Applied physics

, Volume 24, Issue 4, pp 323–329

Structure function in lieu of correlation function

  • E. O. Schulz-DuBois
  • I. Rehberg
Photophysics, Laser Chemistry

Abstract

Using experimental data subject to noise and drift, we find the structure function can be computed to higher accuracy, yet using less data, than the correlation function. While this tendency is in line with theoretical reasoning, we seem to be the first to report on quantitative aspects. Taking wall pressure data from a transsonic wind tunnel, our structure functions are obtained with one to two orders less of data points than correlation functions of comparable information content. These advantages apply to auto- and cross-structure functions alike when compared to auto- and cross-correlation functions, respectively. Some comments are added on the possibility of designing digital “structurators” similar to existing digital correlators, either as software products using the FFT and recursive algorithms, or as hardware products in the form of fast special purpose paralled processors.

PACS

02.07 06.50 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A.N.Kolmogorov: Local structure of turbulence in noncompressible fluid with high Reynolds number. Dokl. Acad. Sci. USSR30, 299 (1941); German translation [Ref. 3, p. 71]Google Scholar
  2. 2.
    A.N.Kolmogorov: Dissipation of energy in locally isotropic turbulence. Dokl. Acad. Sci. USSR32, 19 (1941); German translation [Ref. 3, p. 77]Google Scholar
  3. 3.
    H.Goering (ed.):Sammelband zur statistischen Theorie der Turbulenz (Akademie-Verlag, Berlin 1958)MATHGoogle Scholar
  4. 4.
    A.M.Obukhov, A.M.Yaglom: The microstructure of turbulent flow. Priklad. Math. Mech. Akad. Sci. USSR15, 3 (1941); German translation [Ref. 3, p. 97]Google Scholar
  5. 5.
    A.M.Obuchov: Statistical description of continuous fields. Trud. Geophys. Inst. Acad. Sci. USSR24, 3 (1951)Google Scholar
  6. 6.
    V.I.Tatarski:Wave Propagation in a Turbulent Medium (English translation) (McGraw-Hill, New York 1961)MATHGoogle Scholar
  7. 7.
    S.Panchev:Random Functions and Turbulence (Pergamon Press, London 1971)MATHGoogle Scholar
  8. 8.
    L.D.Landau, E.M.Lifschitz:Course of Theoretical Physics, vol. 6:Fluid Mechanics (Pergamon Press, London 1959)Google Scholar
  9. 9.
    E.K.Butner: On the calculation of structure and correlation functions according to finite interval of observations. Trud.-M.G.O. no. 144/40 (1963)Google Scholar
  10. 10.
    L.R.Rabiner, C.M.Rader (eds.):Digital Signal Processing. (IEEE Press, New York 1972); in particular see papers by J.W.Cooley, J.W.Tukey (p. 223), J.G.Stockham, Jr. (p. 330), and C.M.Rader (p. 339)Google Scholar
  11. 11.
    H.Z.Cummins, E.R.Pike (eds.):Photon Correlation and Light-Beating Spectroscopy (Plenum Press, London 1974)Google Scholar
  12. 12.
    H.Z.Cummins, E.R.Pike (eds.):Photon Correlation Spectroscopy and Velocimetry (Plenum Press, London 1977)Google Scholar
  13. 13.
    G.E.A.Meier: Shock induced flow oscillations. AGARD Proceedings on Flow Separation no. 168 (1974)Google Scholar
  14. 14.
    Y.W.Lee:Statistical Theory of Communication (John Wiley & Sons, New York 1960)MATHGoogle Scholar
  15. 15.
    A.M.Yaglom: An Introduction to the Theory of Stationary Random Functions. Uspekhi Math. Sci.7, no. 5 (1952). Revised English Edition: Prentice Hall (1962)Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • E. O. Schulz-DuBois
    • 1
  • I. Rehberg
    • 1
  1. 1.Max-Planck-Institut für StrömungsforschungGöttingenFed. Rep. Germany
  2. 2.Institut für Angewandte Physik der Universität KielKiel 1Fed. Rep. Germany

Personalised recommendations