= Wind-tunnel turbulence intensity
{title2=$I_u$}
\b[Wind-tunnel turbulence intensity] describes velocity fluctuations in a stated test region relative to its mean flow. For the streamwise <velocity> $u(t)$, define $U=\langle u\rangle>0$ and $u'=u-U$. The streamwise <turbulence intensity> is
$$
I_u=\frac{\sqrt{\langle u'^2\rangle}}{U}.
$$
Its numerator is the <root mean square> of the fluctuation, equivalently its <standard deviation> when the same averaging convention is used. It is not the raw <root mean square> of $u$, which still contains the mean. Component direction, averaging duration, probe position and retained frequency band belong with the reported value.
A <hot-wire anemometer> converts changes in convective cooling into an electrical signal; <measurement calibration> relates that signal to <speed>. <Dan H. Neuhart> and <Catherine B. McGinley>'s NASA study used a survey rake and additional probes, including pressure and temperature measurements for hot-wire calibration. It separated mean and fluctuating channels and used reference wires to identify coherent disturbances. Its frequency-band comparisons show why filtering can change a reported intensity.<Free-Stream Turbulence Intensity in the Langley 14- by 22-Foot Subsonic Tunnel by Dan H. Neuhart and Catherine B. McGinley>[Printed pp. 7–9, Instrumentation and Analysis; Figure 20]{ref}
For an original independent-noise example, suppose measured fluctuations have <standard deviation> $0.30\,\mathrm{m/s}$, additive sensor noise has $0.18\,\mathrm{m/s}$, and $U=30\,\mathrm{m/s}$. If their <covariance> vanishes, the physical fluctuation <variance> is $0.30^2-0.18^2=0.0576\,\mathrm{m^2/s^2}$, giving \b[$I_u=0.8\%$], rather than the uncorrected $1.0\%$. Correlated noise requires an additional covariance term; an estimated noise variance larger than the measured variance signals an inconsistent subtraction model.
Slow drift is another distinct contribution. A deterministic mean change $a(t-T/2)$ over an interval of length $T$ has time-averaged <variance> $a^2T^2/12$. With $a=0.02\,\mathrm{m/s^2}$ and $T=60\,\mathrm s$, its apparent fluctuation <standard deviation> is $0.3464\,\mathrm{m/s}$, despite no random turbulence in this example. This <mean-drift contribution to a turbulence-intensity estimate> cannot be distinguished from turbulence by a single unqualified RMS number.
A tunnel survey should therefore retain the signal-processing convention and spatial positions, rather than only a facility-wide percentage. Changes in <turbulence intensity> can affect <boundary-layer transition>; equal <Reynolds numbers> do not guarantee equal fluctuation environments.
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