Mean-drift contribution to a turbulence-intensity estimate

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.