Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-09T08:55:29.999Z Has data issue: false hasContentIssue false
  • English
  • Français

Local modulated wave model for the reconstruction of space–time energy spectra in turbulent flows

Published online by Cambridge University Press:  14 January 2020

Ting Wu Open the ORCID record for Ting Wu [Opens in a new window]  and
Guowei He Open the ORCID record for Guowei He [Opens in a new window]
Ting Wu
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing100190, China
Guowei He*
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing100190, China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing100049, China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A statistical model is developed to reconstruct space–time energy spectra in turbulent flows from a non-extensive dataset comprising a time series of velocity fluctuations at a finite number of measurement points. This model is based on a higher approximation of energetic flow structures and developed by using local modulated waves. As a result, it can correctly predict the mean wavenumbers and spectral bandwidths. In contrast, Taylor’s frozen-flow hypothesis incorrectly predicts the spectral bandwidths to be zero, and the local wavenumber model significantly under-predicts the spectral bandwidths. An analytical example is formulated to illustrate the present model, and datasets from direct numerical simulations of turbulent channel flows are used to validate this model. The present statistical model is also discussed in terms of the dominating processes of temporal decorrelation in turbulent flows.

JFM classification

Turbulent Flows: Turbulence theory Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 886 , 10 March 2020 , A11
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adrian, R. J. & Moin, P. 1988 Stochastic estimation of organized turbulent structure: homogeneous shear flow. J. Fluid Mech. 190, 531–559.CrossRefGoogle Scholar
Beall, J. M., Kim, Y. C. & Powers, E. J. 1982 Estimation of wavenumber and frequency spectra using fixed probe pairs. J. Appl. Phys. 53 (6), 3933–3940.CrossRefGoogle Scholar
Bossuyt, J., Meneveau, C. & Meyers, J. 2017 Wind farm power fluctuations and spatial sampling of turbulent boundary layers. J. Fluid Mech. 823, 329–344.CrossRefGoogle Scholar
Buxton, O. R. H., de Kat, R. & Ganapathisubramani, B. 2013 The convection of large and intermediate scale fluctuations in a turbulent mixing layer. Phys. Fluids 25, 125105.CrossRefGoogle Scholar
Cenedese, A., Romano, G. P. & Defelice, F. 1991 Experimental testing of Taylor’s hypothesis by L.D.A in highly turbulent flow. Exp. Fluids 11, 351–358.CrossRefGoogle Scholar
Del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15, L41–L44.CrossRefGoogle Scholar
Del Álamo, J. C. & Jiménez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 5–26.CrossRefGoogle Scholar
Deng, B. Q. & Xu, C. X. 2012 Influence of active control on STG-based generation of streamwise vortices in near-wall turbulence. J. Fluid Mech. 710, 234–259.CrossRefGoogle Scholar
Duraisamy, K., Iaccarino, G. & Xiao, H. 2019 Turbulence modeling in the age of data. Annu. Rev. Fluid Mech. 51, 357–377.CrossRefGoogle Scholar
Fisher, M. J. & Davies, P. O. A. 1964 Correlation measurements in a non-frozen pattern of turbulence. J. Fluid Mech. 18, 97–116.CrossRefGoogle Scholar
Geng, C. H., He, G. W., Wang, Y. S., Xu, C. X., Lozano-Durán, A. & Wallace, J. M. 2015 Taylor’s hypothesis in turbulent channel flow considered using a transport equation analysis. Phys. Fluids 27, 025111.CrossRefGoogle Scholar
Ghate, A. S. & Lele, S. K. 2017 Subfilter-scale enrichment of planetary boundary layer large eddy simulation using discrete Fourier-Gabor modes. J. Fluid Mech. 819, 494–539.CrossRefGoogle Scholar
Gibbs, A. L. & Su, F. E. 2002 On choosing and bounding probability metrics. Intl Stat. Rev. 70 (3), 419–435.CrossRefGoogle Scholar
He, G. W., Jin, G. D. & Yang, Y. 2017 Space–time correlations and dynamic coupling in turbulent flows. Annu. Rev. Fluid Mech. 49, 51–70.CrossRefGoogle Scholar
He, G. W., Wang, M. & Lele, S. K. 2004 On the computation of space–time correlations by large-eddy simulation. Phys. Fluids 16 (11), 3859–3867.CrossRefGoogle Scholar
He, G. W. & Zhang, J. B. 2006 Elliptic model for space–time correlations in turbulent shear flows. Phys. Rev. E 73, 055303.Google ScholarPubMed
Howland, M. F. & Yang, X. I. A. 2018 Dependence of small-scale energetics on large scales in turbulent flows. J. Fluid Mech. 852, 641–662.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Hutchins, N., Nickels, T. B., Marusic, I. & Chong, M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103–136.CrossRefGoogle Scholar
Jiménez, J. 2012 Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 44, 27–45.CrossRefGoogle Scholar
de Kat, R. & Ganapathisubramani, B. 2015 Frequency-wavenumber mapping in turbulent shear flows. J. Fluid Mech. 783, 166–190.CrossRefGoogle Scholar
Kevin, K., Monty, J. & Hutchins, N. 2019 The meandering behaviour of large-scale structures in turbulent boundary layers. J. Fluid Mech. 865, R1.CrossRefGoogle Scholar
Kraichnan, R. H. 1964 Kolmogorov’s hypotheses and Eulerian turbulence theory. Phys. Fluids 7, 1723–1734.CrossRefGoogle Scholar
Kraichnan, R. H. 1966 Isotropic turbulence and inertial-range structure. Phys. Fluids 9 (9), 1728–1752.CrossRefGoogle Scholar
Liese, F. & Vajda, I. 2006 On divergences and informations in statistics and information theory. IEEE Trans. Inf. Theory 52 (10), 4394–4412.CrossRefGoogle Scholar
Lumley, J. L. 1965 Interpretation of time spectra measured in high-intensity shear flows. Phys. Fluids 8, 1056–1062.CrossRefGoogle Scholar
Mancinelli, M., Pagliaroli, T., Camussi, R. & Castelain, T. 2018 On the hydrodynamic and acoustic nature of pressure proper orthogonal decomposition modes in the near field of a compressible jet. J. Fluid Mech. 836, 998–1008.CrossRefGoogle Scholar
Moin, P. 2009 Revisiting Taylor’s hypothesis. J. Fluid Mech. 640, 1–4.CrossRefGoogle Scholar
Pope, S. B.2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Renard, N. & Deck, S. 2015 On the scale-dependent turbulent convection velocity in a spatially developing flat plate turbulent boundary layer at Reynolds number Re 𝜃 = 13 000. J. Fluid Mech. 775, 105–148.CrossRefGoogle Scholar
Romano, G. P. 1995 Analysis of two-point velocity measurements in near-wall flows. Exp. Fluids 20, 68–83.CrossRefGoogle Scholar
Taira, K., Brunton, S. L., Dawson, S. T. M., Rowley, C. W., Colonius, T., McKeon, B. J., Schmidt, O. T., Gordeyev, S., Theofilis, V. & Ukeiley, L. S. 2017 Modal analysis of fluid flows: an overview. AIAA J. 4013–4041.CrossRefGoogle Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164, 476–490.CrossRefGoogle Scholar
Tennekes, H. 1975 Eulerian and Lagrangian time microscales in isotropic turbulence. J. Fluid Mech. 67, 561–567.CrossRefGoogle Scholar
Wilczek, M. & Narita, Y. 2012 Wave-number-frequency spectrum for turbulence from a random sweeping hypothesis with mean flow. Phys. Rev. E 86, 066308.Google ScholarPubMed
Wilczek, M., Stevens, R. J. A. M. & Meneveau, C. 2015 Spatio-temporal spectra in the logarithmic layer of wall turbulence: large-eddy simulations and simple models. J. Fluid Mech. 769, R1.CrossRefGoogle Scholar
Wills, J. A. B. 1964 On convection velocities in turbulent shear flows. J. Fluid Mech. 20, 417–432.CrossRefGoogle Scholar
Wu, T., Geng, C. H., Yao, Y. C., Xu, C. X. & He, G. W. 2017 Characteristics of space–time energy spectra in turbulent channel flows. Phys. Rev. Fluids 2 (8), 084609.CrossRefGoogle Scholar
Yang, X. I. A. & Howland, M. F. 2018 Implication of Taylor’s hypothesis on measuring flow modulation. J. Fluid Mech. 836, 222–237.CrossRefGoogle Scholar
Zhao, X. & He, G. W. 2009 Space–time correlations of fluctuating velocities in turbulent shear flows. Phys. Rev. E 79, 046316.Google ScholarPubMed