  We consider a test problem for Navier-Stokes solvers based on the flow around
a cylinder that exhibits chaotic behavior, to examine the behavior of various
numerical methods. We choose a range of Reynolds numbers for which the flow is
time-dependent but can be characterized as essentially two-dimensional. The
problem requires accurate resolution of chaotic dynamics over a long time
interval. It also requires the use of a relatively large computational domain,
part of which is curved. We review the performance of different finite element
methods for the proposed range of Reynolds numbers. These tests indicate that
some of the most established methods do not capture the correct behavior. The
key requirements identified are pressure-robustness of the method, high
resolution, and appropriate numerical dissipation when the smallest scales are
under-resolved.
