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Spatio-temporal spectra in the logarithmic layer of wall turbulence: large-eddy simulations and simple models

  • Michael Wilczek (a1) (a2), Richard J. A. M. Stevens (a1) (a3) and Charles Meneveau (a1)


Motivated by the need to characterize the spatio-temporal structure of turbulence in wall-bounded flows, we study wavenumber–frequency spectra of the streamwise velocity component based on large-eddy simulation (LES) data. The LES data are used to measure spectra as a function of the two wall-parallel wavenumbers and the frequency in the equilibrium (logarithmic) layer. We then reformulate one of the simplest models that is able to reproduce the observations: the random sweeping model with a Gaussian large-scale fluctuating velocity and with additional mean flow. Comparison with LES data shows that the model captures the observed temporal decorrelation, which is related to the Doppler broadening of frequencies. We furthermore introduce a parameterization for the entire wavenumber–frequency spectrum $E_{11}(k_{1},k_{2},{\it\omega};z)$ , where $k_{1}$ , $k_{2}$ are the streamwise and spanwise wavenumbers, ${\it\omega}$ is the frequency and $z$ is the distance to the wall. The results are found to be in good agreement with LES data.


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Albertson, J. D. & Parlange, M. B. 1999 Surface length scales and shear stress: implications for land–atmosphere interaction over complex terrain. Water Resour. Res. 35 (7), 21212132.
Banerjee, T. & Katul, G. G. 2013 Logarithmic scaling in the longitudinal velocity variance explained by a spectral budget. Phys. Fluids 25 (12), 125106.
Bou-Zeid, E., Meneveau, C. & Parlange, M. B. 2005 A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids 17, 025105.
Chen, S. & Kraichnan, R. H. 1989 Sweeping decorrelation in isotropic turbulence. Phys. Fluids A 1 (12), 20192024.
Davidson, P. A., Krogstad, P.-A. & Nickels, T. B. 2006 A refined interpretation of the logarithmic structure function law in wall layer turbulence. Phys. Fluids 18 (6), 065112.
Del Álamo, J. C. & Jiménez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 526.
Fisher, M. J. & Davies, P. O. A. L. 1964 Correlation measurements in a non-frozen pattern of turbulence. J. Fluid Mech. 18, 97116.
George, W. K., Hussein, H. J. & Woodward, S. H.1989 An evaluation of the effect of a fluctuating convection velocity on the validity of Taylor’s hypothesis. In Proceedings of the 10th Australasian Fluid Mech. Conference, University of Melbourne, 1989 (ed. A. E. Perry et al.), vol. II, pp. 11.5–11.8.
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.
Hultmark, M., Vallikivi, M., Bailey, S. C. C. & Smits, A. J. 2012 Turbulent pipe flow at extreme Reynolds numbers. Phys. Rev. Lett. 108 (9), 94501.
Jimenez, J. 2013 Near-wall turbulence. Phys. Fluids 25 (10), 101302.
Katul, G., Parlange, M., Albertson, J. & Chu, C.-R. 1995 The random sweeping decorrelation hypothesis in stratified turbulent flows. Fluid Dyn. Res. 16 (5), 275295.
Kraichnan, R. H. 1964 Kolmogorov’s hypothesis and Eulerian turbulence theory. Phys. Fluids 7, 17231734.
Krogstad, P. Å., Kaspersen, J. H. & Rimestad, S. 1998 Convection velocities in a turbulent boundary layer. Phys. Fluids 10 (4), 949957.
LeHew, J., Guala, M. & McKeon, B. J. 2011 A study of the three-dimensional spectral energy distribution in a zero pressure gradient turbulent boundary layer. Exp. Fluids 51 (4), 9971012.
Lumley, J. L. 1965 Interpretation of time spectra measured in high-intensity shear flows. Phys. Fluids 8 (6), 10561062.
Mann, J. 1994 The spatial structure of neutral atmospheric surface-layer turbulence. J. Fluid Mech. 273, 141168.
Marusic, I. & Kunkel, G. J. 2003 Streamwise turbulence intensity formulation for flat-plate boundary layers. Phys. Fluids 15, 24612464.
Marusic, I., Monty, J. P., Hultmark, M. & Smits, A. J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173217.
Perry, A. E., Henbest, S. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163199.
Porté-Agel, F., Meneveau, C. & Parlange, M. B. 2000 A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J. Fluid Mech. 415, 261284.
Praskovsky, A. A., Gledzer, E. B., Karyakin, M. Yu. & Zhou, Y. 1993 The sweeping decorrelation hypothesis and energy inertial scale interaction in high Reynolds number flows. J. Fluid Mech. 248, 493511.
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353375.
Stevens, R. J. A. M., Wilczek, M. & Meneveau, C. 2014 Large-eddy simulation study of the logarithmic law for second- and higher-order moments in turbulent wall-bounded flow. J. Fluid Mech. 757, 888907.
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.
Tomkins, C. D. & Adrian, R. J. 2005 Energetic spanwise modes in the logarithmic layer of a turbulent boundary layer. J. Fluid Mech. 545, 141162.
Wallace, J. M. 2014 Space–time correlations in turbulent flow: a review. Theor. Appl. Mech. Lett. 4 (2), 22003.
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 Height-dependence of spatio-temporal spectra of wall-bounded turbulence – LES results and model predictions. J. Turbul. (submitted).
Wilczek, M., Stevens, R. J. A. M., Narita, Y. & Meneveau, C. 2014 A wavenumber–frequency spectral model for atmospheric boundary layers. J. Phys.: Conf. Ser. 524 (1), 012104.
Wills, J. A. B. 1964 On convection velocities in turbulent shear flows. J. Fluid Mech. 20, 417432.
Wyngaard, J. C. 2010 Turbulence in the Atmosphere. Cambridge University Press.
Wyngaard, J. C. & Clifford, S. F. 1977 Taylor’s hypothesis and high-frequency turbulence spectra. J. Atmos. Sci. 34 (6), 922929.
Zhao, X. & He, G.-W. 2009 Space–time correlations of fluctuating velocities in turbulent shear flows. Phys. Rev. E 79, 046316.
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Spatio-temporal spectra in the logarithmic layer of wall turbulence: large-eddy simulations and simple models

  • Michael Wilczek (a1) (a2), Richard J. A. M. Stevens (a1) (a3) and Charles Meneveau (a1)


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