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Chaos in models of double convection https://doi.org/10.17863/CAM.106429 Rucklidge, Alastair Michael Weiss, Nigel This dissertation concentrates on the derivation and analysis of low-order sets of ordinary differential equations (ODEs) that accurately describe the behaviour of a fluid in convective motion. A second-order set of ODEs is presented and analysed, and then related to a particular double convection problem (compressible convection in a vertical magnetic field); the low-order model proves to be useful in interpreting the behaviour of the full system. Equations describing several types of double convection (convection in a magnetic field, convection in a rotating layer of fluid and convection in a solute gradient) are reduced to low-order sets of ODEs that are asymptotically exact descriptions of the partial differential equations (PDEs) from which they were derived. The ODE model for incompressible convection in a vertical magnetic field is analysed in detail, and a rich variety of periodic orbits and chaotic behaviour is found. A numerical study of the full set of PDEs for this case confirms that the low-order model provides an asymptotically correct description of the full problem; in particular, the PDEs have the chaotic solutions predicted by the low-order model. University of Cambridge 1991-11 Thesis Doctoral Doctor of Philosophy (PhD) https://www.repository.cam.ac.uk/handle/1810/364970 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/6ab05a5e-ee2c-48a8-a316-8d85a9e791d1/download eb9d2d75cbfff5683a827dd2229be5c0 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/ca79f6a2-cce1-4e46-b0ab-bb7b1b193644/download f0c6e99c02125461325cca1029bad274 https://www.rioxx.net/licenses/all-rights-reserved/ Double convection