Abstract
One presents the spectral two-point closure point of view of turbulence theory. In the three-dimensional incompressible isotropic case, it is shown how these closures lead, in the inviscid limit, to singularities of the vorticity field at a finite time. A theory of non local interactions is developed, which allows to derive a parameterization of the subgrid scales for large-eddy simulations.
Results of direct or large-eddy simulations utilizing the above subgrid-scale parameterization are presented for three-dimensional isotropic turbulence or for a temporally growing mixing layer forced initially with a random perturbation. Two-dimensional calculations of various incompressible and compressible free shear flows are also presented.
Finally, the role of compressibility on the dynamics of the coherent structures in free shear flows is examined.
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References
André, J.C. and Lesieur, M., 1977, J. Fluid Mech., 81, pp 187–207.
Batchelor, G.K., Canuto, V.M., and Chasnov, J.R., 1992, J. Fluid Mech., ?, pp ??–??
Bernai, L.P. and Roshko, A., 1986, J. Fluid Mech., 170, pp 499–525.
Brown, G.L. and Roshko, A., 1974, J. Fluid Mech., 64, pp 775–816.
Chollet, 1983, Thèse de Doctorat d’Etat, Grenoble University.
Chollet, J.P. and Lesieur, M., 1981, J. Atmos. Sci., 38, pp 2747–2757.
Chollet, J.P. and Métais, O., 1989, European Journal of Mechanics B/Fluids, 8, pp 523–548.
Comte, P., Lesieur, M. and Fouillet, Y., 1989, in Topological Fluid Dynamics, Cambridge University Press, H.K. Moffatt ed., pp 649–658.
Comte, P., Lesieur, M. and Lamballais, E., 1992, submitted to Phys. Fluids.
Comte-Bellot, G. and Corrsin, S., 1966, J. Fluid Mech., 25, pp 657–682.
Forster, D., Nelson, D. and Stephen, M.J., 1977, Phys. Rev. A, 16, pp 732–749.
Fouillet, Y., 1991, Thèse, University of Grenoble.
Fournier, J.D., 1977, Thèse, Nice University.
Herring, J.R. and Kraichnan, R.H., 1972, in Statistical models and turbulence, Springer-Verlag, 12, pp 148–194.
Herring, J.R. et al., 1982, J. Fluid Mech., 124, pp 411–437.
Kraichnan, R.H., 1961, J. Math. Phys., 2, pp 124–148.
Kraichnan, R.H., 1966, Phys. Fluids, 9, pp 1728–1752.
Kraichnan, R.H., 1976 J. Atmos. Sci., 33, pp 1521–1536.
Leith, C.E., 1971, J. Atmos. Sci., 28, pp 145–161.
Lele, S.K., 1988, in Proc. of the Conference on the Physics of Compressible Turbulent Mixing, Oct. 24–27, Princeton.
Leray, J., 1934, J. Acta. Math, 63, pp 193–248.
Lesieur, M. and Schertzer, D., 1978, J. Mécanique, 17, pp 609–646.
Lesieur, M., 1987, Turbulence in Fluids, Nijhoff Publishers, Dordrecht. Second edition, 1990, Kluwer Publishers.
Lesieur, M., Montmory, C. and Chollet, J.P., 1987, Phys. Fluids., 30, pp 1278–1286.
Lesieur, M., Staquet, C., Le Roy, P. and Comte, P., 1988, J. Fluid Mech., 192, pp 511–534.
Lesieur, M. and Rogallo, B., 1989, Phys. Fluids A, 1, pp 718–722.
Lesieur, M., Métais and Rogallo, R., 1989, C.R. Acad. Sci., 308, Ser. II, pp 1395–1400.
McLaughlin, Papanicolao and Pironneau, 1985 SIAM J. Appl. Math.
Millionshtchikov, M., 1941, Dokl. Akad. Nauk. SSSR, 32, pp 615–618.
Moin, P. and and Kim, J., 1982, J. Fluid Mech., 118, pp 341–378.
Marion, J.D. 1988, Thèse de l’Ecole Centrale de Lyon.
Métais, O. and Lesieur, M. 1992, J. Fluid Mech., 239, pp 157–194.
Normand, X. and Lesieur, M., 1992, Theor. Comput. Fluid Dynamics, 3, pp 231–252.
Ogura, Y., 1963, J. Fluid Mech., 16, pp 33–40.
Orszag, S. A., 1970, J. Fluid Mech., 41, pp 363–386.
Orszag, S.A. and Patterson, G.K., 1972, in Statistical models and turbulence, Springer-Verlag, 12, pp 127–147.
Papamoschou, D. and Roshko, A., 1988, J. Fluid Mech., 197, pp 453–477.
Sandham, N.D. and Reynolds, W.C., 1991, J. Fluid Mech., 224, pp 133–158.
Silveira-Neto, A., Grand, D., Métais, O. and Lesieur, M., 1991, Phys. Rev. Letters, 66, pp 2320–2323.
Soetrisno, M., Greenough, J.A., Eberhardt, S. and Riley, J., 1989, “Confined compressible mixing layers: part I. Three-dimensional instabilities”, AIAA 20 Fluid Dynamics, Plasma Dynamics and Lasers Conference, Buffalo, pp th st Nat. Fluid Dynamics Congress, Cincinnati, AIAA paper 89-1810.
Warhaft, Z. and Lumley, J.L., 1978, J. Fluid Mech., 88, pp 659–684.
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Lesieur, M. (1992). Advanced Topics in Turbulence Theory. In: Bertin, J.J., Periaux, J., Ballmann, J. (eds) Advances in Hypersonics. Progress in Scientific Computing, vol 8/9. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0371-1_2
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DOI: https://doi.org/10.1007/978-1-4612-0371-1_2
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