It is difficult to read current fluid dynamic literature without coming across the terms bifurcation and chaos. One problem is that most of the work on bifurcation and chaos is computational, there are very few analytic methods which can help with the non-linear Navier-Stokes equations and experiments are carried out but it is very difficult to obtain results close to bifurcation points or to identify chaos in flows. On the computational side, it is well known that dynamics systems without chaos can have chaotic computed solutions and that systems with strange attractors can have chaos suppressed by numerical methods. My interest is that numerical algorithm can also influence the computed solution of non-linear PDE's resulting in misleading interpretation of results.

A very simple bifurcation problem for which we have very comprehensive experimental results is the "Coanda effect" where flow through a symmetric channel expansion attaches preferentially to one wall, so there is a simple pitchfork bifurcation from a symmetric flow to an asymmetric flow as the flow rate increases.

To show how algorithm affects computed solutions the diagrams show a more or less correct solution using one algorithm:

Reynolds number=50 Central differences

and a false solution computed with a different method but exactly the same numerical parameters:

Reynolds number=50 Upwind differences

Anyone interested in the history of this problem should note that there is a typographical error in labelling the Reynolds number axis of figure 7 in Sobey(1985) JFM 151, p395-426 and Reynolds numbers in that figure (only) are double the correct value. I am grateful to A Onoufriou for bringing this error to my attention.

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