  Modal decomposition techniques are showing a fast growth in popularity for
their good properties as data-driven tools. There are several modal
decomposition techniques, yet Proper Orthogonal Decomposition (POD) and Dynamic
Mode Decomposition (DMD) are considered the most demanded methods, especially
in the field of fluid dynamics. Following their magnificent performance on
various applications in several fields, numerous extensions of these techniques
have been developed. In this work we present an ambitious review comparing
eight different modal decomposition techniques, including most established
methods: POD, DMD and Fast Fourier Trasform (FFT), extensions of these
classical methods: based on time embedding systems, Spectral POD (SPOD) and
Higher Order DMD (HODMD), based on scales separation, multi-scale POD (mPOD),
multi-resolution DMD (mrDMD), and based on the properties of the resolvent
operator, the data-driven Resolvent Analysis (RA). The performance of all these
techniques will be evaluated on three different testcases: the laminar wake
around cylinder, a turbulent jet flow, and the three dimensional wake around
cylinder in transient regime. First, we show a comparison between the
performance of the eight modal decomposition techniques when the datasets are
shortened. Next, all the results obtained will be explained in details, showing
both the conveniences and inconveniences of all the methods under investigation
depending on the type of application and the final goal (reconstruction or
identification of the flow physics). In this contribution we aim on giving a --
as fair as possible -- comparison of all the techniques investigated. To the
authors knowledge, this is the first time a review paper gathering all this
techniques have been produced, clarifying to the community what is the best
technique to use for each application.
