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Investigation of internal intermittency by way of higher-order spectral moments

Published online by Cambridge University Press:  03 December 2021

S. Lortie  and
L. Mydlarski Open the ORCID record for L. Mydlarski [Opens in a new window]
S. Lortie
Affiliation:
Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montréal, QC, H3A 0C3, Canada
L. Mydlarski*
Affiliation:
Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montréal, QC, H3A 0C3, Canada
*
†Email address for correspondence: laurent.mydlarski@mcgill.ca
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Abstract

The analysis of turbulence by way of higher-order spectral moments is uncommon, despite the relatively frequent use of such statistical analyses in other fields of physics and engineering. In this work, higher-order spectral moments are used to investigate the internal intermittency of the turbulent velocity and passive-scalar (temperature) fields. This study first introduces the theory behind higher-order spectral moments as they pertain to the field of turbulence. Then, a short-time Fourier-transform-based method is developed to estimate these higher-order spectral moments and provide a relative, scale-by-scale measure of intermittency. Experimental data are subsequently analysed and consist of measurements of homogeneous, isotropic, high-Reynolds-number, passive and active grid turbulence over the Reynolds-number range $35\leq R_{\lambda } \leq ~731$. Emphasis is placed on third- and fourth-order spectral moments using the definitions formalised by Antoni (Mech. Syst. Signal Pr., vol. 20 (2), 2006, pp. 282–307), as such statistics are sensitive to transients and provide insight into deviations from Gaussian behaviour in grid turbulence. The higher-order spectral moments are also used to investigate the Reynolds (Péclet) number dependence of the internal intermittency of velocity and passive-scalar fields. The results demonstrate that the evolution of higher-order spectral moments with Reynolds number is strongly dependent on wavenumber. Finally, the relative levels of internal intermittency of the velocity and passive-scalar fields are compared and a higher level of internal intermittency in the inertial subrange of the scalar field is consistently observed, whereas a similar level of internal intermittency is observed for the velocity and passive-scalar fields for the high-Reynolds-number cases as the Kolmogorov length scale is approached.

JFM classification

Turbulent Flows: Intermittency Turbulent Flows: Isotropic turbulence Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 932 , 10 February 2022 , A20
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Anselmet, F., Gagne, Y., Hopfinger, E.J. & Antonia, R.A. 1984 High-order velocity structure functions in turbulent shear flows. J. Fluid Mech. 140, 63–89.CrossRefGoogle Scholar
Antoni, J. 2006 The spectral kurtosis: a useful tool for characterising non-stationary signals. Mech. Syst. Signal Pr. 20 (2), 282–307.CrossRefGoogle Scholar
Antoni, J. 2007 Fast computation of the kurtogram for the detection of transient faults. Mech. Syst. Signal Pr. 21 (1), 108–124.CrossRefGoogle Scholar
Antoni, J. & Randall, R.B. 2006 The spectral kurtosis: application to the vibratory surveillance and diagnostics of rotating machines. Mech. Syst. Signal Pr. 20 (2), 308–331.CrossRefGoogle Scholar
Batchelor, G.K. & Townsend, A.A. 1949 The nature of turbulent motion at large wave-numbers. P. R. Soc. Lond. A Mat. 199 (1057), 238–255.Google Scholar
Bos, W.J.T., Liechtenstein, L. & Schneider, K. 2007 Small-scale intermittency in anisotropic turbulence. Phys. Rev. E 76 (4), 046310.CrossRefGoogle ScholarPubMed
Brun, C. & Pumir, A. 2001 Statistics of fourier modes in a turbulent flow. Phys. Rev. E 63 (5), 056313.CrossRefGoogle Scholar
Chevillard, L., Mazellier, N., Poulain, C., Gagne, Y. & Baudet, C. 2005 Statistics of Fourier modes of velocity and vorticity in turbulent flows: intermittency and long-range correlations. Phys. Rev. Lett. 95 (20), 200203.CrossRefGoogle ScholarPubMed
Corrsin, S. 1951 On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys. 22 (4), 469–473.CrossRefGoogle Scholar
Djenidi, L., Antonia, R.A. & Tang, S.L. 2019 Scale invariance in finite Reynolds number homogeneous isotropic turbulence. J. Fluid Mech. 864, 244–272.CrossRefGoogle Scholar
Dwyer, R.F. 1983 A technique for improving detection and estimation of signals contaminated by under ice noise. J. Acoust. Soc. Am. 74 (1), 124–130.CrossRefGoogle Scholar
Farge, M. 1992 Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech. 24 (1), 395–458.CrossRefGoogle Scholar
Forbes, C., Evans, M., Hastings, N. & Peacock, B. 2011 Statistical Distributions. John Wiley & Sons.Google Scholar
Frisch, U. 1995 Turbulence: The Legacy of A.N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Holzer, M. & Siggia, E.D. 1994 Turbulent mixing of a passive scalar. Phys. Fluids 6 (5), 1820–1837.CrossRefGoogle Scholar
Hu, Y., Bao, W., Tu, X., Li, F. & Li, K. 2019 An adaptive spectral kurtosis method and its application to fault detection of rolling element bearings. IEEE Trans. Instrum. Meas. 69 (3), 739–750.CrossRefGoogle Scholar
Kennedy, D.A. & Corrsin, S. 1961 Spectral flatness factor and ‘intermittency’ in turbulence and in non-linear noise. J. Fluid Mech. 10 (3), 366–370.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 a Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk. SSSR 32, 16–18.Google Scholar
Kolmogorov, A.N. 1941 b The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk. SSSR 30, 301–305.Google Scholar
Kraichnan, R.H. 1994 Anomalous scaling of a randomly advected passive scalar. Phys. Rev. Lett. 72 (7), 1016–1019.CrossRefGoogle ScholarPubMed
Kuo, A.Y. & Corrsin, S. 1971 Experiments on internal intermittency and fine-structure distribution functions in fully turbulent fluid. J. Fluid Mech. 50 (2), 285–319.CrossRefGoogle Scholar
Landau, L.D. 1944 On the problem of turbulence. Dokl. Akad. Nauk. USSR 44, 311.Google Scholar
Leite, V.C., Borges da Silva, J.G., Borges da Silva, L.E., Veloso, G.F.C., Lambert-Torres, G., Bonaldi, E.L. & de Oliveira, L.E.L. 2016 Experimental bearing fault detection, identification, and prognosis through spectral kurtosis and envelope spectral analysis. Electr. Pow. Compo. Sys. 44 (18), 2121–2132.CrossRefGoogle Scholar
Lepore, J. & Mydlarski, L. 2012 Finite-Péclet-number effects on the scaling exponents of high-order passive scalar structure functions. J. Fluid Mech. 713, 453–481.CrossRefGoogle Scholar
Makita, H. 1991 Realization of a large-scale turbulence field in a small wind tunnel. Fluid Dyn. Res. 8 (1-4), 53–64.Google Scholar
Meneveau, C. 1991 Analysis of turbulence in the orthonormal wavelet representation. J. Fluid Mech. 232, 469–520.CrossRefGoogle Scholar
Meyer, C.R., Mydlarski, L. & Danaila, L. 2018 Statistics of incremental averages of passive scalar fluctuations. Phys. Rev. Fluids 3 (9), 094603.CrossRefGoogle Scholar
Millioz, F., Huillery, J. & Martin, N. 2006 Short time Fourier transform probability distribution for time-frequency segmentation. Intl Conf. Acoust. Speech 3, 448–451.Google Scholar
Mydlarski, L. 2017 A turbulent quarter century of active grids: from Makita (1991) to the present. Fluid Dyn. Res. 49 (6), 061401.CrossRefGoogle Scholar
Mydlarski, L. & Warhaft, Z. 1996 On the onset of high-Reynolds-number grid-generated wind tunnel turbulence. J. Fluid Mech. 320, 331–368.CrossRefGoogle Scholar
Mydlarski, L. & Warhaft, Z. 1998 Passive scalar statistics in high-Péclet-number grid turbulence. J. Fluid Mech. 358, 135–175.CrossRefGoogle Scholar
Nelkin, M. 1990 Multifractal scaling of velocity derivatives in turbulence. Phys. Rev. A 42 (12), 7226.CrossRefGoogle ScholarPubMed
Oboukhov, A.M. 1949 Structure of the temperature field in turbulent flows. Akad. Nauk. SSSR 13, 58–69.Google Scholar
Pagnan, S., Ottonello, C. & Tacconi, G. 1994 Filtering of randomly occurring signals by kurtosis in the frequency domain. In International Journal of Pattern Recognition, pp. 131–133. IEEE.Google Scholar
Peligrad, M. & Wu, W.B. 2010 Central limit theorem for Fourier transforms of stationary processes. Ann. Probab. 38 (5), 2009–2022.CrossRefGoogle Scholar
Press, W.H., William, H., Teukolsky, S.A, Saul, A., Vetterling, W.T. & Flannery, B.P. 2007 Numerical Recipes 3rd edition: The Art of Scientific Computing. Cambridge University Press.Google Scholar
Pumir, A., Shraiman, B.I. & Siggia, E.D. 1991 Exponential tails and random advection. Phys. Rev. Lett. 66 (23), 2984.CrossRefGoogle ScholarPubMed
Sreenivasan, K.R. & Antonia, R.A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29 (1), 435–472.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J.L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Van Atta, C.W. & Antonia, R.A. 1980 Reynolds number dependence of skewness and flatness factors of turbulent velocity derivatives. Phys. Fluids 23 (2), 252–257.CrossRefGoogle Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32 (1), 203–240.CrossRefGoogle Scholar
Welch, P. 1967 The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Acoust. Speech 15 (2), 70–73.Google Scholar
Wyngaard, J.C. 1967 An experimental investigation of the small-scale structure of turbulence in a curved mixing layer, PhD thesis, The Pennsylvania State University.Google Scholar
Yaglom, A.M. 1949 On the local structure of a temperature field in a turbulent flow. Dokl. Akad. Nauk. SSSR 69, 743–746.Google Scholar