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Generation of mode 2 internal waves by the interaction of mode 1 waves with topography

Published online by Cambridge University Press:  18 October 2019

Zihua Liu Open the ORCID record for Zihua Liu [Opens in a new window] ,
Roger Grimshaw Open the ORCID record for Roger Grimshaw [Opens in a new window]  and
Edward Johnson Open the ORCID record for Edward Johnson [Opens in a new window]
Zihua Liu*
Affiliation:
Department of Mathematics, University College London, London, WC1E 6BT, UK
Roger Grimshaw
Affiliation:
Department of Mathematics, University College London, London, WC1E 6BT, UK
Edward Johnson
Affiliation:
Department of Mathematics, University College London, London, WC1E 6BT, UK
*
†Email address for correspondence: zihua.liu.15@ucl.ac.uk
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Abstract

Oceanic internal waves can be decomposed into an infinite set of modes, and the dominant internal mode 1 waves have been extensively investigated. Although mode 2 waves have been observed, they have not received comparable attention, especially the generation mechanisms. In this work, we examine the generation of mode 2 internal waves by the interaction of mode 1 waves with topography. We use a coupled linear long-wave theory with mode coupling through topography, combined with evolution using a Korteweg–de Vries model, to predict the mode 2 wave amplitude, in an ideal three-layer fluid model, in a smooth density stratification and in two realistic oceanic settings. We find that the mode 2 wave amplitude is usually much smaller than the incident mode 1 wave amplitude and is quite sensitive to the pycnocline thickness, topographic slope and background stratification.

JFM classification

Geophysical and Geological Flows: Internal waves Waves/Free-surface Flows: Solitary waves Geophysical and Geological Flows: Topographic effects
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 880 , 10 December 2019 , pp. 799 - 830
Copyright
© 2019 Cambridge University Press 

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