The anisotropic decay of turbulence in a far momentumless wake in a stratified medium

O. F. Voropaeva

Matematičeskoe modelirovanie, Tome 20 (2008) no. 10, pp. 23-38.

Résumé

New numerical model of turbulent wake behind the bodies of revolution in a stable stratified medium based on the semi-empirical third-order turbulence model is constructed. The differential equations for all triple correlations of velocity field transfer and modified algebraic relations of the combined triple correlations of velocity and density fields give comprehensive description of the anisotropic decay of turbulence in a far momentumless wake in a stratified fluid.

Bibliographie

[1] Schooley A. H., Stewart R. W., “Experiments with a self-propelled body submerged in a fluid with vertical density gradient”, J. Fluid Mech., 15:1 (1963), 83–96 | DOI | Zbl

[2] Onufriev A. T., “Turbulentnyi sled v stratifitsirovannoi srede”, PMTF, 1970, no. 5, 68–72

[3] Merrit C. E., “Wake growth in stratified flow”, AIAA J., 12:7 (1974), 940–949 | DOI

[4] Lewellen W. S., Teske M. E., Donaldson C. D., “Examples of variable density flows computed by second-order closure description of turbulence”, AIAA J., 14 (1976), 382–387 | DOI

[5] Vasiliev O. F., Kuznetsov B. G., Lytkin Y. M., Chernykh G. G., “Development of the turbulent mixed region in a stratified medium”, Int. Seminar “Turbulent buoyant convection” (Aug. 30–Sept. 4, Dubrovnic, Yugoslavia), 1976, 123–136

[6] Lin J. T., Pao Y. H., “Wakes in stratified fluids”, Annu. Rev. Fluid Mech., 11 (1979), 317–336 | DOI

[7] Hassid S., “Collapse of turbulent wakes in stable stratified media”, J. Hydronautics, 14 (1980), 25–32 | DOI

[8] Belotserkovskii O. M., Chislennoe modelirovanie v mekhanike sploshnykh sred, Nauka, M., 1984, 520 pp. | MR

[9] Danilenko A. Yu., Kostin V. I., Tolstykh A. I., O neyavnom algoritme rascheta techenii odnorodnoi i neodnorodnoi zhidkosti, Preprint, VTs AN SSSR, M., 1985, 40 pp. | MR

[10] Glushko G. S., Gumilevskii A. G., Polezhaev V. I., “Evolyutsiya turbulentnykh sledov za sharoobraznymi telami v ustoichivo stratifitsirovannykh sredakh”, Izv. AN SSSR. MZhG, 1994, no. 1, 13–22 | MR | Zbl

[11] Voropaeva O. F., Chernykh G. G., “Chislennaya modeldinamiki bezympulsnogo turbulentnogo sleda v piknokline”, PMTF, 38:3 (1997), 69–86 | Zbl

[12] Voropaeva O. F., Chernykh G. G., “Vnutrennie volny, generiruemye bezympulsnym turbulentnym sledom v lineino stratifitsirovannoi srede”, Matem. modelirovanie, 10:6 (1998), 75–89

[13] Chernykh G. G., Voropayeva O. F., “Numerical modeling of momentumless turbulent wake dynamics in a linearly stratified medium”, Computers and Fluids, 28:3 (1999), 281–306 | DOI | Zbl

[14] Dommermuth D. G., Rottman J. W., Innis G. E., Novikov E. A., “Numerical simulation of a momentumless wake in a weakly stratified fluid”, 54th Annual Meeting of the Division of Fluids Dynamics, Meeting ID: DFD03, abstract FH.003 (November 18–20, 2001), American Physical Society, United States, 2001

[15] Spedding G. R., “Anisotropy in turbulence profiles of stratified wakes”, Phys. Fluids, 13:8 (2001), 2361–2372 | DOI

[16] Gourlay M. J., Arendt S. C., Fritts D. C., Werne J., “Numerical modelling of initially turbulent wakes with net momentum”, Phys. Fluids, 13:12 (2001), 3783–3802 | DOI

[17] Voropaeva O. F., Ilyushin B. B., Chernykh G. G., “Chislennoe modelirovanie dalnego bezympulsnogo turbulentnogo sleda v lineino stratifitsirovannoi srede”, DAN, 386:6 (2002), 756–760

[18] Meunier P., Spedding G., “Stratified propelled wakes”, J. Fluid Mech., 552 (2006), 229–256 | DOI | Zbl

[19] Voropaeva O. F., Ilyushin B. B., Chernykh G. G., “Anizotropnoe vyrozhdenie turbulentnosti v dalnem bezympulsnom slede v lineino stratifitsirovannoi srede”, Matem. modelirovanie, 15:1 (2003), 101–110 | Zbl

[20] Voropaeva O. F., Ilyushin B. B., Chernykh G. G., “Chislennoe modelirovanie dalnego bezympulsnogo turbulentnogo sleda v lineino stratifitsirovannoi srede s primeneniem modifitsirovannogo uravneniya perenosa skorosti dissipatsii”, Teplofizika i aeromekhanika, 10:3 (2003), 389–400

[21] Voropaeva O. F., “Chislennye modeli dinamiki bezympulsnogo turbulentnogo sleda v ustoichivo stratifitsirovannoi srede”, Vychislitelnye tekhnologii, 9:4 (2004), 15–41 | Zbl

[22] Chernykh G. G., Voropayeva O. F., “Numerical models of second and third order of the momentumless turbulent wake dynamics in a linearly stratified medium”, RJNAMM, 23:6 (2008), 539–549 | MR | Zbl

[23] Kollman V. (red.), Metody rascheta turbulentnykh techenii, Mir, M., 1984, 464 pp.

[24] Rodi W., “Examples of calculation methods for flow and mixing in stratified fluids”, J. Geophys. Res., 92:C5 (1987), 5305–5328 | DOI

[25] Daly B. J., Harlow F. H., “Transport equations of turbulence”, J. Phys. Fluids, 13 (1970), 2634–2649 | DOI

[26] Gibson M. M., Launder B. E., “On the calculation of the horizontal, turbulent, free shear flows under gravitational influence”, J. Heat Transfer. Trans. ASME Ser. C, 98 (1976), 81–87

[27] Gibson M. M., Launder B.E., “Ground effects on pressure fluctuations in the atmospheric boundary layer”, J. Fluid Mech., 86 (1978), 491–511 | DOI | Zbl

[28] Ilyushin B. B., “Higher-moment diffusion in stable stratification”, Closure Strategies for Turbulent and Transition Flows, Cambridge Univ. Press, Cambridge, 2002, 424–448 | MR | Zbl

[29] Kurbatskii A. F., Modelirovanie nelokalnogo perenosa turbulentnogo impulsa i tepla, Nauka, Sib. otd-nie, Novosibirsk, 1988

[30] Monin A. S., Yaglom A. M., Statisticheskaya gidromekhanika, ch. 1, Gidrometeoizdat, Sankt-Peterburg, 1992

[31] Launder B. E., “Heat and mass transport”, Turbulence, Chapter 6, Topics in Applied Physics, 12, ed. P. Bradshow, Springer Verlag, 1976, 231–287

[32] Voropaeva O. F., “Ierarkhiya poluempiricheskikh modelei turbulentnosti vtorogo i tretego poryadka v raschetakh bezympulsnykh sledov za telami vrascheniya”, Matem. modelirovanie, 19:3 (2007), 29–51 | MR | Zbl

[33] Aleksenko N. V., Kostomakha V. A., “Eksperimentalnoe issledovanie osesimmetrichnogo bezympulsnogo turbulentnogo struinogo techeniya”, PMTF, 1987, no. 1, 65–69

[34] Voropaeva O. F., “Chislennoe modelirovanie dalnego bezympulsnogo osesimmetrichnogo turbulentnogo sleda”, Vychislitelnye tekhnologii, 8:2 (2003), 36–52 | MR | Zbl

[35] Hassid S., “Similarity and decay laws of momentumless wakes”, Phys. Fluids, 23:2 (1980), 404–405 | DOI