Abstract
This paper is a review of some new work on an old problem. We shall first describe the origin of the problem, and then present a few snapshots of some of the solutions. Please forgive us for taking the snapshots from a parochial point of view, because this review is mostly of work done at Bristol.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berman, A.S., 1953, Laminar flow in channels with porous walls, J. Appl. Phys., 24:1232.
Brady, J.F. and Acrivos, A., 1981, Steady flow in a channel or tube with an accelerating surface velocity. An exact solution to the Navier-Stokes equations with reverse flow, J. Fluid Mech., 112: 127.
Calogero, F., 1984, A solvable nonlinear wave equation, Studies Appl. Math., 70:189.
Childress, S., Ierley, G.R., Spiegel, E.A. and Young, W.R., 1989, Blow-up of unsteady two-dimensional Euler and Navier-Stokes solutions having stagnation-point form, J. Fluid Mech., 203:1.
Cox, S.M., 1989, A similarity solution of the Navier-Stokes equations for two-dimensional flow in a porous-walled channel, Ph.D. dissertation, University of Bristol.
Glendinning, P., 1988, Global bifurcations in flows, in “New Directions in Dynamical Systems”, T. Bedford and J. Swift ed., Cambridge University Press.
Hiemenz, K., 1911, Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder, Dinglers J., 326:321.
Homann, F., 1936, Der Einfluss grosser Zähigkeit bei der Strömung um den Zylinder und um die Kugel, Z. angew. Math. Mech., 16:153.
Howarth, L., 1951, The boundary layer in three-dimensional flow. Part II: The flow near a Stagnation point. Phil. Mag., (7) 42:1433.
Newell, A.C., 1906, Side-roll instability — a new solution of the Guiness-Löwenbräu problem, Proc. Irish Narrative Soc, 8:1.
Proudman, I. and Johnson, K., 1962, Boundary-layer growth near a stagnation point, J. Fluid Mech., 12:161.
Raithby, G.D. and Knudsen, D.C., 1974, Hydrodynamic development in a duct with suction and blowing, A.S.M.E. J. Appl. Mech. 41:896.
Stuart, J.T., 1988, Nonlinear Euler partial differential equations: singularities in their solution, in “A Symposium to Honor C.C. Lin”, D.J. Benney, F.H. Shu and C. Yuan ed., World Scientific Publishing, Singapore.
Taylor, C.L., Banks, W.H.H., Zaturska, M.B. and Drazin, P.G., 1990, Three-dimensional flow in a porous channel (to be published).
Terrill, R.M., 1964, Laminar flow in a uniformly porous channel, Aero. Quart., 15:299.
Watson, E.B.B., Banks, W.H.H., Zaturska, M.B. and Drazin, P.G., 1990, On transition to chaos in a two-dimensional channel flow driven symmetrically by accelerating walls, J. Fluid Mech. 212: (in the press).
Watson, P., 1989, Symmetry breaking in a laminar channel flow driven by accelerating walls, M.Sc. dissertation, University of Bristol.
Zaturska, M.B., Drazin, P.G. and Banks, W.H.H., 1988, On the flow of a viscous fluid driven along a channel by suction at porous walls, Fluid Dynamics Res., 4:151.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Plenum Press, New York
About this chapter
Cite this chapter
Drazin, P.G., Banks, W.H.H., Zaturska, M.B. (1990). Transition to Chaos in Non-Parallel Two-Dimensional Flow in a Channel. In: Busse, F.H., Kramer, L. (eds) Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems. NATO ASI Series, vol 225. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5793-3_6
Download citation
DOI: https://doi.org/10.1007/978-1-4684-5793-3_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-5795-7
Online ISBN: 978-1-4684-5793-3
eBook Packages: Springer Book Archive