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The interaction of a mode-1 internal solitary wave with a step and the generation of mode-2 waves

Liu, Z; Grimshaw, R; Johnson, E; (2019) The interaction of a mode-1 internal solitary wave with a step and the generation of mode-2 waves. Geophysical & Astrophysical Fluid Dynamics , 113 (4) pp. 327-347. 10.1080/03091929.2019.1636046. Green open access

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Abstract

In this study we examine the transformation of a mode-1 internal solitary wave incident on a bottom step, and the consequent generation of mode-2 internal solitary waves. A linear long wave theory of mode coupling in the vicinity of the step is used to estimate the mode-1 and mode-2 wave reflection and transmission coefficients, and hence the energy fluxes. Away from the step, the wave evolution of the transmitted and reflected waves is simulated by the Korteweg-de Vries equation. Specific calculations are made using a three-layer fluid model. Three different regimes based on the layer thicknesses are examined and discussed in detail, for either depression or elevation mode-1 incident waves. The common features found are that the transmitted waves (mainly mode-1) are the dominant part; most of the incident energy is transmitted and only a small part is reflected. The amplitudes of the generated mode-2 waves and the reflected mode-1 waves increase, when either the upper or middle layer thickness increases. When the lower layer is thin enough, the amplitude of the transmitted mode-2 wave can be larger than the mode-1 waves and the reflected energy can increase considerably which we infer may be due to a blocking effect of the step on the lower layer. The evolution away from the step is either fission into several solitary waves, or the development of a rarefaction wave followed by an undular bore, depending on the relative signs of the wave amplitudes and the nonlinear coefficient in the Korteweg-de Vries equation

Type: Article
Title: The interaction of a mode-1 internal solitary wave with a step and the generation of mode-2 waves
Open access status: An open access version is available from UCL Discovery
DOI: 10.1080/03091929.2019.1636046
Publisher version: https://doi.org/10.1080/03091929.2019.1636046
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Internal solitary waves; three-layer fluid; linear long wave theory; Korteweg-de Vries equation; mode-2 wave generation
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Chemical Engineering
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10079919
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