Spectral analysis of fluid flows using subNyquistrate PIV data
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 NyquistShannon 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 subNyquistrate sampling. Given a vectorvalued signal, we take measurements randomly in time (at a subNyquist rate) and project the data onto a lowdimensional 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 subNyquistrate sampling.
 Publication:

Experiments in Fluids
 Pub Date:
 September 2014
 DOI:
 10.1007/s0034801418056
 arXiv:
 arXiv:1401.7047
 Bibcode:
 2014ExFl...55.1805T
 Keywords:

 Physics  Fluid Dynamics
 EPrint:
 Exp. Fluids 55(9):1805 (2014)