Attractor dimension and small length scale estimates for the three-dimensional Navier-Stokes equations

Nonlinearity

Volumn 10, Issue 1, 1997, Pages 109-119

  Gibbon, J D ^a   Titi, E S ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013419090     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/10/1/007     Document Type: Article

References (34)

1. Kolmogorov A N 1941 Local structure of turbulence in an incompressible fluid at very high Reynolds numbers Dokl. Akad. Nauk. SSSR 30 299-303
2. Constantin P and Foias C 1985 Global Lyapunov exponents, Kaplan-Yorke formulas and the dimension of the attractors for 2d Navier-Stokes equations. Commun. Pure Appl. Math. 38 1-27
3. Constantin P and Foias C 1988 Navier-Stokes Equations (Chicago, IL: University of Chicago Press)
4. Hale J K 1988 Asymptotic Behaviour of Dissipative Systems vol 25 (Providence, RI: AMS)
5. Temam R 1988 Infinite Dimensional Dynamical Systems in Mechanics and Physics (Applied Mathematical Sciences 68) (New York: Springer)
6. Landau L D and Lifshitz EM 1959 Fluid Mechanics (Course of Theoretical Physics 6) (Oxford: Pergamon)
7. Constantin P, Foias C and Temam R 1988 On the dimension of the attractors in two-dimensional turbulence Physica D 30 284-96
8. Majda A 1991 Vorticity, turbulence and acoustics in fluid flow SIAM Rev. 33 349-88
9. Moffatt H K, Kida S and Ohkitani K 1994 Stretched vortices - the sinews of turbulence; large-Reynolds-number asymptotics J. Fluid Mech. 259 241-64
10. Saffman P G 1993 Vorticity (Cambridge: Cambridge University Press)
11. Constantin P 1994 Geometric statistics in turbulence SIAM Rev. 36 73-98
12. Kerr R 1993 Evidence for a singularity of the three-dimensional, incompressible euler equations Phys. Fluids A 5 1725-46
13. Sulem P L, Angilella J R and Meneguzzi M 1995 Instability of strained vortex layers and vortex tube formation in homogeneous turbulence. J. Fluid Mech. 282 313-38
14. Chorin A 1982 The evolution of a turbulent vortex. Commun. Math Phys. 83 517-35
15. Prasad R R, Meneveau C and Sreenivasan K R 1988 Multifractal nature of the dissipation field of passive scalars in fully turbulent flows Phys. Rev. Lett. 61 74-7
16. Procaccia I, Constantin P and Sreenivasan K R 1991 Fractal geometry of isoscalar surfaces in turbulence: theory and experiments Phys. Rev. Lett. 67 1739-42
17. Constantin P and Procaccia I 1993 Scaling in fluid turbulence: a geometric theory Phys. Rev. E 47 3307
18. Constantin P, Procaccia I and Segel D 1995 Creation and dynamics of vortex tubes in three-dimensional turbulence Phys. Rev. E 51 3207
19. Ukhovskii M and Yudovitch V I 1995 Axially symmetric flows of ideal and viscous fluids filling the whole space J. Appl. Math. Mech. 32 52-62
20. Ladyzhenskaya O A 1963 The Mathematical Theory of Viscous Incompressible Flow 2nd edn (New York: Gordon and Breach)
21. Mahalov A, Titi E S and Leibovitch S 1990 Invariant helical subspaces for the Navier-Stokes equations Arch. Rational Mech. Anal. 112 193-222
22. Leray J 1934 Essai sur le mouvement d'un liquide visquex emplissant l'espace Acta Math. 63 193-248
23. Constantin P, Foias C and Temam R 1985 Attractors representing turbulent flows Memoirs of AMS 53 314
24. Constantin P, Foias C, Manley O P and Temam R 1985 Determining modes and fractal dimension of turbulent flows J. Fluid Mech. 150 427-40
25. Doering C R and Gibbon J D 1995 Applied Analysis of the Navier-Stokes Equations 1st edn (Cambridge: Cambridge University Press)
26. Doering C R and Titi E S 1995 Exponential decay rate of the power spectrum for solutions of the Navier-Stokes Equations Phys. Fluids 7 1384-90
27. Constantin P, Doering C R and Titi E S 1995 Rigorous estimates on small scales in turbulent flows, submitted
28. Kaplan J and Yorke J 1979 Chaotic Behaviour of Multidimensional Difference Equations: Functional Difference Equations and Approximation of Fixed Points (Lecture Notes in Mathematics 730) (Berlin: Springer)
29. Ruelle D 1989 Characteristic exponents for a viscous fluid subject to time dependent forces Commun. Math. Phys. 93 285-300
30. Lieb E 1984 On characteristic exponents in turbulence Commun. Math. Phys. 92 473-80
31. Henshaw W D, Kreiss H O and Reyna L G 1990 On the smallest scale for the incompressible Navier Stokes equations Arch. Rational Mech. Anal. 112 21-44
32. Foias C, Guillopé C and Temam R 1981 New a priori estimates for Navier-Stokes equations in dimension 3 Commun. Part. Diff. Eqns 6 329-59
33. Gibbon J D 1996 A voyage around the Navier-Stokes equations Physica D 92 133-39
34. Bartuccelli M, Doering C R, Gibbon J D and Malham S J A 1993 Length scales in solutions of the Navier Stokes equations Nonlinearity 6 549-68