= Mean-drift contribution to a turbulence-intensity estimate
\b[Mean-drift contribution to a turbulence-intensity estimate] is the apparent fluctuation produced when a changing mean <velocity> is included in the deviations used to estimate <wind-tunnel turbulence intensity>. Subtracting one mean from an entire record removes its constant offset, not its slow evolution.
An original continuous-record model on $0\leq t\leq T$ is
$$
u(t)=U_0+a(t-T/2)+\varepsilon(t).
$$
Assume the time mean of $\varepsilon$ is zero. Writing $\langle g\rangle=T^{-1}\int_0^Tg(t)\,dt$, the record has mean $U_0$ and
$$
\sigma_u^2=\frac{a^2T^2}{12}+\langle\varepsilon^2\rangle
+2a\langle(t-T/2)\varepsilon(t)\rangle.
$$
The first term follows by integrating $(t-T/2)^2$. The last is a <covariance> term: it need not vanish in one finite record even when a stochastic model predicts zero in expectation.
With no random fluctuation, take $U_0=30$ m/s, $a=0.02\,\mathrm{m\,s^{-2}}$ and $T=60$ s. The drift contributes <standard deviation> $|a|T/\sqrt{12}\approx0.3464$ m/s, so an estimate $\sigma_u/U_0$ reports about 1.155% despite zero stipulated <turbulence>. If an uncorrelated fluctuation has <standard deviation> 0.24 m/s, the combined model gives $\sqrt{0.12+0.0576}/30\approx1.405\%$, rather than its fluctuation-only value of 0.800%.
Removing a fitted trend changes the measured quantity. It can remove genuine slowly varying <turbulence> as well as instrumental or operating drift, so a reduced residual <variance> does not identify the physical origin of the removed signal. Report recording duration and the filtering or trend-removal procedure with the estimate.
The NASA tunnel experiment used <hot-wire anemometry> with separate mean and fluctuating signal paths and specified their filters.<Free-Stream Turbulence Intensity in the Langley 14- by 22-Foot Subsonic Tunnel by Dan H. Neuhart and Catherine B. McGinley>[Instrumentation, printed p. 8 and Figure 3; Appendix A, signal reduction and turbulence-intensity definition]{ref} Its apparatus illustrates why a reported fluctuation level includes a <bandwidth>. The linear-drift calculation here is a constructed diagnostic example, not a reinterpretation of those tunnel data.
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