We consider the flow of a viscous, incompressible fluid contained between two parallel, porous walls. The flow is driven by a spatially uniform injection/suction of fluid through the bounding walls. We extend the solution structure of previous investigations to a more general three-dimensional stagnation-point form which can capture a whole range of phenomena in a single class of states. In particular, we show that this form of solution contains states previously discussed under more restrictive assumptions on the flow field. We show that a range of two- and three-dimensional states exist, together with symmetry-broken solutions and periodic states. We discuss the stability of these states and relate the previous results of Drazin, Banks, Zaturska and co-workers to those of Goldshtik and Javorsky on the "bifurcation to swirl" and of Hewitt and Duck on non-axisymmetric von Kármán flows. © 2003 Published by The Japan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserved.
- Berman problem
- Exact Navier-Stokes solutions
- Similarity solution
- Symmetry breaking