Estimating the integral length scale on turbulent flows from the zero crossings of the longitudinal velocity fluctuation

The integral length scale ($\mathcal{L}$) is considered to be characteristic of the largest motions of a turbulent flow, and as such, it is an input parameter in modern and classical approaches of turbulence theory and numerical simulations. Its experimental estimation, however, could be difficult in certain conditions, for instance, when the experimental calibration required to measure $\mathcal{L}$ is hard to achieve (hot-wire anemometry on large scale wind-tunnels, and field measurements), or in 'standard' facilities using active grids due to the behaviour of their velocity autocorrelation function $ρ(r)$, which does not in general cross zero. In this work, we provide two alternative methods to estimate $\mathcal{L}$ using the variance of the distance between successive zero crossings of the streamwise velocity fluctuations, thereby reducing the uncertainty of estimating $\mathcal{L}$ under similar experimental conditions. These methods are applicable to variety of situations such as active grids flows, field measurements, and large scale wind tunnels.

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