  We propose a novel non-linear manifold learning from snapshot data and
demonstrate its superiority over Proper Orthogonal Decomposition (POD) for
shedding-dominated shear flows. Key enablers are isometric feature mapping,
Isomap (Tenenbaum et al., 2000), as encoder and K-nearest neighbours (KNN)
algorithm as decoder. The proposed technique is applied to numerical and
experimental datasets including the fluidic pinball, a swirling jet, and the
wake behind a couple of tandem cylinders. Analyzing the fluidic pinball, the
manifold is able to describe the pitchfork bifurcation and the chaotic regime
with only three feature coordinates. These coordinates are linked to
vortex-shedding phases and the force coefficients. The manifold coordinates of
the swirling jet are comparable to the POD mode amplitudes, yet allow for a
more distinct manifold identification which is less sensitive to measurement
noise. As similar observation is made for the wake of two tandem cylinders
(Raiola et al., 2016). The tandem cylinders are aligned in streamwise distance
which corresponds to the transition between the single bluff body and the
reattachment regimes of vortex shedding. Isomap unveils these two shedding
regimes while the Lissajous plots of first two POD mode amplitudes feature a
single circle. The reconstruction error of the manifold model is small compared
to the fluctuation level, indicating that the low embedding dimensions contains
the coherent structure dynamics. The proposed Isomap-KNN manifold learner is
expected to be of large importance in estimation, dynamic modeling and control
for large range of configurations with dominant coherent structures.
