Goldsmith, Edward;
(2022)
The method of homogenisation as a means to parameterise small-scale processes in the ocean and atmosphere.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
The first part of this thesis examines how finite-amplitude, small-scale topography affects small-amplitude motions in the ocean. The technique of homogenisation is used to develop an ‘averaged’ system based on the rotating shallow water equations in the presence of topography with horizontal extent much less than the wavelengths of the long waves in question. The extent to which the dispersion relations of Poincaré, Kelvin and Rossby waves are modified from their flat-bottomed counterparts is illuminated, using a range of numerical and analytical techniques. 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. We find formulae for the approximate frequency change for all three wave types, with a particularly simple analytic expression for the Rossby wave dispersion relation, extending previous results from the quasi-geostrophic regime. In addition to this, the manner in which trapped topographic Rossby waves affect the dispersion relations for a finite topography is illuminated. The second part examines the propagation of atmospheric waves through a small-scale convective cloud field. The method of homogenisation reveals that the small-scale clouds act to vertically redistribute the horizontal momentum and buoyancy profiles of the large-scale flow. Mathematically, this occurs due to the presence of non-local integral operators involving ‘transilient kernels’ in the homogenised equations. The dispersion relations are plotted for some of the wave modes propagating in a mid-latitude β -channel, which show that the cloud field slows the baroclinic waves, with low-frequency waves most affected.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | The method of homogenisation as a means to parameterise small-scale processes in the ocean and atmosphere |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2022. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | 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 UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10153542 |
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