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On diffraction and oblique interactions of horizontally two-dimensional internal solitary waves

Published online by Cambridge University Press:  11 February 2022

Chunxin Yuan Open the ORCID record for Chunxin Yuan [Opens in a new window]  and
Zhan Wang Open the ORCID record for Zhan Wang [Opens in a new window]
Chunxin Yuan
Affiliation:
School of Mathematical Sciences, Ocean University of China, Qingdao 266100, PR China
Zhan Wang*
Affiliation:
Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China School of Future Technology, University of Chinese Academy of Sciences, Beijing 100049, PR China
*
†Email address for correspondence: zwang@imech.ac.cn
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Abstract

In the context of three-dimensional oceanic internal waves, taking topographic effects into account, a modified Benney–Luke equation is proposed for describing internal wave–wave interactions on a sloping bottom. The derived equation is characterised by isotropy and bi-directional propagation, which are absent in the widely used Kadomtsev–Petviashvili equation. Indeed, these disparities are confirmed by numerical results of the diffraction of a truncated internal solitary wave and the evolution of a partially bent solitary wave. However, a good agreement between the numerical results of the modified Benney–Luke equation and those of the primitive equations confirms the validity of our simplified model. Because the stratification in a realistic ocean environment is usually continuous, in contrast to the assumption of a sharp density discontinuity used here, to maintain the kinematical equivalence, a layering scheme for determining the density and thickness of each layer from a continuous stratification is proposed. In addition, the occasionally observed but rarely examined X-shaped internal wave–wave interactions are shown to feature novel wave patterns, where topographic effects modulate the propagation speed, amplitude and waveform.

JFM classification

Geophysical and Geological Flows: Internal waves Waves/Free-surface Flows: Solitary waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 936 , 10 April 2022 , A20
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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