TY - JOUR

T1 - Spectral analysis of fluid flows using sub-Nyquist-rate PIV data

AU - Tu, Jonathan H.

AU - Rowley, Clarence Worth

AU - Kutz, J. Nathan

AU - Shang, Jessica K.

N1 - Funding Information:
The authors acknowledge funding from the AFOSR and the NSF and thank Steve Brunton for many insightful discussions regarding compressed sensing in the context of dynamical systems.
Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.

PY - 2014/9

Y1 - 2014/9

N2 - Spectral methods are ubiquitous in the analysis of dynamically evolving fluid flows. However, tools like Fourier transformation and dynamic mode decomposition (DMD) require data that satisfy the Nyquist–Shannon sampling criterion. In many fluid flow experiments, such data are impossible to acquire. We propose a new approach that combines ideas from DMD and compressed sensing to accommodate sub-Nyquist-rate sampling. Given a vector-valued signal, we take measurements randomly in time (at a sub-Nyquist rate) and project the data onto a low-dimensional subspace. We then use compressed sensing to identify the dominant frequencies in the signal and their corresponding modes. We demonstrate this method using two examples, analyzing both an artificially constructed dataset and particle image velocimetry data from the flow past a cylinder. In each case, our method correctly identifies the characteristic frequencies and oscillatory modes dominating the signal, proving it to be a capable tool for spectral analysis using sub-Nyquist-rate sampling.

AB - Spectral methods are ubiquitous in the analysis of dynamically evolving fluid flows. However, tools like Fourier transformation and dynamic mode decomposition (DMD) require data that satisfy the Nyquist–Shannon sampling criterion. In many fluid flow experiments, such data are impossible to acquire. We propose a new approach that combines ideas from DMD and compressed sensing to accommodate sub-Nyquist-rate sampling. Given a vector-valued signal, we take measurements randomly in time (at a sub-Nyquist rate) and project the data onto a low-dimensional subspace. We then use compressed sensing to identify the dominant frequencies in the signal and their corresponding modes. We demonstrate this method using two examples, analyzing both an artificially constructed dataset and particle image velocimetry data from the flow past a cylinder. In each case, our method correctly identifies the characteristic frequencies and oscillatory modes dominating the signal, proving it to be a capable tool for spectral analysis using sub-Nyquist-rate sampling.

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U2 - 10.1007/s00348-014-1805-6

DO - 10.1007/s00348-014-1805-6

M3 - Article

AN - SCOPUS:84906799453

VL - 55

SP - 1

EP - 13

JO - Experiments in Fluids

JF - Experiments in Fluids

SN - 0723-4864

IS - 9

ER -