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ORIGINAL PAPER
An overview of Millionschikov's quasi-normality hypothesis applied to turbulence
C. Mamaloukas 1
,
 
H.P. Mazumdar 2
 
 
 
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1
Department of Statistics Athens University of Economics and Business GREECE
 
2
Indian Statistical Institute Calcutta – 700035, INDIA
 
 
Online publication date: 2014-03-07
 
 
Publication date: 2014-02-01
 
 
International Journal of Applied Mechanics and Engineering 2014;19(1):123-132
DOI: https://doi.org/10.2478/ijame-2014-0009
 
 
Article (PDF)
References (21)
 
KEYWORDS
Millionschikov's quasi-normality hypothesis
homogeneous turbulence
isotropic turbulence
correlation tensors
zero-fourth cumulant approximation
 
ABSTRACT
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
 
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