  Reduced-order representations of an ensemble of cylinder wake transients are
investigated. Locally linear embedding identifies a two-dimensional manifold
with a maximum error of 1% from new snapshot data. This representation
outperforms a 50-dimensional POD expansion from the same data and is not
obtainable with cluster-based coarse graining of similar order. This manifold
resolves the steady solution, the stability eigenmodes, the first
post-transient POD modes, the intermediate vortex shedding structure as well as
higher harmonics. The snapshot data are generated by a direct numerical
simulation of the two-dimensional wake behind a circular cylinder at a Reynolds
number of 100. The initial conditions of the 16 transients start near the
steady solution and converge to the period vortex shedding. Many oscillatory
flows can be expected to be characterized on two- or low-dimensional manifolds
identifiable with locally linear embedding. These manifolds have unexplored
potential for prediction, estimation and control.
