Introduction In real fluids, the viscous stresses in turbulent motions will cause the kinetic energy of the motions to dissipate in heat. If there are no external effects present to supply energy continuously for maintaining the turbulent motions, these will decay in the course of time. An interesting problem to investigate is how the flow pattern and the relations between velocities change during decay. Since these relations can be described by the tensor (Qij) A, B of the double velocity

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... lations, we have to consider the change in this tensor with time. Batchelor (1951) obtained an expression for the velocity, covariance between the fluctuating velocities at two different points, a distance r apart in a field of homogeneous isotropic turbulence. Jain (1962) using Chandrasekhar's (1955) new theory of turbulence, derived expressions for pressure and acceleration covariance in ordinary turbulence. A good deal of theoretical studies on magneto hydrodynamic turbulence has been made during last fifteen years. Some authors (see for instance, Ohji, 1964) considered MHD turbulence in the absence of an external magnetic field in order to gain a basic understanding of a self-adjusting process of the mechanical and magnetic modes of turbulence. In a variety of astrophysical and geophysical problems, however, it is often the case that a certain magnetic field such as the cosmic magnetic field, the geomagnetic field, etc. is imposed on a turbulent motion of a conducting fluid. The essential effect of the presence of an imposed magnetic field is that the mechanical and magnetic modes of turbulence interact not only with each other through the self-adjusting processes but also with the external magnetic field. If the external magnetic field is very strong, the effect of the latter interaction will predominate that of the self-adjusting processes. Ohji (1964) presented a first order theory for turbulence of an electrically conducting fluid in the presence of a uniform magnetic field, which is so strong that the nonlinear mechanism as well as the dissipation when compared with the external coupling terms are of minor importance. He discussed the effect of a very strong uniform magnetic field on incompressible MHD turbulence in the presence of a constant angular velocity and Hall effect. Saffman (1962) observed the effect of dust particles on the stability of laminar flow of an incompressible fluid with constant mass concentration of dust particles. He has given the equations describing the motion of a fluid containing small dust particles. Using the equations given by Saffman, Michael and Miller (1966) has discussed the motion of dusty gas occupying the semi-infinite space above a rigid plane boundary. The behaviour of discrete particles in a turbulent flow is of great interest to many branches of technology, particularly if there is a substantial difference in density between the particles and the fluid. The combined flow of solids and fluids or of atomized liquids and gases (flow of mist) is encountered for instance in one or more of the technical applications like gas and liquid cleaners (e.g. cyclone separator), pneumatic conveying, coal washing, and mineral dressing, chemical reactors based on the fluidized solids system. The behaviour of dust particles in a turbulent fluid depends largely. 1. On the concentration of the particles 2. On the size of the particles with respect to the scale of turbulence fluid. At great concentration there is interaction between the particles through collisions and through effects on the flow of the fluid in the neighbourhood of the particles. At extremely high concentrations near that Abstract In this paper we have derived the spectrum equation for the joint propagation of correlations, velocity and magnetic field. Various discussed the problem of very strong uniform magnetic field and rotating system of spectral equation.