 Turbulence intensity

Turbulence intensity expresses the size of a measured velocity fluctuation relative to a specified mean speed. For a streamwise velocity record $u(t)$, defineHere the symbol in the square-root definition is $u_{\mathrm{rms}}$, the root mean square fluctuation, and angle brackets denote the averaging operation. The dimensionless intensity is often reported as $100I$ percent. The averaging interval and measured velocity component are part of the definition.

For four equally weighted observations $9,11,9,11\mathrm{m}{\mathrm{s}}^{-1}$, the mean is $10\mathrm{m}{\mathrm{s}}^{-1}$ and each fluctuation is $\pm 1\mathrm{m}{\mathrm{s}}^{-1}$. Their record root mean square is therefore $1\mathrm{m}{\mathrm{s}}^{-1}$, giving $I=0.10$, or 10 percent. This calculation describes that record; it does not estimate every fluctuation timescale from four observations.

A primary wind-tunnel investigation used hot-wire anemometry, recording mean and fluctuating signals to characterize the wind-tunnel turbulence intensity. Its bandwidth comparison demonstrates that integrating only part of the measured fluctuation spectrum changes the recovered root mean square.^[ref] An instrument's temporal response, filtering and record duration therefore affect the reported intensity. Slow changes of the mean can also contribute to a measured fluctuation unless the averaging convention separates them.

A three-component convention instead useswhere $k$ is the turbulent kinetic energy per unit mass. This agrees with the streamwise definition when the three fluctuation variances are equal, as in isotropic turbulence. A nonzero root mean square alone does not establish turbulence: a periodic laminar velocity oscillation also has a nonzero value. The ratio also becomes ill-conditioned near zero mean speed.