Base on particle Langevin equation of two -phase flows,two different PDF equations on different level are obtained by dealing with colour-noise using the method of state vector expanding and reducing.

• 由颗粒运动的朗之万方程出发,对流体脉动速度采用扩维方法,把色噪声转化为白噪声,再降维从而得到两个不同层次的PDF输运方程。