Frequency–wavenumber spectral analysis of spatiotemporal flows
Abstract
We propose a fully spatiotemporal approach for identifying spatially varying modes of oscillation in fluid dynamics simulation output by means of multitaper frequency–wavenumber spectral analysis. Onedimensional spectrum estimation has proven to be a valuable tool in the analysis of turbulence data applied spatially to determine the rate of energy transport between spatial scales, or temporally to determine frequencies of oscillatory flows. It also allows for the quantitative comparison of flow characteristics between two scenarios using a standard basis. It has the limitation, however, that it neglects coupling between spatial and temporal structures. Twodimensional frequency–wavenumber spectral analysis allows one to decompose waveforms into standing or travelling variety. The extended higherdimensional multitaper method proposed here is shown to have improved statistical properties over conventional nonparametric spectral estimators, and is accompanied by confidence intervals which estimate their uncertainty. Multitaper frequency–wavenumber analysis is applied to a canonical benchmark problem, namely, a direct numerical simulation of von Kármán vortex shedding off a square wallmounted cylinder with two inflow scenarios with matching momentumthickness Reynolds numbers$$Re_{\unicode[STIX]{x1D703}}\approx 1000$$at the obstacle. Frequency–wavenumber analysis of a twodimensional section of these data reveals that although both the laminar and turbulent inflow scenarios show a turbulent$5/3$$cascade in wavenumber ($$\unicode[STIX]{x1D708}$$) and frequency ($$f$$), the flow characteristics differ in that there is a significantly more prominent discrete harmonic oscillation near$$(f,\unicode[STIX]{x1D708})=(0.2,0.21)$in wavenumber and frequency in the laminar inflow scenario than the turbulent scenario. Here, this frequency–wavenumber pair corresponds to a travelling wave with velocity near one near the centre path of the vortex street.
 Authors:

 Argonne National Lab. (ANL), Lemont, IL (United States)
 Argonne National Lab. (ANL), Lemont, IL (United States); Univ. of Chicago, Chicago, IL (United States)
 Publication Date:
 Research Org.:
 Argonne National Lab. (ANL), Argonne, IL (United States)
 Sponsoring Org.:
 National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
 OSTI Identifier:
 1461555
 Grant/Contract Number:
 AC0206CH11357
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Fluid Mechanics
 Additional Journal Information:
 Journal Volume: 848; Journal ID: ISSN 00221120
 Publisher:
 Cambridge University Press
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Coherent Structures; Direct Numerical Simulation; Fourier Analysis; Power Spectrum; WallMounted Square Cylinder; von Karman Vortex Street
Citation Formats
Geoga, Christopher J., Haley, Charlotte L., Siegel, Andrew R., and Anitescu, Mihai. Frequency–wavenumber spectral analysis of spatiotemporal flows. United States: N. p., 2018.
Web. doi:10.1017/jfm.2018.366.
Geoga, Christopher J., Haley, Charlotte L., Siegel, Andrew R., & Anitescu, Mihai. Frequency–wavenumber spectral analysis of spatiotemporal flows. United States. doi:10.1017/jfm.2018.366.
Geoga, Christopher J., Haley, Charlotte L., Siegel, Andrew R., and Anitescu, Mihai. Fri .
"Frequency–wavenumber spectral analysis of spatiotemporal flows". United States. doi:10.1017/jfm.2018.366. https://www.osti.gov/servlets/purl/1461555.
@article{osti_1461555,
title = {Frequency–wavenumber spectral analysis of spatiotemporal flows},
author = {Geoga, Christopher J. and Haley, Charlotte L. and Siegel, Andrew R. and Anitescu, Mihai},
abstractNote = {We propose a fully spatiotemporal approach for identifying spatially varying modes of oscillation in fluid dynamics simulation output by means of multitaper frequency–wavenumber spectral analysis. Onedimensional spectrum estimation has proven to be a valuable tool in the analysis of turbulence data applied spatially to determine the rate of energy transport between spatial scales, or temporally to determine frequencies of oscillatory flows. It also allows for the quantitative comparison of flow characteristics between two scenarios using a standard basis. It has the limitation, however, that it neglects coupling between spatial and temporal structures. Twodimensional frequency–wavenumber spectral analysis allows one to decompose waveforms into standing or travelling variety. The extended higherdimensional multitaper method proposed here is shown to have improved statistical properties over conventional nonparametric spectral estimators, and is accompanied by confidence intervals which estimate their uncertainty. Multitaper frequency–wavenumber analysis is applied to a canonical benchmark problem, namely, a direct numerical simulation of von Kármán vortex shedding off a square wallmounted cylinder with two inflow scenarios with matching momentumthickness Reynolds numbers$Re_{\unicode[STIX]{x1D703}}\approx 1000$at the obstacle. Frequency–wavenumber analysis of a twodimensional section of these data reveals that although both the laminar and turbulent inflow scenarios show a turbulent$5/3$cascade in wavenumber ($\unicode[STIX]{x1D708}$) and frequency ($f$), the flow characteristics differ in that there is a significantly more prominent discrete harmonic oscillation near$(f,\unicode[STIX]{x1D708})=(0.2,0.21)$in wavenumber and frequency in the laminar inflow scenario than the turbulent scenario. Here, this frequency–wavenumber pair corresponds to a travelling wave with velocity near one near the centre path of the vortex street.},
doi = {10.1017/jfm.2018.366},
journal = {Journal of Fluid Mechanics},
number = ,
volume = 848,
place = {United States},
year = {2018},
month = {6}
}
Figures / Tables:
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Figures / Tables found in this record: