Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-29T12:23:09.989Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimation of turbulent convection velocities and corrections to Taylor's approximation

Published online by Cambridge University Press:  29 October 2009

JUAN C. DEL ÁLAMO  and
JAVIER JIMÉNEZ
JUAN C. DEL ÁLAMO
Affiliation:
MAE Department, University of California San Diego, La Jolla, CA 92093, USA
JAVIER JIMÉNEZ*
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, 28040 Madrid, Spain Centre for Turbulence Research, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A new method is introduced for estimating the convection velocity of individual modes in turbulent shear flows that, in contrast to most previous ones, only requires spectral information in the temporal or spatial direction over which a modal decomposition is desired, while only using local derivatives in other directions. If no spectral information is desired, the method provides a natural definition for the average convection velocity, as well as a way to estimate the accuracy of the frozen-turbulence approximation. Existing data from numerical turbulent channels at friction Reynolds numbers Reτ ≤ 1900 are used to validate the new method against classical ones, and to characterize the dependence of the convection velocity on the eddy wavelength and wall distance. The results indicate that the small scales in turbulent channels travel at the local mean velocity, while large ‘global’ modes travel at a more uniform speed proportional to the bulk velocity. To estimate the systematic deviations introduced in experimental spectra by the use of Taylor's approximation with a wavelength-independent convection velocity, a semi-empirical fit to the computed convection velocities is provided. It represents well the data throughout the Reynolds number range of the simulations. It is shown that Taylor's approximation not only displaces the large scales near the wall to shorter apparent wavelengths but also modifies the shape of the spectrum, giving rise to spurious peaks similar to those observed in some experiments. To a lesser extent the opposite is true above the logarithmic layer. The effect increases with the Reynolds number, suggesting that some of the recent challenges to the kx−1 energy spectrum may have to be reconsidered.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 640 , 10 December 2009 , pp. 5 - 26
Copyright
Copyright © Cambridge University Press 2009

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

REFERENCES

del Álamo, J. C. & Jiménez, J. 2002 Characteristics of scalar dispersion in turbulent-channel flow. In Proceedings of Summer Program (ed. Moin, Parviz, Mansour, Nagi N. & Bradshaw, Peter), pp. 203–214. Center for Turbulence Research, Stanford University.Google 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. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205–213.CrossRefGoogle Scholar
del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144.CrossRefGoogle Scholar
del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2006 Self-similar vortex clusters in the logarithmic region. J. Fluid Mech. 561, 329–358.CrossRefGoogle Scholar
Bullock, K. J., Cooper, R. E. & Abernathy, F. H. 1978 Structural similarity in radial correlations and spectra of longitudinal velocity fluctuations in pipe flow. J. Fluid Mech. 88, 585–608.CrossRefGoogle Scholar
Capon, J. 1969 High-resolution frequency–wavenumber spectrum analysis. Proc. IEEE 57 (8), 1408–1418.CrossRefGoogle Scholar
Cess, R. D. 1958 A survey of the literature on heat transfer in turbulent tube flow. Tech. Rep. Report 8-0529-R24. Westinghouse Research.Google Scholar
Choi, H. & Moin, P. 1990 On the space–time characteristics of wall-pressure fluctuations. Phys. Fluids A 2, 1450–1460.CrossRefGoogle Scholar
Comte-Bellot, G. & Corrsin, S. 1971 Single eulerian time correlation of full and narrow band velocity signals in grid-generated ‘isotropic’ turbulence. J. Fluid Mech. 48, 273–337.CrossRefGoogle Scholar
Dennis, D. J. & Nickels, T. B. 2008 On the limitations of Taylor's hypothesis in constructing long structures in a turbulent boundary layer. J. Fluid Mech. 614, 197–206.CrossRefGoogle Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Fisher, M. J. & Davies, P. O. A. L. 1963 Correlation measurements in a non-frozen pattern of turbulence. J. Fluid Mech. 18, 97–116.CrossRefGoogle Scholar
Flores, O. & Jiménez, J. 2006 Effect of wall-boundary disturbances on turbulent channel flows. J. Fluid Mech. 566, 357–376.CrossRefGoogle Scholar
Goldschmidt, V. W., Young, M. F. & Ott, E. S. 1981 Turbulent convective velocities (broadband and wavenumber dependent) in a plane jet. J. Fluid Mech. 105, 327–345.CrossRefGoogle Scholar
Hites, M. 1997 Scaling of high-Reynolds number turbulent boundary layers in the national diagnostic facility. PhD thesis, Illinois Institute of Technology, Chicago, IL.Google Scholar
Hoyas, S. & Jiménez, J. 2006 Turbulent channel simulation at re τ = 2000. Phys. Fluids 18, 011702.CrossRefGoogle Scholar
Hussain, A. K. M. F. & Clark, A. R. 1981 Measurements of wavenumber-celerity spectrum in plane and axisymmetric jets. AIAA J. 19, 51–55.CrossRefGoogle Scholar
Jiménez, J. 2007 Recent developments in wall-bounded turbulence. Rev. R. Acad. Cien. Ser. A, Mat. 101, 187–203.Google Scholar
Jiménez, J., del Álamo, J. C. & Flores, O. 2004 The large-scale dynamics of near-wall turbulence. J. Fluid Mech. 505, 179–199.CrossRefGoogle Scholar
Jiménez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236.CrossRefGoogle Scholar
Kim, J. & Hussain, F. 1993 Propagation velocity of perturbations in turbulent channel flow. Phys. Fluids 6, 695–706.CrossRefGoogle Scholar
Krogstad, P. A., Kaspersen, J. H. & Rimestad, S. 1998 Convection velocities in a turbulent boundary layer. Phys. Fluids 10 (4), 949–957.CrossRefGoogle Scholar
Kunkel, G. J. 2003 An experimental study of the high Reynolds number boundary layer. PhD thesis, Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN.Google Scholar
Kunkel, G. J. & Marusic, I. 2006 Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using atmospheric data. J. Fluid Mech. 548, 375–402.CrossRefGoogle Scholar
Monty, J. & Chong, M. 2008 Comparing experimental and direct numerical simulation results from a turbulent channel flow. In Proceedings of the 61st Annual Meeting Division of Fluid Dynamics, EB-10. American Physical Society.Google Scholar
Morrison, J. F., Jiang, W., McKeon, B. J. & Smits, A. J. 2002 Reynolds number dependence of streamwise velocity spectra in turbulent pipe flow. Phys. Rev. Lett. 88, 214501.CrossRefGoogle ScholarPubMed
Nickels, T. B., Marusic, I., Hafez, S., Hutchins, N. & Chong, M. S. 2007 Some predictions of the attached eddy model for a high Reynolds number boundary layer. Phil. Trans. R. Soc. A 365, 807–822.CrossRefGoogle ScholarPubMed
Perry, A. E. & Abell, C. J. 1975 Scaling laws for pipe-flow turbulence. J. Fluid Mech. 67, 257–271.CrossRefGoogle Scholar
Perry, A. E. & Abell, C. J. 1977 Asymptotic similarity of turbulence structures in smooth- and rough-walled pipes. J. Fluid Mech. 79, 785–799.CrossRefGoogle Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 2007 Numerical Recipes. The Art of Scientific Computing, 3rd edn. Cambridge University Press.Google Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. 164 (919), 476–490.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flows, 2nd edn. Cambridge University Press.Google Scholar
Willmarth, W. W. & Wooldridge, C. E. 1962 Measurements of the fluctuating pressure at the wall beneath a thick turbulent boundary layer. J. Fluid Mech. 14 (2), 187–210.CrossRefGoogle Scholar
Wills, J. A. B. 1964 On convection velocities in turbulent shear flows. J. Fluid Mech. 20, 417–432.CrossRefGoogle Scholar
Zaman, K. B. M. Q. & Hussain, A. K. M. F. 1981 Taylor hypothesis and large-scale coherent structures. J. Fluid Mech. 112, 379–396.CrossRefGoogle Scholar