Wind-tunnel turbulence intensity ($I_u$)

Wind-tunnel turbulence intensity describes velocity fluctuations in a stated test region relative to its mean flow. For the streamwise velocity $u(t)$, define $U=⟨u⟩>0$ and $u^{\prime }=u-U$. The streamwise turbulence intensity isIts 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.^[ref]

For an original independent-noise example, suppose measured fluctuations have standard deviation $0.30m/s$, additive sensor noise has $0.18m/s$, and $U=30m/s$. If their covariance vanishes, the physical fluctuation variance is $0.30^2-0.18^2=0.0576{\mathrm{m}}^2/{\mathrm{s}}^2$, giving $I_u=0.8\%$, 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 $a^2{T}^2/12$. With $a=0.02m/{\mathrm{s}}^2$ and $T=60\mathrm{s}$, its apparent fluctuation standard deviation is $0.3464m/s$, 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.

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 $0\le t\le T$ isAssume the time mean of $\epsilon$ is zero. Writing $⟨g⟩=T^{-1}{\int }_0^{T}g(t)dt$, the record has mean $U_0$ andThe 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, $a=0.02\mathrm{m}{\mathrm{s}}^{-2}$ and $T=60$ s. The drift contributes standard deviation $|a|T/\sqrt{12}\approx 0.3464$ 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 $\sqrt{0.12+0.0576}/30\approx 1.405\%$, 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.^[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.