{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/51806"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/51806","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Active Transport in Chaotic Rayleigh-Bénard Convection","abstract":"The transport of a species in complex flow fields is an important phenomenon related to many areas in science and engineering. There has been significant progress theoretically and experimentally in understanding active transport in steady, periodic flows such as a chain of vortices but many open questions remain for transport in complex and chaotic flows. This thesis investigates the active transport in a three-dimensional, time-dependent flow field characterized by a spatiotemporally chaotic state of Rayleigh-Be?nard convection. A nonlinear Fischer-Kolmogorov-Petrovskii-Piskunov reaction is selected to study the transport within these flows. A highly efficient, parallel spectral element approach is employed to solve the Boussinesq and the reaction-advection-diffusion equations in a spatially-extended cylindrical domain with experimentally relevant boundary conditions. The transport is quantified using statistics of spreading and in terms of active transport characteristics like front speed and geometry and are compared with those results for transport in steady flows found in the literature. The results of the simulations indicate an anomalous diffusion process with a power law 2 < ? < 5/2 a result that deviates from other superdiffusive processes in simpler flows, and reveals that the presence of spiral defect chaos induces strongly anomalous transport. Additionally, transport was found to most likely occur in a direction perpendicular to a convection roll in the flow field. The presence of the spiral defect chaos state of the fluid convection is found to enhance the front perimeter by t^3/2 and by a perimeter enhancement ratio r(p) = 2.3.","abstract_html":"The transport of a species in complex flow fields is an important phenomenon related to many areas in science and engineering. There has been significant progress theoretically and experimentally in understanding active transport in steady, periodic flows such as a chain of vortices but many open questions remain for transport in complex and chaotic flows. This thesis investigates the active transport in a three-dimensional, time-dependent flow field characterized by a spatiotemporally chaotic state of Rayleigh-Be?nard convection. A nonlinear Fischer-Kolmogorov-Petrovskii-Piskunov reaction is selected to study the transport within these flows. A highly efficient, parallel spectral element approach is employed to solve the Boussinesq and the reaction-advection-diffusion equations in a spatially-extended cylindrical domain with experimentally relevant boundary conditions. The transport is quantified using statistics of spreading and in terms of active transport characteristics like front speed and geometry and are compared with those results for transport in steady flows found in the literature. The results of the simulations indicate an anomalous diffusion process with a power law 2 &lt; ? &lt; 5/2 a result that deviates from other superdiffusive processes in simpler flows, and reveals that the presence of spiral defect chaos induces strongly anomalous transport. Additionally, transport was found to most likely occur in a direction perpendicular to a convection roll in the flow field. The presence of the spiral defect chaos state of the fluid convection is found to enhance the front perimeter by t^3/2 and by a perimeter enhancement ratio r(p) = 2.3.","abstract_has_math":false,"creators":["Mehrvarzi, Christopher Omid"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mechanical Engineering","degree_department":"Mechanical Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Paul, Mark R."],"committee_members":["Tafti, Danesh K.","Behkam, Bahareh"],"year":2014,"date_issued":"2014-01-13","date_published":"2014-01-13","updated_at":"2026-07-22T22:18:41Z","subjects":["Transport","Rayleigh-Bénard convection","Spatiotemporal chaos"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:1950"],"render_values":[{"text":"vt_gsexam:1950","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/51806","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Paul, Mark R."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Tafti, Danesh K.","Behkam, Bahareh"]},{"key":"dc:contributor.department","label":"Department","values":["Mechanical Engineering"]},{"key":"dc:creator","label":"Author","values":["Mehrvarzi, Christopher Omid"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-04-25T08:01:35Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-04-25T08:01:35Z"]},{"key":"dc:date.issued","label":"Date","values":["2014-01-13"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Transport","Rayleigh-Bénard convection","Spatiotemporal chaos"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:1950"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/51806"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The transport of a species in complex flow fields is an important phenomenon related to many areas in science and engineering. There has been significant progress theoretically and experimentally in understanding active transport in steady, periodic flows such as a chain of vortices but many open questions remain for transport in complex and chaotic flows. This thesis investigates the active transport in a three-dimensional, time-dependent flow field characterized by a spatiotemporally chaotic state of Rayleigh-Be?nard convection. A nonlinear Fischer-Kolmogorov-Petrovskii-Piskunov reaction is selected to study the transport within these flows. A highly efficient, parallel spectral element approach is employed to solve the Boussinesq and the reaction-advection-diffusion equations in a spatially-extended cylindrical domain with experimentally relevant boundary conditions. The transport is quantified using statistics of spreading and in terms of active transport characteristics like front speed and geometry and are compared with those results for transport in steady flows found in the literature. The results of the simulations indicate an anomalous diffusion process with a power law 2 < ? < 5/2 a result that deviates from other superdiffusive processes in simpler flows, and reveals that the presence of spiral defect chaos induces strongly anomalous transport. Additionally, transport was found to most likely occur in a direction perpendicular to a convection roll in the flow field. The presence of the spiral defect chaos state of the fluid convection is found to enhance the front perimeter by t^3/2 and by a perimeter enhancement ratio r(p) = 2.3."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Active Transport in Chaotic Rayleigh-Bénard Convection"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Paul, Mark R."],"dc:contributor.committeemember":["Tafti, Danesh K.","Behkam, Bahareh"],"dc:contributor.department":["Mechanical Engineering"],"dc:creator":["Mehrvarzi, Christopher Omid"],"dc:date.accessioned":["2015-04-25T08:01:35Z"],"dc:date.available":["2015-04-25T08:01:35Z"],"dc:date.issued":["2014-01-13"],"dc:description.abstract":["The transport of a species in complex flow fields is an important phenomenon related to many areas in science and engineering. There has been significant progress theoretically and experimentally in understanding active transport in steady, periodic flows such as a chain of vortices but many open questions remain for transport in complex and chaotic flows. This thesis investigates the active transport in a three-dimensional, time-dependent flow field characterized by a spatiotemporally chaotic state of Rayleigh-Be?nard convection. A nonlinear Fischer-Kolmogorov-Petrovskii-Piskunov reaction is selected to study the transport within these flows. A highly efficient, parallel spectral element approach is employed to solve the Boussinesq and the reaction-advection-diffusion equations in a spatially-extended cylindrical domain with experimentally relevant boundary conditions. The transport is quantified using statistics of spreading and in terms of active transport characteristics like front speed and geometry and are compared with those results for transport in steady flows found in the literature. The results of the simulations indicate an anomalous diffusion process with a power law 2 < ? < 5/2 a result that deviates from other superdiffusive processes in simpler flows, and reveals that the presence of spiral defect chaos induces strongly anomalous transport. Additionally, transport was found to most likely occur in a direction perpendicular to a convection roll in the flow field. The presence of the spiral defect chaos state of the fluid convection is found to enhance the front perimeter by t^3/2 and by a perimeter enhancement ratio r(p) = 2.3."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:1950"],"dc:identifier.uri":["http://hdl.handle.net/10919/51806"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Transport","Rayleigh-Bénard convection","Spatiotemporal chaos"],"dc:title":["Active Transport in Chaotic Rayleigh-Bénard Convection"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:18:41Z"}