Keywords
closure procedure
differential constraints
invariant sets
third-order closure model
selfsimilar solution
asymptotic behavior
Modelos de turbulencia
procedimiento de clausura
restricciones diferenciales
conjuntos invariantes
modelo de clausura de tercer orden
solución autosimilar
comportamiento asintótico
How to Cite
Abstract
In this article we introduce a concept based on the differential constraints method to examine the closure procedure in Turbulence Models. We show how this concept may be applied to study the problem of interaction and mixing between two semi-infinite homogeneous turbulent flow fields of different scales.
References
Yanenko, N. N. (1991) Selected Works. Nauka, Moscow (in Russian).
Sidorov, A. F.; Shapeev, V. P.; Yanenko, N. N. (1984) The Differential Constraints Method and its Application to Gas Dynamics. Nauka, Novosibirsk (in Russian).
Ilyushin, B. B. (2000) “Higher-moment diffusion in stable stratification”, in: B.E. Launder & N.D. Sandham (Eds.) Closure Strategies for Turbulent and Transition Flows, Cambridge University Press (in press).
Ilyushin, B. B. (1999) “Model of fourth–order cumulants for prediction of turbulent transport by large–scale vortex structure”, J. Appl. Mechan. Tech. Phys. 40(5): 871–876.
Lamb, R. G. (1982) “Diffusion in convective boundary layer”, in: F.T.M. Nieuwstadt & H. van Dop (Eds.) Atmospheric Turbulence and Air Pollution Modelling, Reidel, Boston MS.
Hazen, A. M. (1963) “To nonlinear theory of appearance of turbulence”, Dokl. Acad. Nauk USSR 163: 1282–1287 (in Russian).
Ogura, Y. (1962) “Energy transfer in a normally distributed and isotropic turbulent velocity field in two dimensions”, Phys. Fluids 5(4): 395–401.
Hanjalic, K.; Launder, B. E. (1972) “A Reynolds stress model of turbulence and its application to thin shear flows”, J. Fluid Mech. 52: 609–638.
Ibragimov, N. H. (1985) Transformation Groups Applied to Mathematical Physics. Reidel.
Kaptsov, O. V. (1995) “B-determining equations: applications to nonlinear partial differential equations”, Euro. J. Appl. Math., 6: 265–286.
Hulshof ,J. (1997) “Selfsimilar solutions of Barenblatt’s model for turbulence”, SIAM J. Math. Anal. Appl. 28(1): 33–48.
Barenblatt, G. I. (1996) Scaling, Selfsimilar and Intermediate Asymptotics. Cambridge Texts in Applied Mathematics, 14.
Polubarinova-Kochina, P. Ya. (1948) “On a nonlinear partial differential equation appearing in the filtration theory”, Dokl. Acad. Nauk USSR, 63(6): 623–626 (in Russian).
Ilyushin, B. B.; Kurbatskii, A.F. (1990) “Numerical simulation of the shearless tur-
bulence mixing layer”, Izv. Acad. Nauk USSR (Siberian Branch), Ser. Tech. Nauk. 3: 62–68 (in Russian).
Veeravalli, S.; Warhaft, Z. (1989) “The shearless turbulence mixing layer”, J. Fluid Mech. 207: 191–229.
Grebenev, V. N. (1994) “On a certain system of degenerate parabolic equations which arises in Hydrodynamics”, Sib. Math. J. 35(4): 753–767.
Ladyzhenskaya, O. A.; Solonnikov, V.; Ural’ceva N. (1968) Linear and Quasilinear Equations of Parabolic Type. Amer. Math. Soc.
Vishnevskiy, M. P.; Zelenyak, T. I.; Lavrentjev, M. M. (1995) “Large time behavior solutions for nonlinear parabolic equations”, Sib. Math. J. 36(3): 510–530.