New analytical models for power spectral density and coherence function of wind turbulence relative to a moving vehicle under crosswinds

In this study, new general analytical models for correlation and power spectral density (PSD) functions of wind turbulence relative to a moving vehicle considering different wind direction angles under crosswinds without the use of Taylor's frozen turbulence hypothesis or the isotropic turbulence assumption were proposed. The auto-PSD calculation models relative to a moving vehicle with two different coherence functions relative to the ground were deduced, and a direct generating scheme, which can more efficiently generate the time histories of fluctuating wind speeds relative to a moving vehicle was developed. The accuracy of the proposed auto-PSD models was validated based on the models and direct generating scheme mentioned above. Furthermore, the coherence function model of wind turbulence relative to a moving vehicle was also proposed, and the accuracy of both the proposed coherence function model and the previous model were compared. The results show that without the use of Taylor's frozen turbulence hypothesis or the isotropic turbulence assumption, the proposed auto-PSD and coherence function models of wind turbulence relative to a moving vehicle are all highly in accordance with the numerical solutions, which are calculated based on only the time histories of fluctuating wind speeds relative to a moving vehicle. However, there are large differences between the results of the auto-PSD and coherence functions obtained from the previous models and the results obtained from the corresponding numerical solutions. These differences can be attributed to the fact that the previous models adopted either Taylor's frozen turbulence hypothesis or the isotropic turbulence assumption, or both. The proposed auto-PSD model and coherence function model of wind turbulence relative to a moving vehicle could provide a foundation for considering the effects of crosswinds on moving vehicles in terms of unsteady aerodynamic forces, ride comfort and running safety.