Spectral Theory of Turbulence

Abstract

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.