
SIGMA 8 (2012), 073, 10 pages arXiv:1210.4254
http://dx.doi.org/10.3842/SIGMA.2012.073
Contribution to the Special Issue “Geometrical Methods in Mathematical Physics”
Application of the BDetermining Equations Method to One Problem of Free Turbulence
Oleg V. Kaptsov and Alexey V. Schmidt
Institute of Computational Modeling SB RAS, Akademgorodok, Krasnoyarsk, 660036, Russia
Received May 17, 2012, in final form October 04, 2012; Published online October 16, 2012
Abstract
A threedimensional model of the far turbulent wake behind a selfpropelled body in a passively stratified medium is considered. The model is reduced to a system of ordinary differential equations by a similarity reduction and the Bdetermining equations method. The system of ordinary differential equations satisfying natural boundary conditions is solved numerically. The solutions obtained here are in close agreement with experimental data.
Key words:
turbulence; far turbulent wake; Bdetermining equations method.
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References
 Andreev V.K., Kaptsov O.V., Pukhnachov V.V., Rodionov A.A., Applications of
group theoretical methods in hydrodynamics, Mathematics and its
Applications, Vol. 450, Kluwer Academic Publishers, Dordrecht, 1998.
 Barenblatt G.I., Galerkina N.L., Luneva M.V., Evolution of a turbulent burst,
J. Eng. Phys. Thermophys. 53 (1987), 12461252.
 Cazalbou J.B., Spalart P.R., Bradshaw P., On the behavior of twoequation
models at the edge of a turbulent region, Phys. Fluids 6
(1994), 17971804.
 Chashechkin Yu.D., Chernykh G.G., Voropaeva O.F., The propagation of a passive
admixture from a local instantaneous source in a turbulent mixing zone,
Int. J. Comp. Fluid Dyn. 19 (2005), 517529.
 Chernykh G.G., Fedorova N.N., Moshkin N.P., Numerical simulation of turbulent
wakes, Russian J. Theor. Appl. Mech. 2 (1992), 295304.
 Chernykh G.G., Fomina A.V., Moshkin N.P., Numerical models for turbulent wake
dynamics behind a towed body in a linearly stratified medium,
Russian J. Numer. Anal. Math. Modelling 21 (2006),
395424.
 Efremov I.A., Kaptsov O.V., Chernykh G.G., Selfsimilar solutions of two
problems of free turbulence, Mat. Model. 21 (2009),
137144 (in Russian).
 Gibson M.M., Launder B.E., On the calculation of horizontal, turbulent, free
shear flows under gravitational influence, J. Heat Transfer
98 (1976), 8187.
 Hassid S., Collapse of turbulent wakes in stable stratified media,
J. Hydronautics 14 (1980), 2532.
 Hinze J.O., Turbulence: an introduction to its mechanism and theory,
McGrawHill Series in Mechanical Engineering, McGrawHill Book Co., Inc., New
York, 1959.
 Hulshof J., Selfsimilar solutions of Barenblatt's model for turbulence,
SIAM J. Math. Anal. 28 (1997), 3348.
 Kaptsov O.V., Bdetermining equations: applications to nonlinear partial
differential equations, European J. Appl. Math. 6 (1995),
265286.
 Kaptsov O.V., Efremov I.A., Invariant properties of the far turbulent wake
model, Comput. Technol. 10 (2005), no. 6, 4551 (in
Russian).
 Kaptsov O.V., Efremov I.A., Schmidt A.V., Selfsimilar solutions of the
secondorder model of the far turbulent wake, J. Appl. Mech. Tech.
Phys. 49 (2008), 217221.
 Kaptsov O.V., Shan'ko Yu.V., Family of selfsimilar solutions of one model of
the far turbulent wake, in Proceedinds of International Conference
"Computational and Information Technologies in Sciences, Engineering, and
Education" (September 2022, 2006, Pavlodar, Kazakhstan), Vol. 1, TOO NPF
"EKO", Pavlodar, 2004, 576579 (in Russian).
 Launder B.E., Spalding D.B., Mathematical models of turbulence, Academic Press,
London, 1972.
 Lin J.T., Pao Y.H., Wakes in stratified fluids, Ann. Rev. Fluid Mech.
11 (1979), 317338.
 Olver P.J., Applications of Lie groups to differential equations,
Graduate Texts in Mathematics, Vol. 107, SpringerVerlag, New York,
1986.
 Ovsiannikov L.V., Group analysis of differential equations, Academic Press
Inc., New York, 1982.
 Pope S.B., Turbulent flows, Cambridge University Press, Cambridge, 2000.
 Rodi W., Examples of calculation methods for flow and mixing in stratified
fluids, J. Geophys. Res. 92 (1987), 53055328.
 Schlichting H., Boundary layer theory, McGrawHill, New York, 1955.
 Vasiliev O.F., Kuznetsov B.G., Lytkin Yu.M., Cherhykh G.G., Development of the
turbulized fluid region in a stratified medium, Fluid Dyn. (1974),
no. 3, 4552 (in Russian).
 Voropaeva O.F., Far momentumless turbulent wake in a passively stratified
medium, Comput. Technol. 8 (2003), no. 3, 3246 (in
Russian).
 Voropaeva O.F., Chernykh G.G., On numerical simulation of the dynamics of the
turbulized fluid regions in stratified medium, Comput. Technol.
1 (1992), no. 1, 93104 (in Russian).
 Voropaeva O.F., Moshkin N.P., Chernykh G.G., Internal waves generated by
turbulent wakes in a stably stratified medium, Dokl. Phys.
48 (2003), 517521.
 Wilcox D.C., Turbulence modeling for CFD, DCW Industries, Canada, 1994.

