Self similar flows in finite or infinite two dimensional geometries
Department of Mathematical Sciences
Doctor of Philosophy
Papageorgiou, Demetrius T.
Cummings, Linda Jane
Petropoulos, Peter G.
Rumschitzki, David Sheldon
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.
njit-etd2009-047 (107 pages ~ 5,562 KB pdf)
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Created September 12, 2010