In this dissertation we prove various analytic results for the Navier--Stokes-αβ equations. We establish well-posedness and regularity. In addition we determine estimates for the nodal distance and the number of determining modes. A method of averaging is developed and applied to derive a Kaman--Howarth type equation for the Navier--Stokes-αβ equations. Finally we investigate an anisotropic generalization of the Navier--Stokes-αβ equations. We show that the eigenvalues of the moment of inertia tensor convect with the flow and we derive energy type inequalities for the equations.
","abstract_html":"<p>In this dissertation we prove various analytic results for the Navier--Stokes-αβ equations. We establish well-posedness and regularity. In addition we determine estimates for the nodal distance and the number of determining modes. A method of averaging is developed and applied to derive a Kaman--Howarth type equation for the Navier--Stokes-αβ equations. Finally we investigate an anisotropic generalization of the Navier--Stokes-αβ equations. We show that the eigenvalues of the moment of inertia tensor convect with the flow and we derive energy type inequalities for the equations.</p>","abstract_has_math":false,"creators":["Brady, Joshua John"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Renato Feres"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-05-24T07:00:00Z","date_published":"2012-05-24T07:00:00Z","updated_at":"2026-07-24T06:12:25Z","subjects":["Modes","Navier","Nodes","Stokes","Turbulence","Well-posedness"],"languages":["English (en)"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7936/K73776TG"],"render_values":[{"text":"https://doi.org/10.7936/K73776TG","href":"https://doi.org/10.7936/K73776TG","code":true}]}]},"links":{"outbound_url":"https://openscholarship.wustl.edu/etd/943","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Renato Feres"]},{"key":"dc:creator","label":"Author","values":["Brady, Joshua John"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2012-05-24T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Modes","Navier","Nodes","Stokes","Turbulence","Well-posedness"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English (en)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://openscholarship.wustl.edu/etd/943"]},{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7936/K73776TG"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this dissertation we prove various analytic results for the Navier--Stokes-αβ equations. We establish well-posedness and regularity. In addition we determine estimates for the nodal distance and the number of determining modes. A method of averaging is developed and applied to derive a Kaman--Howarth type equation for the Navier--Stokes-αβ equations. Finally we investigate an anisotropic generalization of the Navier--Stokes-αβ equations. We show that the eigenvalues of the moment of inertia tensor convect with the flow and we derive energy type inequalities for the equations.
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