Graduate Thesis Or Dissertation
 

Stability analysis of homogeneous shear flow : the linear and nonlinear theories and a Hamiltonian formulation

Public Deposited

Downloadable Content

Download PDF
https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/v979v691f

Descriptions

Attribute NameValues
Creator
Abstract
  • The stability of steady-state solutions of the equations governing two-dimensional, homogeneous, incompressible fluid flow are analyzed in the context of shear-flow in a channel. Both the linear and nonlinear theories are reviewed and compared. In proving nonlinear stability of an equilibrium, emphasis is placed on using the stability algorithm developed in Holm et al. (1985). It is shown that for certain types of equilibria the linear theory is inconclusive, although nonlinear stability can be proven. Establishing nonlinear stability is dependent on the definition of a norm on the space of perturbations. McIntyre and Shepherd (1987) specifically define five norms, two for corresponding to one flow state and three to a different flow state, and suggest that still others are possible. Here, the norms given by McIntyre and Shepherd (1987) are shown to induce the same topology (for the corresponding flow states), establishing their equivalence as norms, and hence their equivalence as measures of stability. Summaries of the different types of stability and their mathematical definitions are presented. Additionally, a summary of conditions on shear-flow equilibria under which the various types of stability have been proven is presented. The Hamiltonian structure of the two-dimensional Euler equations is outlined following Olver (1986). A coordinate-free approach is adopted emphasizing the role of the Poisson bracket structure. Direct calculations are given to show that the Casimir invariants, or distinguished functionals, are time-independent and therefore are conserved quantities in the usual sense.
Resource Type
Date Available
Date Issued
Degree Level
Degree Name
Degree Field
Degree Grantor
Commencement Year
Advisor
Academic Affiliation
Non-Academic Affiliation
Subject
Rights Statement
Publisher
Peer Reviewed
Language
Digitization Specifications
  • File scanned at 300 ppi (Monochrome) using ScandAll PRO 1.8.1 on a Fi-6670 in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.
Replaces

Relationships

Parents:

This work has no parents.

In Collection:

Items

Thumbnail Title Date Uploaded Visibility Actions
file details HagelbergCarlR1990.pdf 2017-10-19 Public Download