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.

中文翻译：

---

对湍流风洞中连续波激光雷达测量的光谱形状进行建模

摘要。本文介绍了由短程连续波激光雷达测量的湍流谱模型的开发。激光雷达性能是通过在配备有源网格的开放式喷射风洞中针对一系列不同的湍流风条件使用两台 WindScanner 进行的测量来评估的。一维热线风速计被用作表征激光雷达湍流测量的参考。除了处理统计数据、时间序列与风速平均误差之间的相关性之外，激光雷达测量湍流频谱与使用泰勒冻结湍流假设的理论频谱进行了比较。探针长度平均效应的理论模型应用于频域，使用洛伦兹滤波器与生成的白噪声相结合，并通过定性匹配激光雷达测量光谱进行评估。对于测量的时间序列，观察到热线和 WindScanner 之间的拟合系数高，平均绝对误差低。对于具有可比功率谱形状的情况，相关性显示与流动中普遍的湍流强度呈负相关。激光雷达可以更准确地捕获较大的流动结构，而激光雷达的探头体积平均会部分过滤掉小规模的湍流结构。结果表明，定义激光雷达功率谱开始偏离热线参考谱的频率的准确方法是相干性降至 0.5 以下的点。这种基于相干性的截止频率随平均风速线性增加，通常比探头长度截止频率低一个数量级，根据基于泰勒冻结湍流假设的简单模型估计。在各种不同情况下，在建模和实际 WindScanner 功率谱之间找到了令人信服的匹配，这证实了激光雷达测量功率谱在较高频率范围内的偏差可以通过分析解释和建模为洛伦兹探针长度平均的组合激光雷达测量中的效应和白噪声。