{"id":{"repo_id":"njit","oai_identifier":"oai:digitalcommons.njit.edu:dissertations-1958"},"canonical_url":"https://search.dev.ndltd.org/etd/njit/oai:digitalcommons.njit.edu:dissertations-1958","repository":{"repo_id":"njit","name":"NJIT","base_url":"https://digitalcommons.njit.edu/do/oai/"},"display":{"title":"Self similar flows in finite or infinite two dimensional geometries","abstract":"This study is concerned with several problems related to self-similar flows in pulsating channels. Exact or similarity solutions of the Navier-Stokes equations are of practical and theoretical importance in fluid mechanics. The assumption of self-similarity of the solutions is a very attractive one from both a theoretical and a practical point of view. It allows us to greatly simplify the Navier-Stokes equations into a single nonlinear one-dimensional partial differential equation (or ordinary differential equation in the case of steady flow) whose solutions are also exact solutions of the Navier-Stokes equations in the sense that no approximations are required in order to calculate them. One common characteristic to all applications of self-similar flows in real problems is that they involve fluid domains with large aspect ratios. Self-similar flows are admissible solutions of the Navier-Stokes equations in unbounded domains, and in applications it is assumed that the effects of the boundary conditions at the edge of the domain will have only a local effect and that a self- similar solution will be valid in most of the fluid domain. However, it has been shown that some similarity flows exist only under a very restricted set of conditions which need to be inferred from numerical simulations. Our main interest is to study several self-similar solutions related to flows in oscillating channels and to investigate the hypothesis that these solutions are reasonable approximations to Navier-Stokes flows in long, slender but finite domains.","abstract_html":"This study is concerned with several problems related to self-similar flows in pulsating channels. Exact or similarity solutions of the Navier-Stokes equations are of practical and theoretical importance in fluid mechanics. The assumption of self-similarity of the solutions is a very attractive one from both a theoretical and a practical point of view. It allows us to greatly simplify the Navier-Stokes equations into a single nonlinear one-dimensional partial differential equation (or ordinary differential equation in the case of steady flow) whose solutions are also exact solutions of the Navier-Stokes equations in the sense that no approximations are required in order to calculate them. One common characteristic to all applications of self-similar flows in real problems is that they involve fluid domains with large aspect ratios. Self-similar flows are admissible solutions of the Navier-Stokes equations in unbounded domains, and in applications it is assumed that the effects of the boundary conditions at the edge of the domain will have only a local effect and that a self- similar solution will be valid in most of the fluid domain. However, it has been shown that some similarity flows exist only under a very restricted set of conditions which need to be inferred from numerical simulations. Our main interest is to study several self-similar solutions related to flows in oscillating channels and to investigate the hypothesis that these solutions are reasonable approximations to Navier-Stokes flows in long, slender but finite domains.","abstract_has_math":false,"creators":["Espin Estevez, Leonardo Xavier"],"institution":null,"degree_name":"Doctor of Philosophy in Mathematical Sciences - (Ph.D.)","degree_level":null,"degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":["Demetrius T. Papageorgiou","Linda Jane Cummings","Peter G. Petropoulos"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009-05-31T07:00:00Z","date_published":"2009-05-31T07:00:00Z","updated_at":"2026-07-24T03:23:09Z","subjects":["Applied math","Exact solutions","Fluid dynamics","Self-similar solutions","Numerical simulations","Stability analysis","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.njit.edu/dissertations/903","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Demetrius T. Papageorgiou","Linda Jane Cummings","Peter G. 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Exact or similarity solutions of the Navier-Stokes equations are of practical and theoretical importance in fluid mechanics. The assumption of self-similarity of the solutions is a very attractive one from both a theoretical and a practical point of view. It allows us to greatly simplify the Navier-Stokes equations into a single nonlinear one-dimensional partial differential equation (or ordinary differential equation in the case of steady flow) whose solutions are also exact solutions of the Navier-Stokes equations in the sense that no approximations are required in order to calculate them. One common characteristic to all applications of self-similar flows in real problems is that they involve fluid domains with large aspect ratios. Self-similar flows are admissible solutions of the Navier-Stokes equations in unbounded domains, and in applications it is assumed that the effects of the boundary conditions at the edge of the domain will have only a local effect and that a self- similar solution will be valid in most of the fluid domain. However, it has been shown that some similarity flows exist only under a very restricted set of conditions which need to be inferred from numerical simulations. Our main interest is to study several self-similar solutions related to flows in oscillating channels and to investigate the hypothesis that these solutions are reasonable approximations to Navier-Stokes flows in long, slender but finite domains."]},{"key":"dc:title","label":"Title","values":["Self similar flows in finite or infinite two dimensional geometries"]}]}],"canonical_facts":{"dc:contributor":["Demetrius T. Papageorgiou","Linda Jane Cummings","Peter G. Petropoulos"],"dc:creator":["Espin Estevez, Leonardo Xavier"],"dc:description.abstract":["This study is concerned with several problems related to self-similar flows in pulsating channels. Exact or similarity solutions of the Navier-Stokes equations are of practical and theoretical importance in fluid mechanics. The assumption of self-similarity of the solutions is a very attractive one from both a theoretical and a practical point of view. It allows us to greatly simplify the Navier-Stokes equations into a single nonlinear one-dimensional partial differential equation (or ordinary differential equation in the case of steady flow) whose solutions are also exact solutions of the Navier-Stokes equations in the sense that no approximations are required in order to calculate them. One common characteristic to all applications of self-similar flows in real problems is that they involve fluid domains with large aspect ratios. Self-similar flows are admissible solutions of the Navier-Stokes equations in unbounded domains, and in applications it is assumed that the effects of the boundary conditions at the edge of the domain will have only a local effect and that a self- similar solution will be valid in most of the fluid domain. However, it has been shown that some similarity flows exist only under a very restricted set of conditions which need to be inferred from numerical simulations. Our main interest is to study several self-similar solutions related to flows in oscillating channels and to investigate the hypothesis that these solutions are reasonable approximations to Navier-Stokes flows in long, slender but finite domains."],"dc:identifier":["https://digitalcommons.njit.edu/dissertations/903"],"dc:subject":["Applied math","Exact solutions","Fluid dynamics","Self-similar solutions","Numerical simulations","Stability analysis","Mathematics"],"dc:title":["Self similar flows in finite or infinite two dimensional geometries"],"dc:type":["Dissertation"],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_name":["Doctor of Philosophy in Mathematical Sciences - (Ph.D.)"]},"updated_at":"2026-07-24T03:23:09Z"}