Skip to main content

Numerical simulation of turbulent wakes with variable total excess momentum


Numerical simulation of the dynamics of plane and axisymmetric turbulent wakes in a homogeneous fluid is performed using the modified eɛ model. The calculation results are in good agreement with the known experimental data. Asymptotic decay of axisymmetric turbulent wakes with small nonzero total excess momentum is numerically simulated.

This is a preview of subscription content, access via your institution.


  1. 1.

    Naudascher, E., Flow in the Wake of Self-Propelled Bodies and Related Sources of Turbulence, J. Fluid Mech., 1965, vol. 22,pt. 4, pp. 625–656.

    ADS  MATH  Article  Google Scholar 

  2. 2.

    Ginevskii, A.S., Teoriya turbulentnykh strui i sledov (Theory of Turbulent Jets and Wakes), Moscow: Mashinostroenie, 1969.

    Google Scholar 

  3. 3.

    Rodi, W., The Prediction of Free Turbulent Boundary Layers by Use of Two-Equation Model of Turbulence, Ph. D. Thesis, University of London, 1972.

    Google Scholar 

  4. 4.

    Lewellen, W.S., Teske, M., and Donaldson, C. du P., Application of Turbulence Model Equations to Axisymmetric Wakes, AIAA J., 1974, vol. 12, pp. 620–625.

    ADS  Article  Google Scholar 

  5. 5.

    Finson, M.L., Similarity Behavior of Momentumless Turbulent Wakes, J. Fluid Mech., 1975, vol. 71, pp. 465–479.

    ADS  Article  Google Scholar 

  6. 6.

    Sabelnikov, V.A., Some Special Features of Turbulent Flows with Zero Excess Momentum, Uch. Zap. TsAGI, 1975, vol. 6, pp. 71–74.

    ADS  Google Scholar 

  7. 7.

    Townsend, A.A., The Structure of Turbulent Shear Flow, Cambridge University Press, 1976.

    MATH  Google Scholar 

  8. 8.

    Higuchi, H., Experimental Investigation on Axisymmetric Turbulent Wakes with Zero Momentum Defect, Ph. D. Thesis, California Institute of Technology, 1977.

    Google Scholar 

  9. 9.

    Gorodtsov, V.A., Similarity and Weak Closing Relations for Symmetric Free Turbulence, Fluid Dyn., 1979, vol. 14,iss. 1, pp. 31–37.

    MathSciNet  ADS  MATH  Article  Google Scholar 

  10. 10.

    Hassid, S., Collapse of Turbulent Wakes in Stable Stratified Media, J. Hydronaut., 1980, vol. 14, pp. 25–32.

    ADS  Article  Google Scholar 

  11. 11.

    Hassid, S., Similarity and Decay Law of Momentumless Wakes, Phys. Fluids, 1980, vol. 23, pp. 404–405.

    ADS  Article  Google Scholar 

  12. 12.

    Luchko, N.N., The Influence of the Error in Determining Excess Momentum on the Evolution of an Axisymmetric Turbulent Wake, in Struktura turbulentnykh techenii (The Structure of Turbulent Flows), Proc. of ITMO AN BSSR, Minsk, 1982.

    Google Scholar 

  13. 13.

    Kolovandin, B.A. and Luchko, N.N., The Effect of External Turbulence on the Velocity Field in a Wake behind an Ellipsoid of Revolution, IFZh, 1985, vol. 48, no. 4, pp. 538–546.

    MathSciNet  Google Scholar 

  14. 14.

    Aleksenko, N.V. and Kostomakha, V.A., Experimental Study of an Axisymmetric Nonimpulsive Turbulent Jet, J. Appl. Mech. Tech. Phys., 1987, vol. 28, iss. 1, pp. 60–64.

    ADS  Article  Google Scholar 

  15. 15.

    Dmitrenko, Yu.M., Kovalev, I.I., Luchko, N.N., and Cherepanov, P.Ya., Investigation of a Plane Turbulent Wake with Zero Excess Momentum, IFZh, 1987, vol. 52, pp. 743–750.

    Google Scholar 

  16. 16.

    Aleksenko, N.V. and Kostomakha, V.A., Experimental Investigation of the Dynamics of a Momentumless Turbulent Wake in a Turbulent External Flow, Din. Splosh. Sredy, Novosibirsk, 1988, iss. 81, pp. 14–24.

    Google Scholar 

  17. 17.

    Higuchi, H. and Kubota, T., Axisymmetric Wakes behind a Slender Body Including Zero-Momentum Configurations, Phys. Fluids A, 1990, vol. 2, no. 9, pp. 1615–1623.

    ADS  Article  Google Scholar 

  18. 18.

    Cimbala, J.M. and Park, W.J., An Experimental Investigation of the Turbulent Structure in a Two-Dimensional Momentumless Wake, J. Fluid Mech., 1990, vol. 213, pp. 479–509.

    ADS  Article  Google Scholar 

  19. 19.

    Chernykh, G.G., Demenkov, A.G., and Fedorova, N.N., Numerical Models of Plane and Axisymmetric Turbulent Wakes in Homogeneous Fluid, Int. Conf. on the Methods of Aerophysical Research, Novosibirsk, 1994, pt. 2, pp. 76–81.

    Google Scholar 

  20. 20.

    Fedorova, N.N. and Chernykh, G.G.,Numerical Simulation of Plane Turbulent Wakes, Matem. Mod., 1994, vol. 6, no. 10, pp. 24–34.

    MATH  Google Scholar 

  21. 21.

    Ahn, J.W. and Sung, H.J., Prediction of Two-Dimensional Momentumless Wake by kɛγ Model, AIAA J., 1995, vol. 33, no. 4, pp. 611–617.

    ADS  Article  Google Scholar 

  22. 22.

    Chernykh, G.G. and Demenkov, A.G., On Numerical Simulation of Jet Flows of Viscous Incompressible Fluids, Russian J. Num. Anal. Math. Mod., 1997, vol. 12, no. 2, pp. 111–125.

    MathSciNet  MATH  Google Scholar 

  23. 23.

    Bukreev, V.I., Demenkov, A.G., Kostomakha, V.A., and Chernykh, G.G., Heat Propagation from a Line Source in a Plane Turbulent Wake, J. Appl. Mech. Tech. Phys., 1996, vol. 37, no. 5, pp. 710–719.

    ADS  Article  Google Scholar 

  24. 24.

    Cherepanov, P.Y. and Babenko, V.A., Experimental and Numerical Study of Flat Momentumless Wake, Int. J. Heat Fluid Flow, 1998, vol. 19, pp. 608–622.

    Article  Google Scholar 

  25. 25.

    Grebenev, V.N., Demenkov, A.G., and Chernykh, G.G., Analysis of the Local-Equilibrium Approximation in the Problem of Far Planar Turbulent Wake, Dokl. Phys., 2002, vol. 47, no. 7, pp. 518–521.

    MathSciNet  ADS  Article  Google Scholar 

  26. 26.

    Smirnov, S.A. and Voropayev, S.I., On the Asymptotic Theory of Momentum/Zero-Momentum Wakes, Phys. Lett. A, 2003, vol. 307, pp. 148–153.

    MathSciNet  ADS  MATH  Article  Google Scholar 

  27. 27.

    Afanasyev, Y.D., Wakes behind Towed and Self-Propelled Bodies. Asymptotic Theory, Phys. Fluids, 2004, vol. 16, no. 8, pp. 3235–3238.

    MathSciNet  ADS  Article  Google Scholar 

  28. 28.

    Voropaeva, O.F., Dynamics of a Far Momentumless Turbulent Wake in Passively Stratified Media, Russ. J. Num. Anal. Math. Mod., 2004, vol. 19, no. 1, pp. 83–102.

    MathSciNet  Article  Google Scholar 

  29. 29.

    Lu, M.-H. and Sirviente, A.I., Numerical Study of the Momentumless Wake of an Axisymmetric Body, 43rd AIAA Aerospace Sciences Meeting and Exhibit., Reno, Nevada, 2005, 2005-1109, p. 14.

    Google Scholar 

  30. 30.

    Voropaeva, O. F., A Hierarchy of Second- and Third-Order Turbulence Models for Momentumless Wakes behind Axisymmetric Bodies, Matem. Mod., 2007, vol. 19, no. 3, pp. 29–51.

    MathSciNet  MATH  Google Scholar 

  31. 31.

    Kaptsov, O.V., Efremov, I.A., and Schmidt, A.V., Self-Similar Solutions of the Second-Order Model of the Far Turbulent Wake, J.Appl. Mech. Tech. Phys., 2008, vol. 49, no. 2, pp. 217–221.

    ADS  Article  Google Scholar 

  32. 32.

    Novikov, B.G., Effect of Small Total Pulse on Development of a Wake behind the Self-Propelled Bodies, Thermophys. Aeromech., 2009, no. 4, pp. 597–623.

    Google Scholar 

  33. 33.

    Chernykh, G.G., Moshkin, N.P., and Fomina, A.V., Dynamics of Turbulent Wake with Small Excess Momentum in Stratified Media, Comm. Nonlinear Sci. Num. Sim., 2009, vol. 14, no. 4, pp. 1307–1323.

    MathSciNet  ADS  MATH  Article  Google Scholar 

  34. 34.

    Efremov, I.A., Kaptsov, O.V., and Chernykh, G.G., Self-Similar Solutions for Two Problems of Free Turbulence, Matem. Mod., 2009, vol. 21, no. 12, pp. 137–144.

    MathSciNet  MATH  Google Scholar 

  35. 35.

    Maderich, V. and Konstantinov, S., Asymptotic and Numerical Analysis of Momentumless Turbulent Wakes, Fluid Dyn. Res., 2010, vol. 42, no. 42, 25 p. DOI: 10.1088/0169-5983/42/4/045503.

    Google Scholar 

  36. 36.

    De Stadler, M.B. and Sarkar, S., Simulation of a Propelled Wake with Moderate Excess Momentum in a Stratified Fluid, J. Fluid Mech., 2012, vol. 692, pp. 28–52.

    ADS  MATH  Article  Google Scholar 

  37. 37.

    Lewis, B.J., Cimbala, J.M., and Wouden, A.M., Analysis and Optimization of Guide Vane Jets to Decrease the Unsteady Load on Mixed Flow Hydroturbine Runner Blades, Proc. Seventh Int. Conf. on Computational Fluid Dynamics (ICCFD7), Big Island, Hawaii, 2012, ICCFD7–1701.

    Google Scholar 

  38. 38.

    Kovalev, I.I., Kolovandin, B.A., and Luchko, N.N., Final Stage of Turbulent Velocity Field Decay in a Flow Wake, IFZh, 1985, vol. 49, no. 2, pp. 209–214.

    Google Scholar 

  39. 39.

    Tikhonov, A.N. and Samarskii, A.A., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Nauka, 1966.

    Google Scholar 

  40. 40.

    Kalitkin, N.N., Chislennye metody (Numerical Methods), Moscow: Nauka, 1978.

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to G. G. Chernykh.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chernykh, G.G., Demenkov, A.G. Numerical simulation of turbulent wakes with variable total excess momentum. J. Engin. Thermophys. 22, 143–156 (2013).

Download citation


  • Turbulence Energy
  • Turbulent Wake
  • Velocity Defect
  • Turbulent Reynolds Number