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Numerical simulation of the dynamics of non-zero buoyancy turbulent mixing zone in a linearly stratified medium

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Thermophysics and Aeromechanics Aims and scope

Abstract

A numerical model of the dynamics of a plane localized region of turbulent perturbations of non-zero buoyancy in a linearly stratified medium has been developed on the basis of the mathematical model, including differential equations for Reynolds stresses transfer and algebraic model of a turbulent flux vector of a scalar. The evolution of a heated turbulent spot has been considered. The non-zero buoyancy is the reason of an increase in the geometrical size of the turbulent spot and generation of internal waves of greater amplitude. The generation of the total energy of turbulence is insignificant even in the case when the initial potential energy of a turbulent spot of non-zero buoyancy is comparable to the initial total energy of turbulence in it.

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References

  1. A.S. Monin and A.M. Yaglom, Statistical Fluid Mechanics, Vol. 1, Mechanics of Turbulence, Dover Books on Physics, New York, 2007.

    MATH  Google Scholar 

  2. A.H. Schooley, Wake collapse in a stratified fluid, Sci., 1967. Vol. 157, No. 3787, P. 421–423.

    Article  ADS  Google Scholar 

  3. O.F. Vasiliev, B.G. Kuznetsov, Yu.M. Lytkin, and G.G. Chernykh, Development of the turbulized fluid region in stratified medium, Intern. Symposium on Stratified Flows, Novosibirsk, USSR, Aug. 29–31, 1972. Paper 4.

  4. Yu.N. Vlasov, V.N. Nekrasov, A.M. Trokhan, and Yu.D. Chashechkin, Development of turbulent mixing in a fluid, J. Appl. Mech. Techn. Phys., 1973, Vol. 14, Iss. 2, P. 222–225.

    Article  ADS  Google Scholar 

  5. O.F. Vasiliev, B.G. Kuznetsov, Yu.M. Lytkin, and G.G. Chernykh, Development of the region of a turbulized liquid in a stratified medium, Fluid Dynamics, 1974, Vol. 9, No. 3, P. 368–373.

    Article  ADS  Google Scholar 

  6. A.M. Trokhan and Yu.D. Chashechkin, Generation of internal waves in stratified fluid by an impulse hydrodynamic line source (two-dimensional problem), In: Theory of Diffraction and Propagation of Waves: Abstr. 7th All-Union Symp. on Waves Diffraction and Propagation, Vol. 3, USSR Acad. Sci., Moscow, 1977, P. 186–189.

    Google Scholar 

  7. O.F. Vasiliev, B.G. Kuznetsov, Yu.M. Lytkin, and G.G. Chernykh, Development of the turbulent mixed region in a stratified medium, Heat transfer and turbulent buoyant convection: studies and applications for natural environment, buildings, engineering systems: Seminar of the Inter. Center for Heat and Mass Transfer at Dubrovnik, Yugoslavia, in Aug. 1976, Vol. 1, Hemisphere Pub. Corp., McGraw-Hill Intern. Book Co., Washington, 1977, P. 123–136.

    Google Scholar 

  8. Yu.M. Lytkin and G.G. Chernykh, Similarity of the flow with respect to the density Froude number and energy balance at the evolution of the turbulent mixing zone in a stratified medium, in: Math. Probl. Continuum Mech.: A Collection of Scientific Works, Inst. Hydrodynamics of the USSR Acad. Sci., Novosibirsk, 1980, Iss. 47, P. 70–89.

  9. G.G. Chernykh and O.F. Voropayeva, Numerical modeling of momentumless turbulent wake dynamics in a linearly stratified medium, Computers and Fluids, 1999, Vol. 28, No. 3, P. 281–306.

    Article  Google Scholar 

  10. A. Pal, M.B. De Stadler, and S. Sarkar, The spatial evolution of fluctuations in a self-propelled wake compared to a patch of turbulence, Phys. Fluids, 2013, Vol. 25, P. 095106–1–095106–20.

    Article  ADS  Google Scholar 

  11. S.N. Yakovenko, T.G. Thomas, and I.P. Castro, A turbulent patch arising from a breaking internal wave, J. Fluid Mech., 2011, Vol. 677, P. 103–133.

    Article  ADS  MathSciNet  Google Scholar 

  12. O.F. Voropaeva and G.G. Chernykh, The dynamics of local zones of turbulized fluid under the background disturbances of hydrophysical fields, Fundamentalnaya i Prikladnaya Gidrofizika, 2015, Vol. 8, No. 4, P. 12–17.

    Google Scholar 

  13. I.V. Antropov and V.A. Kronod, On evolution of a thermal in a stratified medium in dependence on initial conditions, Izv. Atmosph. Ocean. Phys. 1989, Vol. 25, No. 12, P. 1261–1266.

    Google Scholar 

  14. G.G. Chernykh, A.V. Fomina, and N.P. Moshkin, Numerical simulation of dynamics of weakly heated turbulent mixing zone in linearly stratified medium, J. Engng Thermophysics, 2020, Vol. 29, Iss. 4, P. 674–685.

    Article  Google Scholar 

  15. W. Rodi, Turbulence Models and their Application in Hydraulics, University of Karlsruhe, 1980.

  16. W. Rodi, Examples of calculation methods for flow and mixing in stratified fluids, J. Geophys. Res., 1987, Vol. 92, No. C5, P. 5305–5328.

    Article  ADS  Google Scholar 

  17. G.G. Chernykh, A.V. Fomina, and N.P. Moshkin, Numerical simulation of dynamics of turbulent wakes behind towed bodies in linearly stratified media, J. Engng Thermophys. 2009, Vol. 18, No. 4, P. 279–305.

    Article  Google Scholar 

  18. J.T. Lin and Y.H. Pao, Wakes in stratified fluids, Annual Review Fluid Mechanics, 1979, Vol. 11, P. 317–338.

    Article  ADS  Google Scholar 

  19. S. Hassid, Collapse of turbulent wakes in stable stratified media, J. Hydronautics, 1980, Vol. 14, No. 1, P. 25–32.

    Article  ADS  Google Scholar 

  20. O.M. Belotserkovskii, Chislennoe Modelirovanie v Mekhanike Sploshnykh Sred, Nauka, Moscow, 1994.

    Google Scholar 

  21. Y.H. Zurigat and A.J. Chajar, Comparative study of weighted upwind and second order upwind difference schemes, Numerical Heat Transfer. Part B: Fundamentals, 1990, Vol. 18, Iss. 1, P. 61–80.

    Article  ADS  Google Scholar 

  22. N.P. Moshkin, On splitting methods in numerical models of drag turbulent wakes in stratified fluid, Computational Technologies, 2009, Vol. 14, No. 4, P. 81–92.

    MathSciNet  MATH  Google Scholar 

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Moshkin, N.P., Fomina, A.V. & Chernykh, G.G. Numerical simulation of the dynamics of non-zero buoyancy turbulent mixing zone in a linearly stratified medium. Thermophys. Aeromech. 29, 167–178 (2022). https://doi.org/10.1134/S0869864322020020

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  • DOI: https://doi.org/10.1134/S0869864322020020

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