A microscale λ is defined by the curvature of the autocorrelation coefficient at the origin
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(22.3) |
Expanding ρ in a Taylor 's series about the origin for small τ
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(22.4) |
Note that there is no 1st power in the series. This is due to the symmetry condition
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(22.5) |
Thus the scale λ (usually referred to as microscale) is the intercept of the parabola that matches ρ(τ) at the origin.
The Fourier transform S(ω) of ρ(  ) is known as the power spectral density or simply spectrum .
Figure 22.1: Sketch of an autocorrelation coefficient
from Tennekes and Lumley (1987)
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(22.6) |
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