Kolmogorov theory via finite-time averages

Physica D: Nonlinear Phenomena - Tập 212 - Trang 245-270 - 2005
C. Foias1,2, M.S. Jolly2, O.P. Manley, R. Rosa3, R. Temam2,4
1Department of Mathematics, Texas A&M University, College Station, TX 77843, United States
2Department of Mathematics, Indiana University, Bloomington, IN 47405, United States
3Departamento de Matemática Aplicada, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530 Ilha do Fundão, Rio de Janeiro, RJ 21945-970, Brazil
4Laboratoire d’Analyse Numérique et EDP, Université de Paris-Sud, Orsay, France

Tài liệu tham khảo

Batchelor, 1953 Bercovici, 1995, Exponential decay of the power spectrum of turbulence, J. Stat. Phys., 80, 579, 10.1007/BF02178549 Childress, 2001, Bounds on dissipation for Navier–Stokes flow with Kolmogorov forcing, Phys. D, 158, 105, 10.1016/S0167-2789(01)00320-7 Constantin, 1994, Variational bounds on energy dissipation in incompressible flows: shear flow, Phys. Rev. E, 49, 4087, 10.1103/PhysRevE.49.4087 Constantin, 1995, Variational bounds on energy dissipation in incompressible flows II: channel flow, Phys. Rev. E, 51, 3192, 10.1103/PhysRevE.51.3192 Constantin, 1988 Constantin, 1983, Connexion entre la théorie mathématique des équations de Navier–Stokes et la théorie conventionnelle de la turbulence, C. R. Acad. Sci. Paris, Sér. I, 297, 599 Constantin, 1985, Attractors representing turbulent flows, Mem. Amer. Math. Soc., 53 Doering, 1992, Energy dissipation in shear driven turbulence, Phys. Rev. Lett., 69, 1648, 10.1103/PhysRevLett.69.1648 Doering, 2003, Energy dissipation in body-forced plane shear flow, J. Fluid Mech., 494, 275, 10.1017/S002211200300613X Doering, 2002, Energy dissipation in body-forced turbulence, J. Fluid Mech., 467, 289, 10.1017/S0022112002001386 Doering, 1995, Applied Analysis of the Navier–Stokes Equations, 10.1017/CBO9780511608803 Foias, 1997, What do the Navier–Stokes equations tell us about turbulence?, Contemp. Math., 208, 151, 10.1090/conm/208/02739 Foias, 2005, Kraichnan turbulence via finite time averages, Commun. Math. Phys., 255, 329, 10.1007/s00220-004-1274-5 Foias, 2002, Statistical estimates for the Navier–Stokes equations and the Kraichnan theory of 2-D fully developed turbulence, J. Stat. Phys., 108, 591, 10.1023/A:1015782025005 Foias, 2003, On the Landau–Lifschitz degrees of freedom in 2-D turbulence, J. Stat. Phys., 111, 1017, 10.1023/A:1022814702548 Foias, 2001, Navier–Stokes Equations and Turbulence, vol. 83 Foias, 2001, Cascade of energy in turbulent flows, C. R. Acad. Sci. Paris, Sér. I, 332, 509, 10.1016/S0764-4442(01)01831-6 Foias, 2001, Estimates for the energy cascade in three-dimensional turbulent flows, C. R. Acad. Sci. Paris, Sér. I, 333, 499, 10.1016/S0764-4442(01)02008-0 Foias, 1993, Bounds for the mean dissipation of 2-D enstrophy and 3-D energy in turbulent flows, Phys. Lett. A, 174, 210, 10.1016/0375-9601(93)90760-W Frisch, 1995 Kerswell, 1998, Unification of variational methods for turbulent shear flows: the background method of Doering–Constantin and the mean-fluctuation method of Howard-Busse, Phys. D, 121, 175, 10.1016/S0167-2789(98)00104-3 Kolmogorov, 1941, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, C. R. (Doklady) Acad. Sci. URSS (N.S.), 30, 301 Hinze, 1975 Ladyzhenskaya, 1963 Landau, 1971, Mécanique des Fluids, Tome 6 Lesieur, 1997, Turbulence in Fluids, vol. 40 Marchioro, 1994, Remark on the energy dissipation in shear driven turbulence, Phys. D, 74, 395, 10.1016/0167-2789(94)90203-8 Miranville, 1996, Upper bounds on the dimension of attractors for Navier–Stokes equations with non-homogeneous boundary conditions, Discrete Contin. Dyn. Syst., 2, 95, 10.3934/dcds.1996.2.95 Monin, 1975 Nicodemus, 1998, The background flow method. Part 1. Constructive approach to bounds on energy dissipation, J. Fluid Mech., 363, 281, 10.1017/S0022112098001165 Rosa, 2002, Some results on the Navier–Stokes equations in connection with the statistical theory of stationary turbulence, Appl. Math., 47, 485, 10.1023/A:1023297721804 Rose, 1978, Fully developed turbulence and statistical mechanics, J. Physique, 39, 441, 10.1051/jphys:01978003905044100 Sreenivasan, 1998, An update on the energy dissipation rate in isotropic turbulence, Phys. Fluids, 10, 528, 10.1063/1.869575 Temam, 1984, Navier–Stokes Equations. Theory and Numerical Analysis Temam, 1995, Navier–Stokes Equations and Nonlinear Functional Analysis, vol. 66 Temam, 1988, Infinite Dimensional Dynamical Systems in Mechanics and Physics, vol. 68 Wang, 1997, Time averaged energy dissipation rate for shear driven flows in Rn, Phys. D, 99, 555, 10.1016/S0167-2789(96)00161-3 Wang, 2000, Effect of tangential derivative in the boundary layer on time averaged energy dissipation rate, Phys. D, 144, 142, 10.1016/S0167-2789(00)00066-X