Chaos in models of double convection

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.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

1991

Author dc:creator

• Rucklidge, Alastair Michael

Advisor dc:contributor.advisor

• Weiss, Nigel

• Double convection

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/6ab05a5e-ee2c-48a8-a316-8d85a9e791d1/download
• https://www.rioxx.net/licenses/all-rights-reserved/

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.106429

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/364970