This paper proposes a method to design a wind turbulence model based on real wind spectral characteristics. It uses models based on Cole-Cole fractional functions to approximate the wind turbulence power spectral density. Von Kármán model is the most commonly used model but originally designed for aircraft in high altitude. Therefore, it is not suitable for systems operating at low altitude, hence the need for more accurate models in these specific conditions. Shaping filters issued from the fractional models are employed to generate realistic random wind speed turbulence from a random white noise input. Then, a grey box model is proposed from physical parameters such as the classic von Kármán ones (mean speed, turbulence intensity and length scale).