Spectral Theory of Turbulence

  • Walter Frost


The statistical correlations described in the preceding chapter are useful in turbulence analyses and are relatively easy to measure. However, another powerful tool for describing turbulence is the method of spectral analysis. The spectral theory and the correlation theory are intimately connected mathematically with one another by the Fourier transformation. There is no additional information contained in the spectra that is not already contained in the correlations, but the two methods of description put different emphases on different aspects of the problem. For example, we discussed earlier the concept of energy transfer between different scales or orders of eddies. Spectral analysis allows us to describe the exchange of kinetic energy associated with different eddy sizes or with different fluctuation frequencies occurring in the turbulence.


Turbulence Kinetic Energy Spectral Theory Spectral Density Function Average Kinetic Energy Inertial Subrange 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Churchill, R. V., Fourier Series and Boundary Value Problems, McGraw-Hill Book Co., New York (1941).Google Scholar
  2. 2.
    Yaglom, A. M., An Introduction to the Theory of Stationary Random Functions, translated and edited by R. A. Silverman, Prentice-Hall Inc., New Jersey (1962).Google Scholar
  3. 3.
    Taylor, A. E., Advanced Calculus, Ginn and Company, New York (1955).MATHGoogle Scholar
  4. 4.
    Gnedenko, B. V., The Theory of Probability, translated by B. D. Sickler, Chelsea Publishing Co., New York (1962).Google Scholar
  5. 5.
    Reynolds, A. J., Turbulent Flows in Engineering, John Wiley and Sons, New York (1974).Google Scholar
  6. 6.
    Batchelor, G. K., Homogeneous Turbulence, Cambridge University Press, London (1967).Google Scholar
  7. 7.
    Hinze, J. O., Turbulence, McGraw-Hill Book Co., New York (1957).Google Scholar
  8. 8.
    Tennekes, H., and J. L. Lumley, A First Course in Turbulence, MIT Press, Cambridge, Massachusetts (1972).Google Scholar
  9. 9.
    Panchev, S., Random Functions and Turbulence, Pergamon Press, Oxford, England (1971).MATHGoogle Scholar

Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • Walter Frost
    • 1
  1. 1.The University of Tennessee Space InstituteTullahomaUSA

Personalised recommendations