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

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Strony
123--132
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
  • Department of Statistics Athens University of Economics and Business GREECE
  • Indian Statistical Institute Calcutta – 700035, INDIA
Bibliografia
  • Antonia R.A., Chambers A.J. and Bradley E.F. (1982): Third- and fourth-order mixed moments of turbulent velocity and temperature fluctuations in the atmospheric surface layer. - Boundary Layer Meteorology. - vol.22, pp.421-430.
  • Batchelor G.K. and Proudman I. (1956): The large-scale structure of homogeneous turbulence. - Phil. Trans. Roy. Soc., vol.248A, p.167.
  • Canuto V.M. (1992): Turbulent convection with overshooting: Reynolds stress approach. - Astrophys. J., vol.392, pp.218-232.
  • Chow W.L. (1940): Über Systeme von linearen partiellen differentialgleichungen erster ordnung. - J. Math. Ann., pp.98-105.
  • Ghosh K.M. (1972): Some concequences of Millionschikov’s hypothesis in the early-period decay process of turbulence. - Indian Journal of Pure and Appl. Math., vol.3, No.1, p.157.
  • Gryanik V.M., Hartmann J, Raasch S. and Schröter M. (2005): A Refinement of the Millionshchikov quasi-normality hypothesis for convective boundary layer turbulence. - J. Atmos. Sci., vol.62, pp.2632-2638.
  • Heisenberg (1948): On the theory of statistical and isotropic turbulence. - Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences vol.195, No.1042, pp.402-406.
  • Losch M. (2004): On the validity of the Millionshchikov quasi-normality hypothesis for open-ocean deep convection. - Geophysical Research Letters, vol.31, L23301, No.4 pp., Doi:10.1029/2004GL021412.
  • Mazumdar H.P. (1976): On the decay process of turbulence at large Reynolds and Peclet numbers. - App. Sci. Res., vol.32, p.571.
  • Mazumdar H.P. (1979): On the pressure fluctuations associated with a general type of turbulence. - Appl. Sci. Res. vol.35, No.5-6, pp.367-371.
  • Mazumdar H.P. (1984): On the fluctuations of total pressure associated with general type of hydromagnetic turbulence. - Archeves of Mechanics, vol.36, pp.233-240.
  • Mazumdar H.P. (2010): On Incompressible Hydromagnetic Turbulence. (Research Monograph). - Calcutta Mathematical Society.
  • Mazumdar H.P. and Mandal B.C. (2009): On persen theory of two dimensional turbulent boundary layer. - Int. J. of Appl. Mech. and Engineering, vol.14, No.4, pp.1009-1028.
  • Millionschikov M. (1941): On the theory of homogeneous isotropic turbulence. - Dokl. Akad. Nauk SSSR, vol.32, pp.615-618.
  • Mirabel A.P. (1969): Application of Millionschikov’s hypothesis to the problem of isotropic turbulence degeneration. - Izv. AN SSSR. Mekhanika Zhidkosti i Gaza, vol.4, No.5, pp.171-175.
  • Monin A.S. and Yaglom A.M. (1975): Statistical Fluid Mechanics. - Vol. II, MIT Press, Cambridge, MA.
  • Ogura Y. (1963): A consequence of the zero-fourth-cumulant approximation in the decay of isotropic turbulence. - Journal of Fluid Mechanics, vol.16, pp.33-40.
  • Panchev S. (1971): Random functions and turbulence. - Oxford: Pergamon Press., p.444.
  • Proudman I. and Reid W.H. (1954): On the decay of a normally distributed and homogeneous turbulent velocity field. - Phil. Trans. Roy. Soc. vol.247A, p.163-189.
  • Uberoi M.S. (1953): Quadruple velocity correlations and pressure fluctuations in isotropic turbulence. - J. Aeronaut. Sci., vol.20, p.197.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-844376a1-a30f-4437-9478-8bb58cf9b5b8
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