In this paper, we examine the zero-fourth cumulant approximation that was applied to fluctuating velocity components of homogeneous and isotropic turbulence by M.D. Millionschikov. Since the publication of the remarkable paper of Millionschikov, many authors have applied this hypothesis to solve the closure problem of turbulence. We discuss here various studies by the other authors on the developments of this hypothesis and their applications to the incompressible velocity temperature, hydrodynamic and magnetohydrodynamic fluctuating pressure fields and the general magnetohydrodynamic turbulence field. Lastly, we discuss broadly the computational difficulties that arise in turbulence problems and their possible refinements. We include also some enlightments of the process of future work that could be undertaken in this field of research.
In this paper, the unsteady unidirectional motion of an incompressible vicous fluid, produced by sinusoidal oscillation of a rigid plane wall and subjected to a uniform magnetic field acting perpendicularly to the flow direction is investigated. The basic equation, governing the motion of such a flow is expressed in non-dimensional form. It is shown that this equation admits two solutions which satisfy the respective sets of boundary and initial conditions. The results, showing the development of the velocity field in time for different values of the magnetic parameter, are presented graphically and discussed.
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