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Mathematical Models and Computer Simulations

, Volume 1, Issue 5, pp 605–619 | Cite as

Anisotropic turbulence decay in a far momentumless wake in a stratified medium

  • O. F. Voropaeva
Article

Abstract

A new numerical model is constructed of turbulent wake dynamics behind bodies of revolution in a stably stratified medium based on a semiempirical third-order turbulence model. The employed differential transport equations of all triple correlations of velocity field oscillations, written with allowance for fourth-order cumulants and improved algebraic representations of joint triple correlations of velocity and density fluctuations, enable the comprehensive description of an anisotropic turbulence decay in a far momentumless wake in a stratified medium

Keywords

Reynolds Stress Turbulent Energy Order Moment Turbulent Wake Stratify Medium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. H. Schooley and R.W. Stewart, “Experiments with a Self-Propelled Body Submerged in a Fluid with Vertical Density Gradient,” J. Fluid Mech. 15(1), 83–96 (1963).MATHCrossRefGoogle Scholar
  2. 2.
    A. T. Onufriev, “Turbulent Wake in a Stratified Medium,” PMTF No. 5, 68–72 (1970).Google Scholar
  3. 3.
    C. E. Merrit, “Wake Growth in Stratified Flow,” AIAA J. 12(7), 940–949 (1974).CrossRefGoogle Scholar
  4. 4.
    W. S. Lewellen, M. E. Teske, and C. D. Donaldson, “Examples of Variable Density Flows Computed by Second-Order Closure Description of Turbulence,” AIAA J. 14, 382–387 (1976).CrossRefGoogle Scholar
  5. 5.
    O. F. Vasiliev, B. G. Kuznetsov, Y. M. Lytkin, and G. G. Chernykh, “Development of the Turbulent Mixed Region in a Stratified Medium,” in Proceedings of International Seminar “Turbulent Buoyant Convection” Aug. 30–Sept. 4, Dubrovnic, Yugoslavia, 1976.Google Scholar
  6. 6.
    J. T. Lin and Y. H. Pao, “Wakes in Stratified Fluids,” Annu. Rev. Fluid Mech. 11, 317–336 (1979).CrossRefGoogle Scholar
  7. 7.
    S. Hassid, “Collapse of Turbulent Wakes in Stable Stratified Media,” J. Hydronautics 14, 25–32 (1980).CrossRefGoogle Scholar
  8. 8.
    O. M. Belotserkovskii, Numerical Modeling in Continuum Mechanics (Nauka, Moscow, 1984) [in Russian].Google Scholar
  9. 9.
    A. Yu. Danilenko, V. I. Kostin, and A. I. Tolstykh, “On Implicit Algorithm for Calculating the Flows of Homogeneous and Non-Homogeneous Fluids,” Preprint of the Computing Center of the USSR Academy of Sciences, Moscow, 1985.Google Scholar
  10. 10.
    G. S. Glushko, A. G. Gumilevskii, and V. I. Polezhayev, “Evolution of Turbulent Wakes behind Globular Bodies in Stably Stratified Media,” Izv. Akad. Nauk SSSR, MZhG No. 1, 13–22 (1994).Google Scholar
  11. 11.
    O. F. Voropaeva and G. G. Chernykh, “Numerical Model for Dynamics of Momentumless Trubulent Wake in Pycnocline,” PMTF 38(3), 69–86 (1997).MATHGoogle Scholar
  12. 12.
    O. F. Voropaeva and G. G. Chernykh, “Internal Waves Generated by Momentumless Trubulent Wake in a Linearly Stratified Medium,” Mathematical modeling 10(6), 75–89 (1998).Google Scholar
  13. 13.
    G. G. Chernykh and O. F. Voropaeva, “Numerical Modeling of Momentumless Turbulent Wake Dynamics in a Linearly Stratified Medium,” Computers and Fluids., 28(3), 281–306 (1999).MATHCrossRefGoogle Scholar
  14. 14.
    D. G. Dommermuth, J. W. Rottman, G. E. Innis, and E. A. Novikov, “Numerical Simulation of a Momentumless Wake in a Weakly Stratified Fluid,” abstract FH.003 In Proceedings of American Physical Society, 54th Annual Meeting of the Division of Fluids Dynamics, November 18–20, 2001, United States (2001).Google Scholar
  15. 15.
    Spedding G.R. Anisotropy in turbulence profiles of stratified wakes // Phys. Fluids 13(8), 2361–2372 (2001).CrossRefGoogle Scholar
  16. 16.
    M. J. Gourlay, S. C. Arendt, B. C. Fritts, and J. Werne, “Numerical Modelling of Initially Turbulent Wakes with Net Momentum,” Phys. Fluids, 13(12), 3783–3802 (2001).CrossRefGoogle Scholar
  17. 17.
    O. F. Voropaeva, B. B. Ilyushin, and G. G. Chernykh, “Numerical Modeling of Far Momentumless Trubulent Wake in a Linearly Stratified Medium,” DAN 386(6), 756–760 (2002).Google Scholar
  18. 18.
    P. Meunier and G. Spedding, “Stratified Propelled Wakes,” J. Fluid Mech., 552, 229–256 (2006).MATHCrossRefGoogle Scholar
  19. 19.
    O. F. Voropaeva, B. B. Ilyushin, and G. G. Chernykh, “Anisotropic Turbulence Decay in a Far Momentumless Trubulent Wake in a Linearly Stratified Medium” // Mathematical modeling 15(1), 101–110 (2003).MATHGoogle Scholar
  20. 20.
    O. F. Voropaeva, B. B. Ilyushin, and G. G. Chernykh, “Numerical Modeling of a Far Momentumless Trubulent Wake in a Linearly Stratified Medium using Modified Equation of Dissipation Velocity Transfer,” Thermal Physics and Air Mechanics, 10(3), 389–400 (2003).Google Scholar
  21. 21.
    O. F. Voropaeva, “Numerical Models of Momentumless Trubulent Wake Dynamics in a Stably Stratified Medium,” Computational Technologies 9(4), 15–41 (2004).MATHGoogle Scholar
  22. 22.
    G. G. Chemykh and O. F. Voropaeva, “Numerical Models of Second- and Third-Order of the Momentumless Turbulent Wake Dynamics in a Linearly Stratified Medium,” RJNAMM (in print).Google Scholar
  23. 23.
    Methods for Turbulent Flows Calculation (ed. by V. Kollman) (Mir, Moscow, 1984) [in Russian].Google Scholar
  24. 24.
    W. Rodi, “Examples of Calculation Methods for Flow and Mixing in Stratified Fluids,” J. Geophys. Res., 92(C5), 5305–5328 (1987).CrossRefGoogle Scholar
  25. 25.
    B. J. Daly and F. H. Harlow, “Transport Equations of Turbulence,” J. Phys. Fluids 13, 2634–2649 (1970)CrossRefGoogle Scholar
  26. 26.
    M. M. Gibson and B. E. Launder, “On the Calculation of the Horizontal, Turbulent, Free Shear Flows under Gravitational Influence,” J. Heat Transfer. Trans. ASME, No. 98C, 81–87 (1976).Google Scholar
  27. 27.
    M. M. Gibson and B. E. Launder, “Ground Effects on Pressure Fluctuations in the Atmospheric Boundary Layer,” J. Fluid Mech. 86, 491–511 (1978).MATHCrossRefGoogle Scholar
  28. 28.
    B. B. Ilyushin, “Higher-Moment Diffusion in Stable Stratification,” in Closure Strategies for Turbulent and Transition Flows (Cambridge Univ. Press. Cambridge, 2002).Google Scholar
  29. 29.
    A. F. Kurbatskii, Modeling Nonlocal Transfer of Turbulent Momentum and Heat (Nauka, Sib. Division, Novosibirsk, 1988) [in Russian].Google Scholar
  30. 30.
    A. S. Monin and A. M. Yaglom, Statistical Hydromechanics (Gidrometeoizdat, St. Petersburg 1992).Google Scholar
  31. 31.
    B. E. Launder, Heat and Mass Transport. Turbulence. Chapter 6. Topics in Applied Physics (Ed. by P. Bradshow), Volume 12. (Springer Verlag., Berlin, Heidelberg,1976).Google Scholar
  32. 32.
    O. F. Voropaeva, “Hierarchy of Semi-Empirical Models of Second- and Third-Order Turbulence in the Calculations of Momentumless Wakes behind Solids of Revolution,” Mathematical modeling 19(3), 29–51 (2007).MATHMathSciNetGoogle Scholar
  33. 33.
    N. V. Aleksenko and V. A. Kostomakha, “Experimental Study of Axially Symmetric Momentumless Turbulent Jet Flow,” PMTF, No.1, 65–69 (1987).Google Scholar
  34. 34.
    O. F. Voropaeva, “Numerical Modeling of Far Momentumless Axially Symmetrical Turbulent Wake,” Computational Technologies 8(2), 36–52 (2003).MathSciNetGoogle Scholar
  35. 35.
    S. Hassid, “Similarity and Decay Laws of Momentumless Wakes,” Phys. Fluids., 23(2), 404, 405 (1980).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • O. F. Voropaeva
    • 1
  1. 1.Institute of Computational TechnologiesRussian Academy of Sciences, Siberian BranchNovosibirskRussia

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