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«GEORGE TREVIÑO CHIRES Incorporated, PO Box 201481, San Antonio, TX 78220-8481, U.S.A. EDGAR L. ANDREAS U. S. Army Cold Regions Research and ...»

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An H = 2 T history of S(γ ) is required to ascertain the instantaneous mean ¯ and the random part χ(γ ), t − T ≤ γ ≤ t; see (1) and (2) and recall that S(t) t represents the present time. Comparing m.s.e. with the sensor accuracy defines T, see Equation (3). The memory L is then found from χ(γ ), see (5) and (6).

Based on the physical interpretation of L, AW is then defined as 10L and used to obtain (t, ω), see Equation (7), et seq.

The method formulated here (i) is frequency-shift invariant, meaning that it is independent of the frequency domain of χ(γ ); (ii) eliminates effects of userspecific biases such as user-selected window lengths; (iii) eliminates corruption caused by using a static algorithm (such as FFT) to analyse dynamic phenomena;

(iv) avoids degradation caused by using information from the future; (v) identifies, in real time, if and how frequency content, distribution, domain, and bandwidth, are changing; and (vi) reduces the possibility that short-lived information is lost or masked due to uncharacteristically long (or short) averaging intervals.

The three parameters σ, η, and L, obtained serve to quantify the local structure of the ABL. A fourth parameter, the t-dependent mean, is also determined but, since it is removed from S, does not affect the behaviour of. This parameter can be thought of as an instantaneous DC component. The exact relationship between T and AW is known only a posteriori. Specifically, ( T /AW) 0.1(σ /ACC)2, ¯ where (recall) that ACC is 0.01S for our data.

As a final point, turbulence researchers agree that the proper choice of scale is important in the search for Reynolds-number-independent features. Yet they typically use the same time interval for Reynolds averaging of all correlations being examined. The fact that classical Reynolds averaging has been used to investigate the structure of higher-order correlations and has not yet yielded an appreciable understanding of the turbulence problem might be due to an inappropriate choice of averaging times. The method formulated here addresses this concern.

246 GEORGE TREVIÑO AND EDGAR L. ANDREAS

–  –  –

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

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

14, 554–564.

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.

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

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

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

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

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

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.

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

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

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

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.

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

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.

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

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

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.

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.

SPECTRAL ANALYSIS OF NONSTATIONARY TURBULENCE

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

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



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