Kolmogorov theory via finite-time averages
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