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

Spectral analysis of fluid flows using sub-Nyquist-rate PIV data 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Experiments in Fluids Springer Journals

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

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2014 by Springer-Verlag Berlin Heidelberg
Subject
Engineering; Engineering Fluid Dynamics; Fluid- and Aerodynamics; Engineering Thermodynamics, Heat and Mass Transfer
ISSN
0723-4864
eISSN
1432-1114
D.O.I.
10.1007/s00348-014-1805-6
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Experiments in FluidsSpringer Journals

Published: Sep 4, 2014

References

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