Stability of Flow in a Diverging Channel
The linear, weakly nonlinear, and nonlinear stability of flows of a viscous incompressible fluid in a diverging channel will be treated theoretically. The results will be related to observations of flows, to computational fluid dynamics, to bifurcations of the solutions describing the flows as the Reynolds number increases, and to transition towards chaos. This will also serve as a case study of the concepts and methods of the theory of stability of all flows.
KeywordsSteady Flow Bifurcation Diagram Basic Flow Lorenz System Null Solution
Unable to display preview. Download preview PDF.
- Nakayama, Y. ed. 1988 Visualized Flow. Oxford: Pergamon Press.Google Scholar
- Drazin, P.G. 1988 Perturbations of Jeffery-Hamel flows. On pp. 129–133 of A Symposium to Honor C.C. Lin, eds, D.J. Benney, F.H. Shu & C. Yuan, Singapore: World Scientific Press.Google Scholar
- Buitrago, S.E. 1983 Detailed analysis of the higher Jeffery-Hamel solutions. M.Phil, thesis, University of Sussex.Google Scholar
- Sobey, I.J. & Mullin, T. 1992 Calculation of multiple solutions for the two-dimensional Navier-Stokes equations. Proc. ICFD Conference, Reading. Google Scholar
- Cliffe, K.A. & Greenfield, A.C. 1982 Some comments on laminar flow in symmetric two-dimensional channels. Rep. TP 939. AERE, Harwell.Google Scholar
- Dennis, S.C.R., Banks, W.H.H., Drazin, P.G. & Zaturska, M.B. 1994 Flow along a diverging channel. (To be published.)Google Scholar
- King, G.P. & Stewart, I.N. 1992 Symmetric chaos. On pp. 257–315 of Nonlinear Equations in the Applied Sciences, eds. W.F. Ames & C.F. Rogers. New York: Academic Press.Google Scholar