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An overview of Millionschikov's quasi-normality hypothesis applied to turbulence

Mamaloukas C., Mazumdar H. P.

International Journal of Applied Mechanics and Engineering

2014

Vol. 19, no. 1

123--132

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.

Two-points statistics of kinematic velocity models in isotropic turbulence

Wacławczyk M., Pozorski J.

Turbulence : international journal

2002

Vol. 8-9

99-112

Kinematic models for 2D and 3D velocity fields of homogeneous isotropic turbulence are considered. Numerical simulation is performed to obtain a number of independent realisations of the field and some two-point statistics are computed and discussed. The statistics include the velocity correlations and the spectral energy density.

Self-similarity in the decay of homogeneous and isotropic turbulence

Chanda A., Das P., De A., Das J.

Journal of Technical Physics

2000

Vol. 41, no 1

43-47

Decay of turbulent energy in isotropic and homogeneous conditions has been discussed from the point of view of geometrical and statistical self similarity. Assuming the presence of self-similar eddies in the inertial subrange, a model of the inertial transfer of turbulent energy in the sense of fractal has been built. A method to extend the model to multifractal formalism has been also suggested.