An Iterative Method for Estimating Turbulence Kinetic Energy Dissipation Rate Considering Random Sweeping and Sensor Low-Pass Filtering Effects

This work concerns the estimation of the turbulence kinetic energy dissipation rate from time series recorded by a fixed-point sensor or from lidar data. For such estimates, it is usually assumed that the wind velocity spectrum follows Kolmogorov scaling at small scales. To convert the measured time series into space-dependent data, the Taylor frozen-eddy hypothesis is typically employed, in which the mean wind velocity is assumed to advect turbulence structures past the sensor without distortion. This assumption works well for strong winds and when the turbulence intensity (defined as the ratio of the root-mean-square of the wind velocity fluctuations to the mean wind speed) is small.

However, the Taylor hypothesis is not always fulfilled, for example in the convective regime with weak winds, or in the neutral or stable boundary layer when the wind becomes weaker but decaying turbulent motions are still present. As the turbulence intensity increases, it can no longer be assumed that turbulence structures, “frozen” in time, are simply advected past the sensor. Instead, the sweeping of small eddies by larger ones becomes an important mechanism, considerably affecting the frequency spectra. In this case, no simple relationship between frequency and wavenumber exists. In addition, the measured time series are subject to effective spectral cut-offs due to the finite sampling frequency of the sensor. This acts as a low-pass filter, which may also affect the resolved large-scale motions.

In this work, we consider an iterative method for estimating the turbulence kinetic energy dissipation rate, originally proposed by Wacławczyk et al. (Atmos. Measur. Tech., 10, 2017) and Akinlabi et al. (J. Atmos. Sci., 76, 2019), and extend it to account for the effects of random sweeping and the finite frequency of the sensor. The iterative method has several advantages over standard spectral estimates. In spectral methods (or methods based on structure functions), a fitting range in which Kolmogorov scaling holds must be defined a priori. In contrast, the iterative method requires only the calculation of the time derivative of the time series, its standard deviation, and a correcting factor that accounts for the shape of the unresolved part of the spectrum. In the proposed improved iterative method, the assumed spectral form incorporates modifications due to both random sweeping and low-pass filtering by the sensor.