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An H = 2 T history of S(γ ) is required to ascertain the instantaneous mean ¯ and the random part χ(γ ), t − T ≤ γ ≤ t; see (1) and (2) and recall that S(t) t represents the present time. Comparing m.s.e. with the sensor accuracy deﬁnes T, see Equation (3). The memory L is then found from χ(γ ), see (5) and (6).
Based on the physical interpretation of L, AW is then deﬁned as 10L and used to obtain (t, ω), see Equation (7), et seq.
The method formulated here (i) is frequency-shift invariant, meaning that it is independent of the frequency domain of χ(γ ); (ii) eliminates effects of userspeciﬁc biases such as user-selected window lengths; (iii) eliminates corruption caused by using a static algorithm (such as FFT) to analyse dynamic phenomena;
(iv) avoids degradation caused by using information from the future; (v) identiﬁes, in real time, if and how frequency content, distribution, domain, and bandwidth, are changing; and (vi) reduces the possibility that short-lived information is lost or masked due to uncharacteristically long (or short) averaging intervals.
The three parameters σ, η, and L, obtained serve to quantify the local structure of the ABL. A fourth parameter, the t-dependent mean, is also determined but, since it is removed from S, does not affect the behaviour of. This parameter can be thought of as an instantaneous DC component. The exact relationship between T and AW is known only a posteriori. Speciﬁcally, ( T /AW) 0.1(σ /ACC)2, ¯ where (recall) that ACC is 0.01S for our data.
As a ﬁnal point, turbulence researchers agree that the proper choice of scale is important in the search for Reynolds-number-independent features. Yet they typically use the same time interval for Reynolds averaging of all correlations being examined. The fact that classical Reynolds averaging has been used to investigate the structure of higher-order correlations and has not yet yielded an appreciable understanding of the turbulence problem might be due to an inappropriate choice of averaging times. The method formulated here addresses this concern.
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