fluid are computed numerically. A numerical ocean model is utilised, the set-up of which is designed and tuned to replicate the previously published experimental results of Carr and Davies (Phys Fluids 18(1):016,601–1–016,601–10, 2006). Excellent agreement is found between the two data sets and, in particular, the numerical simulation replicates the finding of a reverse flow along the bed aft of the wave. The numerically computed velocity and pressure gradients confirm that the occurrence of the reverse flow is a consequence of boundary layer separation in the adverse pressure gradient region. In addition, vortices associated with the reverse flow are seen to form near the bed.

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Acknowledgements

This research is a result of the contribution given from the University of Bergen (Legacy and foundation) for inviting Magda Carr and Peter Davies to Norway, and the two Norwegian Research Council projects Cordino (NFR 146526/420) and Ecorais (NFR 190474/s40). Figures 3a, 4a and 5a have been reprinted with permission from Carr and Davies (2006) The motion of an internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid. Physics of Fluids 18(1):016601-01–016601-10. Copyright 2006, American Institute of Physics. The authors would like to thank two anonymous reviewers for constructive comments, which led to an improvement of the paper.

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Authors and Affiliations

  1. The Bergen Center for Computational Science, Uni Research, Thormøhlensgt. 55, 5008, Bergen, Norway

    Øyvind Thiem

  2. Department of Mathematics, University of Bergen, Johannes Bruns gt. 12, 5008, Bergen, Norway

    Jarle Berntsen

  3. School of Mathematics and Statistics, University of St. Andrews, St. Andrews, KY16 9SS, UK

    Magda Carr

  4. Department of Civil Engineering, University of Dundee, Dundee, DD1 4HN, UK

    Peter A. Davies

Authors
  1. Øyvind Thiem
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  2. Magda Carr
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  3. Jarle Berntsen
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  4. Peter A. Davies
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Correspondence to Øyvind Thiem.

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Responsible Editor: Phil Peter Dyke

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Thiem, Ø., Carr, M., Berntsen, J. et al. Numerical simulation of internal solitary wave—induced reverse flow and associated vortices in a shallow, two-layer fluid benthic boundary layer. Ocean Dynamics 61, 857–872 (2011). https://doi.org/10.1007/s10236-011-0396-5

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