Turbulence correlation between moving trains and anemometer towers: Theoretical analysis, field measurements and simulation

A precise command of railway operations according to the measured instantaneous wind speed on an anemometer tower along a railway line is the development trend, whose challenges lie in the unknown transfer relation(s) between wind speed fluctuations on a moving train and an anemometer tower, i.e. the turbulence correlation between them. To address this issue, in the current work, the cross-correlation functions of wind speed fluctuations at the moving train and anemometer tower are derived, and an empirical formula of the coherence functions is obtained. The turbulence correlation is inversely related to the separation distance from the anemometer tower to the line, and there is little correlation when this distance is longer than double the longitudinal turbulence length scale. Field measurements of wind characteristics were carried out on an anemometer tower and a moving vehicle, and the turbulence correlation and its expression were validated. Three methods are proposed and compared to evaluate the instantaneous wind speed at the anemometer tower and moving train with this correlation. The methods based on the cross-spectral density and coherence function can accurately simulate the correlation, and the latter performance is slightly better (its simulation of the frequency domain correlation is 52.9% better than the former); the method based on solely independent and identically distributed random phases cannot fully simulate the correlation. From this, the effects of the correlation on train operations are studied and analysed in detail. Our analysis shows that neglecting this correlation leads to conservative estimates: wind speed differences between the anemometer tower and the moving train are at least 18.1% greater, and the safety and economic assessments of train operations in crosswinds are underestimated by at least 32.0%. Considering the correlation can reduce the (excess) safety risk/margin and is an inevitable development of adapting to the detailed assessment of the crosswind stability of vehicles. The quantitative description and simulation of the correlation presented in this work point to the critical importance of wind speed monitoring systems for the detailed crosswind assessment, and provide a theoretical basis for further research work on the crosswind stability of vehicles under true/realistic turbulent flow wind.