Application of an Ideal-Like Recursive Filter with Cut-Off Frequencies Estimated by means of Anisotropy Analysis of Turbulence

A key point in the analysis of surface-layer turbulence is the separation of the pure turbulent flow from other motion components, which configure as low-frequency fluctuations. The observation of low-frequency components is more frequent in complex terrain, due to surface heterogeneities, but it can be also found in much more ''ideal'' sites, especially under stable conditions.

The identification and separation of these components is difficult because their time-scales are typically smaller than the investigation period (e.g. 30 min, 1 h). Turbulence is commonly obtained by applying one of the following separation criteria: block average, linear detrending, time-domain filters (e.g. running averages) or recursive filters. However, block average and linear detrending are ineffective, as they act on time-scales greater than the investigation period. Time-domain filters detect the low-frequency components, but in the spectrum of the filtered signal the cut-off is not sharp. More accurate results are provided by recursive filters, when they are properly designed and tuned.

In this contribution, a recursive-filtering procedure is presented together with an application of the anisotropy analysis of turbulence for the estimate of a physically-based cut-off frequency. The filter is designed to return an unattenuated, zero-phase signal in which any filter-induced distortions are corrected. The anisotropy analysis of turbulence, instead, allows to identify as cut-off frequency the one associated to the greatest time-scale at which turbulence can be regarded as isotropic.

The described procedure is applied and tested on a real dataset. The dataset is composed of high-frequency data collected at about 8.5 m above the valley floor of the Adige Valley (Italy) by means of a Gill HS sonic anemometer (sampling frequency 50 Hz). In particular, the cut-off frequency is obtained by performing an anisotropy analysis for each investigated period (1 h), and the effectiveness of the procedure is evaluated in terms of thickening of the experimental points on similarity relationships.