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Wave propagation in rotating shallow water in the presence of small-scale topography

Goldsmith, EJ; Esler, JG; (2021) Wave propagation in rotating shallow water in the presence of small-scale topography. Journal of Fluid Mechanics , 923 , Article A24. 10.1017/jfm.2021.573. Green open access

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Abstract

The question of how finite-amplitude, small-scale topography affects small-amplitude motions in the ocean is addressed in the framework of the rotating shallow water equations. The extent to which the dispersion relations of Poincaré, Kelvin and Rossby waves are modified in the presence of topography is illuminated, using a range of numerical and analytical techniques based on the method of homogenisation. Both random and regular periodic arrays of topography are considered, with the special case of regular cylinders studied in detail, because this case allows for highly accurate analytical results. The results show that, for waves in a β-channel bounded by sidewalls, and for steep topographies outside of the quasi-geostrophic regime, topography acts to slow Poincaré waves slightly, Rossby waves are slowed significantly and Kelvin waves are accelerated for long waves and slowed for short waves, with the two regimes being separated by a narrow band of resonant wavelengths. The resonant band, which is due to the excitation of trapped topographic Rossby waves on each seamount, may affect any of the three wave types under the right conditions, and for physically reasonable results requires regularisation by Ekman friction. At larger topographic amplitudes, for cylindrical topography, a simple and accurate formula is given for the correction to the Rossby wave dispersion relation, which extends previous results for the quasi-geostrophic regime.

Type: Article
Title: Wave propagation in rotating shallow water in the presence of small-scale topography
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/jfm.2021.573
Publisher version: http://dx.doi.org/10.1017/jfm.2021.573
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: shallow water flows, topographic effects, rotating flows, BRAGG SCATTERING, ROSSBY WAVES, PLANE, ARRAY
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/10139159
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