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Internal wave generation by tidal flow over a two-dimensional ridge: energy flux asymmetries induced by a steady surface trapped current

Published online by Cambridge University Press:  11 December 2017

Kevin G. Lamb Open the ORCID record for Kevin G. Lamb [Opens in a new window]  and
M. Dunphy
Kevin G. Lamb*
Affiliation:
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
M. Dunphy
Affiliation:
Institute of Ocean Sciences, Fisheries and Oceans Canada, Sidney, British Columbia, Canada V8L 4B2
*
†Email address for correspondence: kglamb@uwaterloo.ca
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Abstract

The effects of a surface trapped steady background current on internal waves generated by tidal currents oscillating over a small symmetric ridge are investigated using a two-dimensional primitive equation model. A rigid lid is used with a linearly stratified fluid and the effects of rotation are not considered. We consider uni-directional background currents $\bar{U}(z)\geqslant 0$ confined to a surface layer lying well above the ridge. The current introduces asymmetries in the generated wave field. For sufficiently narrow ridges the upstream energy flux is larger than the downstream flux while the opposite is the case for sufficiently wide ridges. The total energy flux radiating away from the ridge is not significantly affected by the current. Mean second-order currents and pressure fields are shown to make important contributions to the total energy flux. A first-order linear theory, valid for a general stratification and surface current, which accurately predicts the wave field is also developed.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 836 , 10 February 2018 , pp. 192 - 221
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Copyright
© 2017 Cambridge University Press 

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