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Implication of Taylor’s hypothesis on measuring flow modulation

Published online by Cambridge University Press:  11 December 2017

X. I. A. Yang Open the ORCID record for X. I. A. Yang [Opens in a new window]  and
M. F. Howland Open the ORCID record for M. F. Howland [Opens in a new window]
X. I. A. Yang
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
M. F. Howland*
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: [email protected]
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Abstract

A convective velocity must be specified when using Taylor’s frozen eddy hypothesis to relate temporal and spatial fluctuations. Depending on the quantity of interest, using different convective velocities (i.e. time-mean velocity, global convective velocity, etc.) may lead to different conclusions. Often, using Taylor’s hypothesis, the relation between temporal and spatial fluctuations is simplified by assuming a temporally averaged velocity as the convection velocity. In flows where turbulence fluctuations are much smaller than the mean flow velocity, the above treatment does not bring in much error (at least for short periods of time). However, when turbulence fluctuations are comparable to the mean velocity, using a constant convective velocity for fluid motions of all scales can sometimes be problematic. In the context of wall-bounded flows, turbulence fluctuations are comparable to the mean flow in the near-wall region, and as a result, using a constant global convective velocity for converting temporal signals to spatial ones distorts the spatial eddies. Although such distortion will not significantly affect measurements of flow quantities including central moments and power spectra, the significance of amplitude modulation is largely overestimated. Here, we show that if temporal hot-wire data are to be used for studying spatial amplitude modulation, the local fluid velocity must be used as the local convective velocity. The impact of amplitude modulation on power spectra and skewness are reconsidered using the proposed correction.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 836 , 10 February 2018 , pp. 222 - 237
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Copyright
© 2017 Cambridge University Press 

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References

Agostini, L. & Leschziner, M. A. 2014 On the influence of outer large-scale structures on near-wall turbulence in channel flow. Phys. Fluids 26 (7), 075107.Google Scholar
Baars, W. J., Hutchins, N. & Marusic, I. 2017 Reynolds number trend of hierarchies and scale interactions in turbulent boundary layers. Phil. Trans. R. Soc. Lond. A 375 (2089), 20160077.Google Scholar
Baars, W. J., Talluru, K. M., Hutchins, N. & Marusic, I. 2015 Wavelet analysis of wall turbulence to study large-scale modulation of small scales. Exp. Fluids 56 (10), 188.Google Scholar
Bandyopadhyay, P. R. & Hussain, A. 1984 The coupling between scales in shear flows. Phys. Fluids 27 (9), 2221–2228.Google Scholar
Chernyshenko, S. I., Marusic, I. & Mathis, R.2012 Quasi-steady description of modulation effects in wall turbulence. arXiv:1203.3714.Google Scholar
Choi, H. & Moin, P. 2012 Grid-point requirements for large eddy simulation: Chapman’s estimates revisited. Phys. Fluids 24 (1), 011702.Google 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.Google Scholar
Del Alamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144.Google Scholar
Doron, P., Bertuccioli, L., Katz, J. & Osborn, T. R. 2001 Turbulence characteristics and dissipation estimates in the coastal ocean bottom boundary layer from PIV data. J. Phys. Oceanogr. 31 (8), 2108–2134.Google Scholar
Dróżdż, A. & Elsner, W. 2017 Amplitude modulation and its relation to streamwise convection velocity. Intl J. Heat Fluid Flow 63, 67–74.CrossRefGoogle Scholar
Ganapathisubramani, B., Hutchins, N., Monty, J. P., Chung, D. & Marusic, I. 2012 Amplitude and frequency modulation in wall turbulence. J. Fluid Mech. 712, 61–91.CrossRefGoogle Scholar
Geng, C., He, G., Wang, Y., Xu, C., Lozano-Durán, A. & Wallace, J. M. 2015 Taylor’s hypothesis in turbulent channel flow considered using a transport equation analysis. Phys. Fluids 27 (2), 025111.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.Google Scholar
Hultmark, M., Vallikivi, M., Bailey, S. C. C. & Smits, A. J. 2012 Turbulent pipe flow at extreme Reynolds numbers. Phys. Rev. Lett. 108 (9), 094501.CrossRefGoogle ScholarPubMed
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365 (1852), 647–664.Google Scholar
Hutchins, N., Nickels, T. B., Marusic, I. & Chong, M. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103–136.Google Scholar
Kim, J. & Hussain, F. 1993 Propagation velocity of perturbations in turbulent channel flow. Phys. Fluids 5 (3), 695–706.CrossRefGoogle Scholar
Lee, M., Malaya, N. & Moser, R. D. 2013 Petascale direct numerical simulation of turbulent channel flow on up to 786k cores. In Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, p. 61. ACM.Google Scholar
Lee, M. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to Re 𝜏 ≈ 5200. J. Fluid Mech. 774, 395–415.Google Scholar
Lozano-Durán, A. & Jiménez, J. 2014a Effect of the computational domain on direct simulations of turbulent channels up to Re 𝜏 = 4200. Phys. Fluids 26 (1), 011702.Google Scholar
Lozano-Durán, A. & Jiménez, J. 2014b Time-resolved evolution of coherent structures in turbulent channels: characterization of eddies and cascades. J. Fluid Mech. 759, 432–471.Google Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193–196.Google Scholar
Marusic, I., Monty, J. P., Hultmark, M. & Smits, A. J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.Google Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009a Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.Google Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2011a A predictive inner-outer model for streamwise turbulence statistics in wall-bounded flows. J. Fluid Mech. 681, 537–566.Google Scholar
Mathis, R., Marusic, I., Chernyshenko, S. I. & Hutchins, N. 2013 Estimating wall-shear-stress fluctuations given an outer region input. J. Fluid Mech. 715, 163.CrossRefGoogle Scholar
Mathis, R., Marusic, I., Hutchins, N. & Sreenivasan, K. 2011b The relationship between the velocity skewness and the amplitude modulation of the small scale by the large scale in turbulent boundary layers. Phys. Fluids 23 (12), 121702.Google Scholar
Mathis, R., Monty, J. P., Hutchins, N. & Marusic, I. 2009b Comparison of large-scale amplitude modulation in turbulent boundary layers, pipes, and channel flows. Phys. Fluids 21 (11), 111703.Google Scholar
McKeon, B. 2017 The engine behind (wall) turbulence: perspectives on scale interactions. J. Fluid Mech. 817, doi:10.1017/jfm.2017.115.Google Scholar
Moin, P. 2009 Revisiting Taylor’s hypothesis. J. Fluid Mech. 640, 1–4.CrossRefGoogle Scholar
Park, G., Howland, M. F., Lozano-Duran, A. & Moin, P. 2016 Prediction of wall shear-stress fluctuations in wall-modeled large-eddy simulation. In APS Meeting Abstracts.Google Scholar
Piomelli, U. & Balaras, E. 2002 Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34 (1), 349–374.Google Scholar
Rao, K. N., Narasimha, R. & Narayanan, M. A. B. 1971 The ‘bursting’ phenomenon in a turbulent boundary layer. J. Fluid Mech. 48 (02), 339–352.Google Scholar
Schlatter, P. & Örlü, R. 2010 Quantifying the interaction between large and small scales in wall-bounded turbulent flows: a note of caution. Phys. Fluids 22 (5), 051704.Google Scholar
Sidebottom, W., Cabrit, O., Marusic, I., Meneveau, C., Ooi, A. & Jones, D. 2014 Modelling of wall shear-stress fluctuations for large-eddy simulation. In Proc. 19th Australasian Fluid Mechanics Conf., Melbourne, Australia.Google Scholar
Squire, D. T., Hutchins, N., Morrill-Winter, C., Schultz, M. P., Klewicki, J. C. & Marusic, I. 2017 Applicability of Taylor’s hypothesis in rough- and smooth-wall boundary layers. J. Fluid Mech. 812, 398–417.Google Scholar
Talluru, K. M., Baidya, R., Hutchins, N. & Marusic, I. 2014 Amplitude modulation of all three velocity components in turbulent boundary layers. J. Fluid Mech. 746, R1.Google Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164, 476–490.Google Scholar
Yang, X. I. A., Marusic, I. & Meneveau, C. 2016a Hierarchical random additive process and logarithmic scaling of generalized high order, two-point correlations in turbulent boundary layer flow. Phys. Rev. Fluids 1 (2), 024402.CrossRefGoogle Scholar
Yang, X. I. A., Marusic, I. & Meneveau, C. 2016b Moment generating functions and scaling laws in the inertial layer of turbulent wall-bounded flows. J. Fluid Mech. 791, R2.CrossRefGoogle Scholar
Yang, X. I. A., Meneveau, C., Marusic, I. & Biferale, L. 2016c Extended self-similarity in moment-generating-functions in wall-bounded turbulence at high Reynolds number. Phys. Rev. Fluids 1 (4), 044405.Google 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.Google Scholar
Zhang, C. & Chernyshenko, S. I. 2016 Quasisteady quasihomogeneous description of the scale interactions in near-wall turbulence. Phys. Rev. Fluids 1 (1), 014401.Google Scholar