  A method, referred to as the principal correlation decomposition (PCD), is
proposed in this paper to optimally dissect complex flows into mutually
orthogonal modes that are ranked by their correlated energy with an observable.
It is particularly suitable for identifying the observable-correlated flow
structures, while effectively excluding those uncorrelated even though they may
be highly energetic. Therefore, this method is capable of extracting coherent
flow features under very low signal-to-noise ratio (SNR). A numerical
validation is conducted and shows that the new method can robustly identify the
observable-correlated flow events even though the underlying signal is
corrupted by random noise that is four orders of magnitude more energetic.
Moreover, the resolution continues to improve if the flow is sampled for a
longer duration, which is often readily available in experimental measurements.
This method is subsequently used to analyse the unsteady vortex shedding from a
cylinder and a subsonic turbulent jet. This new decomposition represents a
data-driven method of effective order-reduction for highly noisy experimental
and numerical data and is very effective in identifying the source and
descendent events of a given observable. It is expected to find wide
applications in flow observable diagnosis and its control such as noise
control.
