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Averaging Intervals For Spectral Analysis Of Nonstationary Turbulence

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Abstract

We formulate a method for determining the smallest time interval Δ Tover which a turbulence time series can be averaged to decompose it intoinstantaneous mean and random components. From the random part the method defines the optimal interval (or averaging window) AW over which this part should be averaged to obtain the instantaneous spectrum. Both Δ T and AW vary randomly with time and depend on physical properties of the turbulence. Δ T also depends on the accuracy of the measurements and is thus independent of AW. Interesting features of the method are its real-time capability and the non-equality between AW and Δ T.

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References

  • Andreas, E. L.: 1988, ‘Estimating Averaging Times for Point and Path-Averaged Measurements of Turbulence Spectra’, J. Appl. Meteorol. 27, 295–304.

    Google Scholar 

  • Andreas, E. L. and Treviño, G.: 1997, ‘Using Wavelets to Detect Trends’, J. Atmos. Oceanic Tech. 14, 554–564.

    Google Scholar 

  • Andreas, E. L., Hill, R. J., Gosz, J. R., Moore, D. I., Otto, W. D., and Sarma, A. D.: 1998, ‘Statistics of Surface-Layer Turbulence over Terrain with Metre-Scale Heterogeneity’, Boundary-Layer Meteorol. 86, 379–408.

    Google Scholar 

  • Bendat, J. S. and Piersol, A. G.: 1971, Random Data: Analysis and Measurement Procedures, Wiley-Interscience, New York, 407 pp.

    Google Scholar 

  • Blackwelder, R. F. and Kaplan, R. E.: 1976, ‘On the Wall Structure of the Turbulent Boundary Layer’, J. Fluid Mech. 76, 89–113.

    Google Scholar 

  • Bradshaw, P.: 1971, An Introduction to Turbulence and Its Measurement, Pergamon Press, Oxford, U.K., 218 pp.

    Google Scholar 

  • Cohen, L.: 1995, Time-Frequency Analysis, Prentice-Hall, New Jersey, 299 pp.

    Google Scholar 

  • Gluhovsky, A. and Agee, E.: 1994, ‘A Definitive Approach to Turbulence Statistical Studies in Planetary Boundary Layers’, J. Atmos. Sci. 51, 1682–1690.

    Google Scholar 

  • Gupta, A. K.: 1996, ‘Short-Time Averaging of Turbulent Shear Flow Signals’, in G. Treviño, J. C. Hardin, B. Douglas, and E. L. Andreas (eds.), Current Topics in Nonstationary Analysis, World Scientific, Singapore. pp. 159–173.

    Google Scholar 

  • Gupta, A. K., Laufer, J., and Kaplan, R. E.: 1971, ‘Spatial Structure in the Viscous Sublayer’, J. Fluid Mech. 50, 493–513.

    Google Scholar 

  • Henjes, K.: 1997, ‘Isotropic and Anisotropic Correlations in Turbulent Wind Speed Data’, Boundary-Layer Meteorol. 84, 149–167.

    Google Scholar 

  • Holman, R. E. and Hart, G. C.: 1972, ‘Structural Response to Segmented Nonstationary Random Excitation’, AIAA Journal 10, 1473–1478.

    Google Scholar 

  • Jones, D. L. and Parks, T. W.: 1990, ‘A High Resolution Data-Adaptive Time-Frequency Representation’, IEEE Trans. Acous., Speech Signal Proc. 38, 2127–2135.

    Google Scholar 

  • Kaimal, J. C., Clifford, S. F., and Lataitis, R. J.: 1989, ‘Effect of Finite Sampling on Atmospheric Spectra’, Boundary-Layer Meteorol. 47, 337–347.

    Google Scholar 

  • Lenschow, D. H., Mann, J., and Kristensen, L.: 1994, ‘How Long Is Long Enough When Measuring Fluxes and Other Turbulence Statistics?’, J. Atmos. Oceanic Tech. 11, 661–673.

    Google Scholar 

  • Lumley, J. L. and Panofsky, H. A.: 1964, The Structure of Atmospheric Turbulence, Interscience Publishers, New York, 239 pp.

    Google Scholar 

  • Papoulis, A.: 1965, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, New York, 583 pp.

    Google Scholar 

  • Sreenivasan, K. R., Chambers, A. J., and Antonia, R. A.: 1978, ‘Accuracy of Moments of Velocity and Scalar Fluctuations in the Atmospheric Surface Layer’, Boundary-Layer Meteorol. 14, 341–359.

    Google Scholar 

  • Treviño, G.: 1982, ‘The Frequency Spectrum of Nonstationary Random Processes’, in O. D. Anderson (ed.), Time Series Analysis: Theory and Practice 2, North-Holland, pp. 237–246.

  • Treviño, G.: 1985, ‘A Method for Approximating the Mean-Value of Nonstationary Random Data’, in O. D. Anderson (ed.), Time Series Analysis: Theory and Practice 7, North-Holland, pp. 465–473.

  • Wyngaard, J. C.: 1973, ‘On Surface-Layer Turbulence’, in D. A. Haugen (ed.), Workshop on Micrometeorology, American Meteorological Society, Boston, pp. 101–149.

    Google Scholar 

  • Wyngaard, J. C. and Clifford, S. F.: 1978, ‘Estimating Momentum, Heat and Moisture Fluxes from Structure Parameters’, J. Atmos. Sci. 35, 1204–1211.

    Google Scholar 

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Authors and Affiliations

  1. CHIRES Incorporated, PO Box 201481, San Antonio, TX, 78220-8481, U.S.A.

    George Treviño

  2. U. S. Army Cold Regions Research and Engineering Laboratory, Hanover, NH, 03755-1290, U.S.A.

    Edgar L. Andreas

Authors
  1. George Treviño
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  2. Edgar L. Andreas
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Treviño, G., Andreas, E.L. Averaging Intervals For Spectral Analysis Of Nonstationary Turbulence. Boundary-Layer Meteorology 95, 231–247 (2000). https://doi.org/10.1023/A:1002632004254

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  • DOI: https://doi.org/10.1023/A:1002632004254

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