Skip to main content Accessibility help
×
Home

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

  • Ting Wu (a1) and Guowei He (a1) (a2)

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.

Copyright

Corresponding author

Email address for correspondence: hgw@lnm.imech.ac.cn

References

Hide All
Adrian, R. J. & Moin, P. 1988 Stochastic estimation of organized turbulent structure: homogeneous shear flow. J. Fluid Mech. 190, 531559.
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), 39333940.
Bossuyt, J., Meneveau, C. & Meyers, J. 2017 Wind farm power fluctuations and spatial sampling of turbulent boundary layers. J. Fluid Mech. 823, 329344.
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.
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, 351358.
Del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15, L41L44.
Del Álamo, J. C. & Jiménez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 526.
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, 234259.
Duraisamy, K., Iaccarino, G. & Xiao, H. 2019 Turbulence modeling in the age of data. Annu. Rev. Fluid Mech. 51, 357377.
Fisher, M. J. & Davies, P. O. A. 1964 Correlation measurements in a non-frozen pattern of turbulence. J. Fluid Mech. 18, 97116.
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.
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, 494539.
Gibbs, A. L. & Su, F. E. 2002 On choosing and bounding probability metrics. Intl Stat. Rev. 70 (3), 419435.
He, G. W., Jin, G. D. & Yang, Y. 2017 Space–time correlations and dynamic coupling in turbulent flows. Annu. Rev. Fluid Mech. 49, 5170.
He, G. W., Wang, M. & Lele, S. K. 2004 On the computation of space–time correlations by large-eddy simulation. Phys. Fluids 16 (11), 38593867.
He, G. W. & Zhang, J. B. 2006 Elliptic model for space–time correlations in turbulent shear flows. Phys. Rev. E 73, 055303.
Howland, M. F. & Yang, X. I. A. 2018 Dependence of small-scale energetics on large scales in turbulent flows. J. Fluid Mech. 852, 641662.
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 128.
Hutchins, N., Nickels, T. B., Marusic, I. & Chong, M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103136.
Jiménez, J. 2012 Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 44, 2745.
de Kat, R. & Ganapathisubramani, B. 2015 Frequency-wavenumber mapping in turbulent shear flows. J. Fluid Mech. 783, 166190.
Kevin, K., Monty, J. & Hutchins, N. 2019 The meandering behaviour of large-scale structures in turbulent boundary layers. J. Fluid Mech. 865, R1.
Kraichnan, R. H. 1964 Kolmogorov’s hypotheses and Eulerian turbulence theory. Phys. Fluids 7, 17231734.
Kraichnan, R. H. 1966 Isotropic turbulence and inertial-range structure. Phys. Fluids 9 (9), 17281752.
Liese, F. & Vajda, I. 2006 On divergences and informations in statistics and information theory. IEEE Trans. Inf. Theory 52 (10), 43944412.
Lumley, J. L. 1965 Interpretation of time spectra measured in high-intensity shear flows. Phys. Fluids 8, 10561062.
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, 9981008.
Moin, P. 2009 Revisiting Taylor’s hypothesis. J. Fluid Mech. 640, 14.
Pope, S. B.2000 Turbulent Flows. Cambridge University Press.
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, 105148.
Romano, G. P. 1995 Analysis of two-point velocity measurements in near-wall flows. Exp. Fluids 20, 6883.
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. 40134041.
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164, 476490.
Tennekes, H. 1975 Eulerian and Lagrangian time microscales in isotropic turbulence. J. Fluid Mech. 67, 561567.
Wilczek, M. & Narita, Y. 2012 Wave-number-frequency spectrum for turbulence from a random sweeping hypothesis with mean flow. Phys. Rev. E 86, 066308.
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.
Wills, J. A. B. 1964 On convection velocities in turbulent shear flows. J. Fluid Mech. 20, 417432.
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.
Yang, X. I. A. & Howland, M. F. 2018 Implication of Taylor’s hypothesis on measuring flow modulation. J. Fluid Mech. 836, 222237.
Zhao, X. & He, G. W. 2009 Space–time correlations of fluctuating velocities in turbulent shear flows. Phys. Rev. E 79, 046316.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

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

  • Ting Wu (a1) and Guowei He (a1) (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed