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The interaction of internal wave groups with a uniform sloping boundary

Published online by Cambridge University Press:  26 February 2021

S.A. Thorpe Open the ORCID record for S.A. Thorpe [Opens in a new window]
S.A. Thorpe*
Affiliation:
School of Ocean Sciences, Bangor University, Menai Bridge, AngleseyLL59 5AB, UK
*
Email address for correspondence: oss413@bangor.ac.uk
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Abstract

Internal wave groups are modified by reflection from a uniform slope. At small values of the azimuth angle, θI, of a group approaching a slope the group's volume is decreased on reflection, but at sufficiently large θI volume increases. Group shape is also generally changed on reflection. Wave breaking can be driven by resonant interactions between the incident and reflecting waves or through convective and Kelvin–Helmholtz instability (CI and KHI) of steepening internal waves. Breaking through resonant interactions can occur only in a boundary layer within which incident and reflected groups co-exist. This imposes conditions that depend on the dimensions of incident groups, which may be severe requiring extremely large aspect ratios and implying that in practice the breaking of internal waves in groups incident on or reflected from a slope through CI and KHI often contributes more than resonant wave–wave interactions to mixing near a sloping boundary. Wave breaking associated with self-induced instability of waves in groups will have a greater and possibly more extensive effect on the boundary layer over a slope when the direction in which groups of waves continue to break is close to the up-slope direction of the boundary in the plane of the waves, the effective slope. This is possible only at the small slope angles which are typical of the oceanic continental slopes. Over these slopes internal wave breaking may contribute significantly to the diapycnal mixing of the deep ocean.

JFM classification

Turbulent Flows: Stratified turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 913 , 25 April 2021 , A23
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

†

Present address: 1A, Green Edge, Beaumaris, Anglesey LL58 8BY, UK.

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