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Measurement of Turbulent Spatial Structure and Kinetic Energy Spectrum—Part 1: Convection Record Method

  • Preben BuchhaveEmail author
  • Clara M. Velte
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 196)

Abstract

A novel exact temporal to spatial mapping for point measurements in turbulence has been developed. The spatial record is obtained based on the instantaneous velocity magnitude, \(u=|\mathbf {u}|\), creating an exact mapping between the sampling interval, \(\varDelta t\), and the spatial record counterpart, \(\varDelta s\), through the relation \(\varDelta s_n = u_n \varDelta t_n\). n indicates the sample number in a measurement sequence. Summation of the consecutive streakline elements, \(\varDelta s\), corresponding to the convection distance of the fluid, results in a spatial “convection record”. The exact mapping applies to all flows, since it is based on the instantaneous velocity magnitude, thereby incorporating all relevant aspects of the flow dynamics. Even high intensity non-equilibrium spatial records can be measured using this mapping, which is most straightforwardly applied using laser Doppler anemometry measurements. Computer simulated high intensity LDA data demonstrate the technique. The method will also be demonstrated on measurements in a round turbulent jet in part 2.

References

  1. 1.
    P. Buchhave, C.M. Velte, Conversion of measured turbulence spectra from temporal to spatial domain. in Whither Turbulence and Big Data in the 21st Century? (Springer International Publishing, 2017), pp. 343–362Google Scholar
  2. 2.
    G.I. Taylor, The spectrum of turbulence. Proc. R. Soc. Lond., Ser. A 164, 476 (1938)Google Scholar
  3. 3.
    C.C. Lin, On Taylor’s hypothesis and the acceleration terms in the Navier-Stokes equations. J. App. Math. 10, 295 (1953)MathSciNetzbMATHGoogle Scholar
  4. 4.
    J.L. Lumley, Interpretation of time spectra measured in high-intensity shear flows. Phys. Fluids 8, 1056 (1965)CrossRefzbMATHGoogle Scholar
  5. 5.
    M.J. Fisher, P.O.A.L. Davies, Correlation measurements in a nonfrozen pattern of turbulence. J. Fluid Mech. 18, 97–116 (1964)CrossRefzbMATHGoogle Scholar
  6. 6.
    J.C. Wyngaard, S.F. Clifford, Taylor’s hypothesis and high frequency turbulence spectra. J. Atm. Sci. 34, 922 (1977)CrossRefGoogle Scholar
  7. 7.
    A.S. Gurvich, Influence of the temporal evolution of turbulent inhomogeneities on frequency spectra. Atmos. Ocean. Phys. 16, 231–237 (1980)Google Scholar
  8. 8.
    R.A. Antonia, N. Phan-Thien, A.J. Chambers, Taylor’s hypothesis and the probability density functions of temporal velocity and temperature derivatives in a turbulent flow. J. Fluid Mech. 100, 193 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    J.W. Deardorff, G.E. Willis, Investigation of the frozen-turbulence hypothesis for temperature spectra in a convectively mixed layer. Phys. Fluids 25, 21–28 (1982)CrossRefGoogle Scholar
  10. 10.
    J.C. Kaimal, R.A. Eversole, D.H. Lenschow, B.B. Stankov, P.H. Kahn, J.A. Businger, Spectral characteristics of the convective boundary layer over uneven terrain. J. Atmos. Sci. 39, 1098–1114 (1982)CrossRefGoogle Scholar
  11. 11.
    G. Heskestad, A generalized Taylor hypothesis with application for high Reynolds number turbulent shear flows. J. Appl. Math. 32, 735 (1965)Google Scholar
  12. 12.
    H. Tennekes, Eulerian and Lagrangian time microscales in isotropic turbulence. J. Fluid Mech. 67, 561 (1975)CrossRefzbMATHGoogle Scholar
  13. 13.
    W.C. Thacker, A transformation relating temporal and spatial spectra of turbulent kinetic energy. Boulder, Colo. : Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, Atlantic Oceanographic and Meteorological Laboratories, Miami, Florida (1977)Google Scholar
  14. 14.
    F.H. Champagne, The fine-scale structure of the turbulent velocity field. J. Fluid Mech. 78, 67 (1978)CrossRefGoogle Scholar
  15. 15.
    K.B.M.Q. Zaman, A.K.M.F. Hussain, Taylor’s hypothesis and large-scale coherent structures. J. Fluid Mech. 112, 379 (1981)CrossRefGoogle Scholar
  16. 16.
    J. Mi, R.A. Antonia, Corrections to Taylor’s hypothesis in a turbulent circular jet. Phys. Fluids 6, 1548 (1994)CrossRefzbMATHGoogle Scholar
  17. 17.
    E. Gledzer, On the Taylor hypothesis corrections for measured energy spectra of turbulence. Physica D 104, 163 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    P. Buchhave, Errors and correction methods in turbulence measurements with the LDA. PhD Dissertation, State University of New York at Buffalo (1979)Google Scholar
  19. 19.
    C.M. Velte, Characterization of vortex generator induced flow. PhD Dissertation, Technical University of Denmark (2009)Google Scholar
  20. 20.
    C.M. Velte, W.K. George, P. Buchhave, Estimation of burst-mode LDA power spectra. Exp. Fluids 55, 1674 (2014)CrossRefGoogle Scholar
  21. 21.
    P. Buchhave, W.K. George, J.L. Lumley, The measurement of turbulence with the laser-Doppler anemometer. Ann. Rev. Fluid Mech. 11, 443 (1979)CrossRefGoogle Scholar
  22. 22.
    P. Buchhave, C.M. Velte, Reduction of noise and bias in randomly sampled power spectra. Exp Fluids 56, 79 (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Intarsia OpticsBirkerødDenmark
  2. 2.Technical University of DenmarkKgs. LyngbyDenmark

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