Impact of non-isotropy on the statistics of turbulence relative to moving vehicles

The isotropic turbulence assumption, though widely used, may not accurately represent real-world conditions in stochastic wind models for turbulence relative to moving vehicles. This study derives the statistical properties of non-isotropic turbulence relative to moving vehicles, focusing on correlation functions, power spectral densities (PSDs), and coherence functions of wind speed fluctuations. A quantitative parameter characterizing the impact of non-isotropic turbulence is introduced, enabling an in-depth analysis of its effects on turbulence statistics. Non-isotropic turbulence notably increases PSDs in frequency regions critical to vehicle stability under crosswinds, underscoring the need to account for these effects in quantitative assessments. Without considering non-isotropic influences, crosswind stability may be overestimated. Non-isotropic turbulence impacts the PSDs both indirectly, by altering the lateral-to-longitudinal turbulence length scale ratio, and directly, through additional influences on PSDs. Prior studies have largely focused on the indirect effect, but both effects should be considered, as omitting the direct effect results in up to a 28.9% underestimation of PSDs at low frequencies, potentially overestimating running safety. The analysis also reveals that the relative wind angle, defined as the difference between the vehicle's running direction wind angle and its yaw angle, is the primary factor influencing turbulence characteristics, consistent for both isotropic and non-isotropic conditions. Additionally, the spatial correlation of wind speed fluctuations depends largely on the separation distance relative to the longitudinal turbulence length scale. Therefore, in qualitative studies of wind fluctuation effects on crosswind stability, non-isotropic turbulence may be disregarded. This work enhances the accuracy of stochastic wind models across different scenarios, providing a foundation for future research on crosswind safety in railway operations under turbulent wind conditions.