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Modelling of the interaction of small and large eddies in two dimensional turbulent flows. (English) Zbl 0663.76054
Our aim in this article is to present some results concerning the modeling of the interaction of small and large eddies in two-dimensional turublent flows. We show that the amplitude of small structures decays exponentially to a small value and we infer form this a simplified interaction law of small and large eddies. Beside their intrinsic interest for the understanding of the physics of turbulence, these results lead to new numerical schemes which will be studied in a separate work.
Reviewer: Reviewer (Berlin)

76F99 Turbulence
35Q99 Partial differential equations of mathematical physics and other areas of application
Full Text: DOI EuDML
[1] H. BRÉZIS and T. GALLOUET, < Nonlinear Schroedinger evolution equation> , Nonlinear Analysis Theory Methods and Applications, Vol.4, 1980, p. 677. Zbl0451.35023 MR582536 · Zbl 0451.35023 · doi:10.1016/0362-546X(80)90068-1
[2] C. FOIAS, O. MANLEY and R. TEMAM, < Sur l’interaction des petits et grands tourbillons dans des écoulements turbulents> , C.R. Ac. Sc.Paris, 305, Série I, 1987; pp. 497-500. Zbl0624.76072 MR916319 · Zbl 0624.76072
[3] C. FOIAS, O. MANLEY and R. TEMAM, to appear. MR1205478
[4] C. FOIAS, O. MANLEY, R. TEMAM and Y. TREVE, < Asymptotic analysis of the Navier-Stokes equations> , Physica 6D, 1983, pp. 157-188. Zbl0584.35007 MR732571 · Zbl 0584.35007 · doi:10.1016/0167-2789(83)90297-X
[5] C. FOIAS, B. NICOLAENKO, G. SELL and R. TEMAM, < Variétés inertielles pour l’équation de Kuramoto-Sivashinsky> ,C. R. Ac. Sc. Paris, 301, Série I, 1985pp. 285-288 and < Inertial Manifolds for the Kuramoto-Sivashinsky équations and an estimate of their lowest dimension> , J. Math. Pure AppL, 1988. Zbl0591.35063 MR803219 · Zbl 0591.35063
[6] [6] C. FOIAS and G. PRODI, < Sur le comportement global des solutions non stationnaires des équations de Navier-Stokes en dimension 2> , Rend. Sem. Mat. Padova, Vol. 39, 1967, pp. 1-34. Zbl0176.54103 MR223716 · Zbl 0176.54103 · numdam:RSMUP_1967__39__1_0 · eudml:107242
[7] C. FOIAS and R. TEMAM, < Some analytic and geometrie properties of the solutions of the Navier-Stokes equations> , J. Math. Pure Appl, Vol.58, 1979, pp. 339-368. Zbl0454.35073 MR544257 · Zbl 0454.35073
[8] C. FOIAS and R. TEMAM, Finite parameter approximative structures of actual flows> , in Nonlinear Problems : Present and Future, A. R. Bishop, D. K. Campbell, B. Nicolaenko (eds.), North Holland, Amsterdam, 1982. Zbl0493.76026 MR675639 · Zbl 0493.76026
[9] A. N. KOLMOGOROV, C. R. Ac. Sc URSS, Vol.30, 1941, p. 301; Vol. 31, 1941, p. 538; Vol. 32, 1941, p. 16.
[10] R. H. KRAICHNAN, < Inertial ranges in two dimensional turbulence> , Phys. Fluids, Vol. 10, 1967, pp. 1417-1423.
[11] G. MÉTIVIER, < Valeurs propres d’opérateurs définis sur la restriction de systèmes variationnels à des sous-espaces> , J. Math. Pure Appl., Vol. 57, 1978, pp. 133-156. Zbl0328.35029 MR505900 · Zbl 0328.35029
[12] R. TEMAM, Navier-Stokes Equations, 3rd Revised Ed., North Holland, Amsterdam, 1984. Zbl0568.35002 · Zbl 0568.35002
[13] R. TEMAM, Navier-Stokes Equations and Nonlinear Functional Analysis, NSF/CBMS Regional Conferences Series in Appl. Math., SIAM, Philadelphia, 1983. Zbl0833.35110 MR764933 · Zbl 0833.35110
[14] R. TEMAM, Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, 1988. Zbl0662.35001 MR953967 · Zbl 0662.35001
[15] E. TITI, Article in preparation.
[16] J. H. WELLS and L. R. WILLIAMS, Imbeddings and Extensions in Analysis, Springer-Verlag, Heidelberg, New York Zbl0324.46034 · Zbl 0324.46034
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