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Internal solitary wave-induced flow over a corrugated bed

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Abstract

A combined numerical and experimental study of the propagation of an internal solitary wave (ISW) over a corrugated bed is presented, in which the amplitude and the wavelength of the corrugated bed, together with the wave amplitude and wave speed of the ISW, have been varied parametrically. Both ISWs of elevation and depression have been considered. The wave-induced currents over the corrugated bed cause flow separation at the apex of the corrugations and a sequence of lee vortices forms as a result. These vortices develop fully after the main wave has passed over the topographic feature, resulting in deformation of the overlying pycnocline and, in some instances, significant vertical mixing. It is found that the intensity of the vortex formation is dependent on both the amplitude and wavelength of the bottom topography. In the case of an ISW of depression, the generation of vertically (upward)-propagating vortices is seen to result in entrainment of fluid from a bottom boundary jet (Carr and Davies, Phys Fluids 18:016601, 2006), while, in the elevation case, a second mechanism is present to induce significant turbulent mixing in the water column. It occurs when the bottom corrugations reach into, or are very near, the pycnocline at rest. Large waves of elevation that are stable on approach to the corrugations exhibit evidence of a spatio-temporally developing shear instability as they interact with the bottom corrugation. The shear instability takes the form of billows that have a vertical extent that can reach 50% of the wave amplitude.

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Notes

  1. According to one anonymous reviewer of this paper, recent acoustic studies in the Northern South China Sea have identified sand-dunes in 400 to 600 m deep water that are 16 m tall and 100 m wide. These are the tallest sand dunes ever observed.

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Acknowledgements

This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) under its Physics-Engineering Programme and the Natural Sciences and Engineering Research Council of Canada. Invaluable technical support was provided at the University of Dundee by John Anderson and Gary Conacher. Helpful discussions with Stuart Dalziel and John Grue on aspects of the work are acknowledged with gratitude. The authors would like to thank two anonymous referees whose comments have led to improvements in the paper. The authors are pleased to contribute to this Special Issue in honour of Professor Gjevik in recognition of his outstanding achievements as a scientist and ambassador for his subject.

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Authors and Affiliations

  1. School of Mathematics & Statistics, University of St Andrews, St Andrews, KY16 9SS, UK

    Magda Carr

  2. Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Marek Stastna

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

    Peter A. Davies

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  1. Magda Carr
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  2. Marek Stastna
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  3. Peter A. Davies
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Correspondence to Magda Carr.

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Responsible Editor: John Grue

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Carr, M., Stastna, M. & Davies, P.A. Internal solitary wave-induced flow over a corrugated bed. Ocean Dynamics 60, 1007–1025 (2010). https://doi.org/10.1007/s10236-010-0286-2

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