By P. Bradshaw
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Extra info for An Introduction to Turbulence and its Measurement
We can measure either the frequency spectrum or the autocorrelation fairly easily but we cannot directly measure the so-called wave number spectrum, which is the Fourier transform, with respect to r, of the space correlation: since the wave number spectrum is usually more convenient than the space correlation for theoretical purposes, Fourier transform relations are invaluable in this case. 6. 1. 22(/i ? -component MEASURABLE QUANTITIES AND THEIR PHYSICAL SIGNIFICANCE 35 correlation with separation r1 in the x direction, which according to Taylor's hypothesis is nearly the same as the ^-component autocorrelation with time delay — r^U (or equivalently +r1/U).
1. Turbulence behind a Grid of Bars(2) (Fig. 16) The wakes of the individual bars become turbulent close behind the grid and then interact in some very complicated way so that, at a large number of mesh lengths from the plane of the grid, the turbulence is more or less homogeneous. M—C 48 TURBULENCE AND ITS MEASUREMENT Decaying turbulence Close-up of adjacent bars FIG. 16. Turbulence behind a grid of bars. energy other than the shear flow close to the grid. As the turbulence decays, the energy transfer from the large eddies to the small eddies decreases so that the intensity of the small eddies decreases faster than that of the large eddies.
Physically, the correlation with separation r is a measure of the strength of eddies whose length in the direction of the vector r is greater than the magnitude of r (since eddies smaller than this will not contribute to the correlation): as a warning that this is an imprecise concept, note that the correlations for the three velocity components will in general be different for the same r. 4. When we speak of the length scale of the energy00 containing eddies we mean a length of order j Rar (actually called the "integral scale").