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The propagation of internal undular bores over variable topography

Grimshaw, R; Yuan, C; (2016) The propagation of internal undular bores over variable topography. Physica D: Nonlinear Phenomena , 333 pp. 200-207. 10.1016/j.physd.2016.01.006. Green open access

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Abstract

In the coastal ocean, large amplitude, horizontally propagating internal wave trains are commonly observed. These are long nonlinear waves and can be modelled by equations of the Korteweg–de Vries type. Typically they occur in regions of variable bottom topography when the variable-coefficient Korteweg–de Vries equation is an appropriate model. Of special interest is the situation when the coefficient of the quadratic nonlinear term changes sign at a certain critical point. This case has been widely studied for a solitary wave, which is extinguished at the critical point and replaced by a train of solitary waves of the opposite polarity to the incident wave, riding on a pedestal of the original polarity. Here we examine the same situation for an undular bore, represented by a modulated periodic wave train. Numerical simulations and some asymptotic analysis based on Whitham modulation equations show that the leading solitary waves in the undular bore are destroyed and replaced by a developing rarefaction wave supporting emerging solitary waves of the opposite polarity. In contrast the rear of the undular bore emerges with the same shape, but with reduced wave amplitudes, a shorter overall length scale and moves more slowly.

Type: Article
Title: The propagation of internal undular bores over variable topography
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.physd.2016.01.006
Publisher version: https://doi.org/10.1016/j.physd.2016.01.006
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: Whitham modulation theory, Undular bores, Internal waves change of polarity
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
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/10051741
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