Bifurcations in flow patterns : some applications of the qualitative theory of differential equations in fluid dynamics /
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| Author / Creator: | Bakker, P. G. |
|---|---|
| Imprint: | Dordrecht ; Boston : Kluwer Academic, c1991. |
| Description: | xi, 209 p. : ill. ; 25 cm. |
| Language: | English |
| Series: | Nonlinear topics in the mathematical sciences v. 2 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/1318021 |
Table of Contents:
- Ch. I. Some Elements of the Qualitative Theory of Differential Equations. 1. Phase space representation of a dynamical system. 2. Phase portraits near singular points. 3. Topological structure of phase portraits, structural stability, bifurcation. 4. Higher-order singularities in R[superscript 2]. 5. Bifurcation of vector fields, unfoldings. 6. Center manifolds. 7. An approach to physical unfoldings in flow patterns
- Ch. II. Topology of Conical Flow Patterns. 2. Local conical stagnation point solutions in irrotational flow. 3. Classification of conical stagnation points in conical flows. 4. Analytical unfoldings in conical flows. 5. External corner flow; a nonanalytical unfolding of a starlike node
- Ch. III. Topological Aspects of Steady Viscous Flows Near Plane Walls. 1. A way to obtain local solutions of the Navier-Stokes equations. 2. Steady viscous flow near a plane wall, elementary singular points in the flow patterns. 3. Higher-order singularities in the flow pattern. 4. Unfolding of the topological saddle point of the third order. 5. Unfolding of a topological saddle point of the fifth order. 6. Unfolding of a saddle point with three hyperbolic sectors in a half plane, [Tau][subscript xx] [actual symbol not reproducible] 0. 7. Unfolding of a saddle point with two or four hyperbolic sectors in a half plane, [Tau][subscript xx] [actual symbol not reproducible] 0. 8. Viscous flow near a circular cylinder at low Reynolds numbers.