{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/134980"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/134980","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Numerical and Theoretical Developments for Coherent Structures","abstract":"The field of nonautonomous dynamical systems has undergone an exceptional amount of growth over the last few decades, with the geometric viewpoint leading to the development of Lagrangian and objective Eulerian coherent structures. This theory extends notions developed for autonomous systems to those that may have arbitrary dependence on time and whose flow data may not be known or available for all time. The structures obtained from this theory are material surfaces that have an exceptional effect on the contents of a flow and are key for understanding transport. These structures organize the contents of a flow and lead to a qualitative description of the fate of material under the influence of a flow. While these methods have been adopted in geophysical and engineering applications, the theory is still relatively new. This dissertation aims to contribute to the maturation of this theory and its numerical implementations by providing an efficient and user-friendly software package for these tools, demonstrating the usefulness of these methods on a large-scale transport application, further extending the theory in a specific context, and presenting a new numerical framework for computing LCS from their variational theory.","abstract_html":"The field of nonautonomous dynamical systems has undergone an exceptional amount of growth over the last few decades, with the geometric viewpoint leading to the development of Lagrangian and objective Eulerian coherent structures. This theory extends notions developed for autonomous systems to those that may have arbitrary dependence on time and whose flow data may not be known or available for all time. The structures obtained from this theory are material surfaces that have an exceptional effect on the contents of a flow and are key for understanding transport. These structures organize the contents of a flow and lead to a qualitative description of the fate of material under the influence of a flow. While these methods have been adopted in geophysical and engineering applications, the theory is still relatively new. This dissertation aims to contribute to the maturation of this theory and its numerical implementations by providing an efficient and user-friendly software package for these tools, demonstrating the usefulness of these methods on a large-scale transport application, further extending the theory in a specific context, and presenting a new numerical framework for computing LCS from their variational theory.","abstract_has_math":false,"creators":["Jarvis, Albert Joseph"],"institution":"Virginia Tech","degree_name":"Doctor of Philosophy","degree_level":"doctoral","degree_discipline":"Engineering Mechanics","degree_department":"Engineering Science and Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Ross, Shane David"],"committee_members":["Bollt, Erik Matthew","Foroutan, Hosein","Iliescu, Traian"],"year":2025,"date_issued":"2025-06-02","date_published":"2025-06-02","updated_at":"2026-07-22T22:18:52Z","subjects":["Time-dependent Dynamical Systems","Lagrangian Coherent Structures","Material transport","Automatic differentiation"],"languages":["en"],"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:43145"],"render_values":[{"text":"vt_gsexam:43145","href":null,"code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10919/134980","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Ross, Shane David"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Bollt, Erik Matthew","Foroutan, Hosein","Iliescu, Traian"]},{"key":"dc:contributor.department","label":"Department","values":["Engineering Science and Mechanics"]},{"key":"dc:creator","label":"Author","values":["Jarvis, Albert Joseph"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-06-03T08:01:53Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-06-03T08:01:53Z"]},{"key":"dc:date.issued","label":"Date","values":["2025-06-02"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering Mechanics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"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":["Time-dependent Dynamical Systems","Lagrangian Coherent Structures","Material transport","Automatic differentiation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"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:43145"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10919/134980"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The field of nonautonomous dynamical systems has undergone an exceptional amount of growth over the last few decades, with the geometric viewpoint leading to the development of Lagrangian and objective Eulerian coherent structures. This theory extends notions developed for autonomous systems to those that may have arbitrary dependence on time and whose flow data may not be known or available for all time. The structures obtained from this theory are material surfaces that have an exceptional effect on the contents of a flow and are key for understanding transport. These structures organize the contents of a flow and lead to a qualitative description of the fate of material under the influence of a flow. While these methods have been adopted in geophysical and engineering applications, the theory is still relatively new. This dissertation aims to contribute to the maturation of this theory and its numerical implementations by providing an efficient and user-friendly software package for these tools, demonstrating the usefulness of these methods on a large-scale transport application, further extending the theory in a specific context, and presenting a new numerical framework for computing LCS from their variational theory."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["Understanding how some material moves through a fluid flow has wide-reaching applications in the physical sciences. Dust or smoke moving through the atmosphere, oil drifting through the ocean, or even a missing person carried by ocean currents can all be studied through the lens of material transport in a fluid flow. When the velocity field that describes the fluid flow does not change in time (time-independent), there is a rich theory dating back over a hundred years that defines key regions and structures in a flow, leading to a qualitative understanding of the fate of material being transported in that flow. However, when the velocity field changes with time (time-dependent) in a complex way, this classical theory falls short, as it was not developed with such flows in mind. These time-dependent flows are the rule rather than the exception in many geophysical applications (like those described above). Over the last few decades, a new theory has been developed to extend many of the notions of the time-independent setting to the more general time-dependent setting. This dissertation aims to contribute to the maturation of this theory and its numerical implementations by providing an efficient and user-friendly software package for these tools, demonstrating the usefulness of these methods on a large-scale transport application, further extending the theory in a specific context, and presenting a new numerical framework for computing certain versions of these structures."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Doctor of Philosophy"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Numerical and Theoretical Developments for Coherent Structures"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Ross, Shane David"],"dc:contributor.committeemember":["Bollt, Erik Matthew","Foroutan, Hosein","Iliescu, Traian"],"dc:contributor.department":["Engineering Science and Mechanics"],"dc:creator":["Jarvis, Albert Joseph"],"dc:date.accessioned":["2025-06-03T08:01:53Z"],"dc:date.available":["2025-06-03T08:01:53Z"],"dc:date.issued":["2025-06-02"],"dc:description.abstract":["The field of nonautonomous dynamical systems has undergone an exceptional amount of growth over the last few decades, with the geometric viewpoint leading to the development of Lagrangian and objective Eulerian coherent structures. This theory extends notions developed for autonomous systems to those that may have arbitrary dependence on time and whose flow data may not be known or available for all time. The structures obtained from this theory are material surfaces that have an exceptional effect on the contents of a flow and are key for understanding transport. These structures organize the contents of a flow and lead to a qualitative description of the fate of material under the influence of a flow. While these methods have been adopted in geophysical and engineering applications, the theory is still relatively new. This dissertation aims to contribute to the maturation of this theory and its numerical implementations by providing an efficient and user-friendly software package for these tools, demonstrating the usefulness of these methods on a large-scale transport application, further extending the theory in a specific context, and presenting a new numerical framework for computing LCS from their variational theory."],"dc:description.abstractgeneral":["Understanding how some material moves through a fluid flow has wide-reaching applications in the physical sciences. Dust or smoke moving through the atmosphere, oil drifting through the ocean, or even a missing person carried by ocean currents can all be studied through the lens of material transport in a fluid flow. When the velocity field that describes the fluid flow does not change in time (time-independent), there is a rich theory dating back over a hundred years that defines key regions and structures in a flow, leading to a qualitative understanding of the fate of material being transported in that flow. However, when the velocity field changes with time (time-dependent) in a complex way, this classical theory falls short, as it was not developed with such flows in mind. These time-dependent flows are the rule rather than the exception in many geophysical applications (like those described above). Over the last few decades, a new theory has been developed to extend many of the notions of the time-independent setting to the more general time-dependent setting. This dissertation aims to contribute to the maturation of this theory and its numerical implementations by providing an efficient and user-friendly software package for these tools, demonstrating the usefulness of these methods on a large-scale transport application, further extending the theory in a specific context, and presenting a new numerical framework for computing certain versions of these structures."],"dc:description.degree":["Doctor of Philosophy"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:43145"],"dc:identifier.uri":["https://hdl.handle.net/10919/134980"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Time-dependent Dynamical Systems","Lagrangian Coherent Structures","Material transport","Automatic differentiation"],"dc:title":["Numerical and Theoretical Developments for Coherent Structures"],"dc:type":["Dissertation"],"thesis:degree_discipline":["Engineering Mechanics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:18:52Z"}