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.
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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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