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A comparative study of data-driven modal decomposition analysis of unforced and forced cylinder wakes


The present study on the recognition of coherent structures in flow fields was conducted using three typical data-driven modal decomposition methods: proper orthogonal decomposition (POD), dynamic mode decomposition (DMD), and Fourier mode decomposition (FMD). Two real circular cylinder wake flows (forced and unforced), obtained from two-dimensional particle image velocimetry (2D PIV) measurements, were analyzed to extract the coherent structures. It was found that the POD method could be used to extract the large-scale structures from the fluctuating velocity in a wake flow, the DMD method showed potential for dynamical mode frequency identification and linear reconstruction of the flow field, and the FMD method provided a significant computational efficiency advantage when the dominant frequency of the flow field was known. The limitations of the three methods were also identified: The POD method was incomplete in the spatial–temporal decomposition and each mode mixed multiple frequencies leading to unclear physics, the DMD method is based on the linear assumption and thus the highly nonlinear part of the flow field was unsuitable, and the FMD method is based on global power spectrum analysis while being overwhelmed by an unknown high-frequency flow field.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.


2D, 3D:



Discrete Fourier transform


Dynamic mode decomposition


Fourier mode decomposition


Particle image velocimetry


Proper orthogonal decomposition


Reduced-order model


Reynolds shear stress


Singular value decomposition


Turbulent kinetic energy

\(\varepsilon\) :

Relative error

Β :

Blockage ratios

\({\omega }_{r},{\omega }_{i}\) :

Critical values of the quadratic mappings

\({\omega }_{z}\) :

Spanwise vorticity

\({\lambda }_{1},{\lambda }_{2},{\lambda }_{N}\) :


\({\phi }_{n}\) :

POD modal decomposition substrate

c k :

Global spectral information

D :

Characteristic diameter of the square cylinder

E j :

Mode energy

f e :

Excitation frequency

f 0 :

Vortex shedding domain frequency

\({F}_{j}\) :

Dmd modal frequency

\({G}_{j}\) :

Growth rate

L :

Span-wise length of the mode

m, n :

Temporal and special index


Reynolds number


Strouhal number

T :

Vortex shedding period

\({u}^{\mathrm{^{\prime}}}\) :

Fluctuation flow

U 0 :

Incoming airflow velocity

\(\overline{U}\) :

Mean velocity of x direction

\(\overline{V}\) :

Mean velocity of y direction


Profile of flow direction and lateral velocity fluctuations

Y :

Correlation matrix

X/D, Y/D:

X, Y direction dimensionless length


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The present study was funded by the National Natural Science Foundation of China (52278494, 52008140, U2106222).

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XC contributed to experiments; data and figures; and writing of the manuscript. DG contributed to conceptualization; supervision; methodology; funding acquisition; and editing of the manuscript.

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Correspondence to Donglai Gao.

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Chang, X., Gao, D. A comparative study of data-driven modal decomposition analysis of unforced and forced cylinder wakes. J Vis (2023).

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  • Proper orthogonal decomposition (POD)
  • Dynamic mode decomposition (DMD)
  • Fourier mode decomposition (FMD)
  • Vortex dynamics