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Topographic effect on oblique internal wave–wave interactions

Published online by Cambridge University Press:  28 September 2018

C. Yuan Open the ORCID record for C. Yuan [Opens in a new window] ,
R. Grimshaw Open the ORCID record for R. Grimshaw [Opens in a new window] ,
E. Johnson Open the ORCID record for E. Johnson [Opens in a new window]  and
Z. Wang Open the ORCID record for Z. Wang [Opens in a new window]
C. Yuan*
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
R. Grimshaw
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
E. Johnson
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
Z. Wang
Affiliation:
Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
*
†Email address for correspondence: [email protected]
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Abstract

Based on a variable-coefficient Kadomtsev–Petviashvili (KP) equation, the topographic effect on the wave interactions between two oblique internal solitary waves is investigated. In the absence of rotation and background shear, the model set-up featuring idealised shoaling topography and continuous stratification is motivated by the large expanse of continental shelf in the South China Sea. When the bottom is flat, the evolution of an initial wave consisting of two branches of internal solitary waves can be categorised into six patterns depending on the respective amplitudes and the oblique angles measured counterclockwise from the transverse axis. Using theoretical multi-soliton solutions of the constant-coefficient KP equation, we select three observed patterns and examine each of them in detail both analytically and numerically. The effect of shoaling topography leads to a complicated structure of the leading waves and the emergence of two types of trailing wave trains. Further, the case when the along-crest width is short compared with the transverse domain of interest is examined and it is found that although the topographic effect can still modulate the wave field, the spreading effect in the transverse direction is dominant.

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 856 , 10 December 2018 , pp. 36 - 60
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Copyright
© 2018 Cambridge University Press 

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