Abstract
A novel type of conversion of point-measured temporal turbulence power spectra to wavenumber space is proposed. By converting the temporal measurement records into spatial connected streakline elements, the classical assumption of a local mean velocity in Taylor’s hypothesis can be completely bypassed. The presented method is illustrated with examples from both hot-wire anemometry and laser Doppler velocimetry, but may in principle just as well be applied to any flow field property such as pressure, temperature, concentration, or density. Computer generated data of a large eddy with a sharp modulation frequency as well as a turbulent von Karman spectrum are presented to demonstrate the correctness of the principle. Laser Doppler velocimetry measurements, which in themselves appear to be particularly suitable for application of this technique, taken at different off-center positions in a round turbulent jet are then used to demonstrate the difference between the current and the classical temporal-to-spatial domain conversions. The novel method displays the behavior expected from spatial spectra measured along homogeneous directions in the very same turbulent axisymmetric jet, while the classical Taylor’s hypothesis, as expected, shows increasing deviation further away from the center axis where the turbulence intensity grows rapidly. Interpretation of first-order statistics as well as different kinds of spectral estimates is proposed and discussed.
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G. Taylor, The spectrum of turbulence. Proc. R. Soc. Lond. (1938)
J.L. Lumley, Interpretation of time spectra measured in high intensity shear flows. Phys. Fluids 8, 1056 (1965)
F.H. Champagne, The fine-scale structure of the turbulent velocity field. J. Fluid Mech. 86, 67–108 (1978)
J.C. Wyngaard, S.F. Clifford, Taylor’s hypothesis and high-frequency turbulence spectra. J. Atmos. Sci. 34 (1977)
W.K. George, H.H. Hussein, S.H. Woodward, An evaluation of the effect of a fluctuation convection velocity on the validity of Taylor’s hypothesis, in Proceedings of the 10th Australasian Fluid Mechanics Conference, Melbourne, vol. 11.5 (1989)
G.K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge University Press, Cambridge, 1953)
D. Schlipf, D. Trabucchi, O. Bischoff, M. Hofsäß, J. Mann, T. Mikkelsen, A. Rettenmeier, J.J. Trujillo, M. Kühn, Testing of frozen turbulence hypothesis for wind turbine applications with a scanning LIDAR system, in 15th International Symposium for the Advancement of Boundary Layer Remote Sensing, Paris, June 28–30, 2010
A.K.M. Uddin, A.E. Perry, I. Marusic, On the validity of Taylor’s hypothesis in wall turbulence. J. Mech. Eng. Res. Dev., 19–20 (1997)
H. Sadeghi, A. Pollard, Axial velocity spectra scaling in a round, free jet. Turb. Heat Mass Transf. 7 (2012)
J. Mi, R.A. Antonia, Corrections to Taylor’s hypothesis in a turbulent circular jet. Phys. Fluids 6, 1548 (1994)
K.B.M.Q. Zaman, A.K.M.F. Hussain, Taylor hypothesis and large-scale coherent structures. J. Fluid Mech. 112, 379–396 (1981)
M. Wilczek, H. Xu, Y. Narita, A note on Taylor’s hypothesis under large-scale flow variation. Nonlin. Proc. Geophys. 21, 645–649 (2014)
J.C. Del Alamo, J. Jimenez, Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 5–26 (2009)
J.-F. Pinton, R. Labbé, Correction to the Taylor hypothesis in swirling flows. J. Phys. II France 4, 1461–1468 (1994)
P. Buchhave, W.K. George, J. Lumley, The measurement of turbulence with the laser-Doppler anemometer. Ann. Rev. Fluid Mech. 11, 443–504 (1979)
C.M. Velte, W.K. George, P. Buchhave, Estimation of burst-mode LDA power spectra. Exp. Fluids 55, 1674 (2014)
P. Buchhave, C.M. Velte, Reduction of noise and bias in randomly sampled power spectra. Exp. Fluids 56, 79 (2015)
C.M. Velte, P. Buchhave, W.K. George, Dead time effects in laser Doppler anemometry measurements. Exp. Fluids 55, 1836 (2014)
P. Buchhave, C.M. Velte, W.K. George, The effect of dead time on randomly sampled power spectral estimates. Exp. Fluids 55, 1680 (2014)
Hodžić, PIV measurements on a Turbulent Free Jet, MSc dissertation, Technical University of Denmark, Department of Mechanical Engineering, 2014
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Buchhave, P., Velte, C.M. (2017). Conversion of Measured Turbulence Spectra from Temporal to Spatial Domain. In: Pollard, A., Castillo, L., Danaila, L., Glauser, M. (eds) Whither Turbulence and Big Data in the 21st Century?. Springer, Cham. https://doi.org/10.1007/978-3-319-41217-7_18
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DOI: https://doi.org/10.1007/978-3-319-41217-7_18
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