Modelling the Spectral Shape of Continuous-Wave Lidar Measurements in a Turbulent Wind Tunnel

Abstract. This paper describes the development of a model for the turbulence spectrum measured by a short-range, continuous-wave lidar. The lidar performance was assessed by measurements conducted with two WindScanners in an open jet wind tunnel equipped with an active grid, for a range of different turbulent wind conditions. A one-dimensional hot wire anemometer was used as a reference for characterising the lidar turbulence measurement. In addition to addressing the statistics, the correlation between the time series and the mean error on the wind speed, the lidar measurement turbulence spectrum is compared with a theoretical spectrum using Taylor's frozen turbulence hypothesis. A theoretical model for the probe length averaging effect is applied in the frequency domain, using a Lorentzian filter in combination with generated white noise, and evaluated by qualitatively matching the lidar measurement spectrum. High goodness of fit coefficients and low mean absolute errors between hot wire and WindScanner were observed for the measured time series. The correlation showed an inverse relationship with the prevalent turbulence intensity in the flow for cases with a comparable power spectrum shape. Larger flow structures can be captured more accurately by the lidar, whereas small-scale turbulent flow structures are partly filtered out as a result of the lidars' probe volume averaging. It is demonstrated that an accurate way to define the frequency at which the lidar power spectrum starts to deviate from the hot wire reference spectrum is the point at which the coherence drops below 0.5. This coherence-based cut-off frequency increases linearly with the mean wind speed and is generally an order of magnitude lower than the probe length cut-off frequency, estimated according to a simple model based on Taylor's frozen turbulence hypothesis. A convincing match between the modelled and the actual WindScanner power spectrum was found for various different cases, which confirmed that the deviation of the lidar measurement power spectrum in the higher frequency range can be analytically explained and modelled as a combination of a Lorentzian probe length averaging effect and white noise in the lidar measurement.