  We propose an image-based flow decomposition developed from the
two-dimensional (2D) tensor empirical wavelet transform (EWT) (Gilles 2013).
The idea is to decompose the instantaneous flow data, or its visualisation,
adaptively according to the averaged Fourier supports for the identification of
spatially localised structures. The resulting EWT modes stand for the
decomposed flows, and each accounts for part of the spectrum, illustrating
fluid physics with different scales superimposed in the original flow. With the
proposed method, decomposition of an instantaneous 3D flow becomes feasible
without resorting to its time series. Examples first focus on the interaction
between a jet plume and 2D wake, where only experimental visualisations are
available. The proposed method is capable of separating the jet/wake flows and
their instabilities. Then the decomposition is applied to an early stage
boundary layer transition, where direct numerical simulations provided a full
data-set. The tested inputs are the 3D flow data and its visualisation using
streamwise velocity & {\lambda}2 vortex identification criterion. With both
types of inputs, EWT modes robustly extract the streamwise-elongated streaks,
multiple secondary instabilities and helical vortex filaments. Results from
bi-global stability analysis justify the EWT modes that represent the streak
instabilities. In contrast to Proper Orthogonal Decomposition or Dynamic Modal
Decomposition that extract spatial modes according to energy or frequency, EWT
provides a new strategy as to decompose an instantaneous flow from its spatial
scales.
