{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/364970"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/364970","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Chaos in models of double convection","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Rucklidge, Alastair Michael"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Weiss, Nigel"],"committee_chairs":[],"committee_members":[],"year":1991,"date_issued":"1991-11","date_published":"1991-11","updated_at":"2026-07-22T22:24:27Z","subjects":["Double convection"],"languages":[],"rights":[],"rights_urls":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/6ab05a5e-ee2c-48a8-a316-8d85a9e791d1/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.106429","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Weiss, Nigel"]},{"key":"dc:creator","label":"Author","values":["Rucklidge, Alastair Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["1991-11"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/364970"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Double convection"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/6ab05a5e-ee2c-48a8-a316-8d85a9e791d1/download","https://www.rioxx.net/licenses/all-rights-reserved/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.17863/CAM.106429"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/ca79f6a2-cce1-4e46-b0ab-bb7b1b193644/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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. 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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."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["eb9d2d75cbfff5683a827dd2229be5c0","f0c6e99c02125461325cca1029bad274"]},{"key":"dc:title","label":"Title","values":["Chaos in models of double convection"]}]}],"canonical_facts":{"dc:contributor.advisor":["Weiss, Nigel"],"dc:creator":["Rucklidge, Alastair Michael"],"dc:date.issued":["1991-11"],"dc:description.abstract":["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. 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