derivation of turbulent energy in presence of dust particles

Energy equation for dusty fluid turbulent flow has been derived in terms of correlation tensors of second order. In presence of dust particles, mathematical modeling of turbulent energy is discussed including the correlation between the pressure fluctuations and velocity fluctuations at two points of the flow field, where the correlation tensors are the functions of space coordinates, distance between two points and time. To reveal the relation of turbulent energy between the two points, one point has been taken as origin of the coordinate system.