Recently, there have been great demands on wind farm installations all over the world. However, it has been well recognised that wind turbines (WTs) may cause severe interferences on radar systems because of their scattering and motional behaviour. In this study, a novel signal model for pulse-Doppler radars (PDRs) which considers time-varying scattering and complicated motional characteristics of WTs is introduced. Using the proposed model, some applications including WT detection, construction of WT detection probability distribution and assessment of the detection performance of a target in the vicinity of a WT are demonstrated. In addition, an analytical and probabilistic model for WT clutter (WTC) is developed with the help of the proposed signal model. The signal model, applications and WTC model put forth within this study would be helpful in determining the deteriorating WT effects on PDRs before mitigation or other advanced processes to overcome WT effects.