On a Leray-α model of turbulence

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 461, Issue 2055, 2005, Pages 629-649

  Cheskidov, Alexey ^a,b   Holm, Darryl D ^c,d   Olson, Eric ^e   Titi, Edriss S ^f,g  

^a INDIANA UNIVERSITY   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

^c LOS ALAMOS NATIONAL LABORATORY   (United States)

^d IMPERIAL COLLEGE LONDON   (United Kingdom)

^e UNIVERSITY OF NEVADA   (United States)

^f University of California at Irvine   (United States)

^g WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

Leray model; Subgrid scale models; Turbulence models

Indexed keywords

ANALYTIC METHOD; ARTICLE; CHEMICAL STRUCTURE; COMPUTATIONAL FLUID DYNAMICS; FLOW RATE; PARTICLE SIZE; PHYSICOCHEMICAL MODEL; SCALE UP; SIMULATION; STRUCTURE ANALYSIS; TURBULENT FLOW; VISCOELASTICITY;

EID: 17144376124     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2004.1373     Document Type: Article

References (40)

1. Babin, A. V. & Vishik, M. I. 1992 Attractors of evolution equations. Studies in Mathematics and its Applications, vol. 25. Amsterdam: North-Holland.
2. Cao, C., Holm, D. D. & Titi, E. S. 2005 On the Clark-α model of turbulence: global regularity and long-time dynamics. (Preprint).
3. Chen, S., Foias, C., Holm, D. D., Olson, E., Titi, E. S. & Wynne, S. 1998 The Camassa-Holm equations as a closure model for turbulent channel and pipe flow. Phys. Rev. Lett. 81, 5338-5341.
4. Chen, S., Foias, C., Holm, D. D., Olson, E., Titi, E. S. & Wynne, S. 1999a A connection between the Camassa-Holm equations and turbulent flows in pipes and channels. Phys. Fluids 11, 2343-2353.
5. Chen, S., Foias, C., Holm, D. D., Olson, E., Titi, E. S. & Wynne, S. 1999b The Camassa-Holm equations and turbulence. Physica D 133, 49-65.
6. Chen, S., Holm, D. D., Margolin, L. G. & Zhang, R. 1999c Direct numerical simulations of the Navier-Stokes alpha model. Physica D 133, 66-83.
7. Chepyzhov, V. V. & Ilyin, A. A. 2004 On the fractal dimension of invariant sets: applications to Navier-Stokes equations. Discrete Contin. Dynam. Syst. 10, 117-135.
8. Cheskidov, A. 2002 Turbulent boundary layer equations. C. R. Acad. Sci. Paris Sér. I 334, 423-427.
9. Cheskidov, A. 2004 Boundary layer for the Navier-Stokes-alpha model of fluid turbulence. Arch. Ration. Mech. Analysis 172, 333-362.
10. Clark, R. A., Ferziger, J. H. & Reynolds, W. C. 1979 Evaluation of subgrid scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91, 1-16.
11. Constantin, P. 2001 An Eulerian-Lagrangian approach to the Navier-Stokes equations. Commun. Math. Phys. 216, 663-686.
12. Constantin, P. & 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.
13. Constantin, P. & Foias, C. 1988 Navier-Stokes equations. Chicago Lectures in Mathematics. University of Chicago Press.
14. Constantin, P., Foias, C., Manley, O. P. & Temam, R. 1985 Determining modes and fractal dimension of turbulent flows. J. Fluid Mech. 150, 427-440.
15. Constantin, P., Nie, Q. & Tanveer, S. 1999 Bounds for second order structure functions and energy spectrum in turbulence. Phys. Fluids 11, 2251-2256.
16. Foias, C. 1997 What do the Navier-Stokes equations tell us about turbulence? In Harmonic analysis and nonlinear differential equations. Contemporary Mathematics Series, vol. 208, pp. 151-180. Providence, RI: American Mathematical Society.
17. Foias, C., Holm, D. D. & Titi, E. S. 2001a The Navier-Stokes-alpha model of fluid turbulence. Physica D 152, 505-519.
18. Foias, C., Manley, O., Rosa, R. & Temam, R. 2001b Navier-Stokes equations and turbulence. Cambridge University Press.
19. Foias, C., Holm, D. D. & Titi, E. S. 2002 The three-dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory. J. Dynam. Diff. Equat. 14, 1-35.
20. Geurts, B. J. & Holm, D. D. 2002a Alpha-modeling strategy for LES of turbulent mixing. In Turbulent flow computation (ed. D. Drikakis & B. J. Geurts), pp. 237-278. Kluwer.
21. Geurts, B. J. & Holm, D. D. 2002b Leray simulation of turbulent shear layers. In Advances in Turbulence IX: Proc. 9th European Turbulence Conf. (ed. J. P. Castro & P. E. Hancock), pp. 337-340. Barcelona: CIMNE.
22. Geurts, B. J. & Holm, D. D. 2003 Regularization modeling for large-eddy simulation. Phys. Fluids 15, L13-L16.
23. Holm, D. D. 1999 Fluctuation effects on 3D Lagrangian mean and Eulerian mean fluid motion. Physica D 133, 215-269.
24. Holm, D. D. 2002a Variational principles for Lagrangian-averaged fluid dynamics. J. Phys. A 35, 679-688.
25. Holm, D. D. 2002b Kármán-Howarth theorem for the Lagrangian averaged Navier-Stokes alpha (LANS-α) model. J. Fluid Mech. 467, 205-214.
26. Holm, D. D. & Nadiga, B. T. 2003 Modeling mesoscale turbulence in the barotropic double-gyre circulation. J. Phys. Oceanogr. 33, 2355-2365.
27. Holm, D. D., Marsden, J. E. & Ratiu, T. S. 1998 Euler-Poincaré models of ideal fluids with nonlinear dispersion. Phys. Rev. Lett. 80, 4173-4176.
28. Holm, D. D., Putkaradze, V., Weidman, P. D. & Beth, B. A. 2003 Boundary effects on exact solutions of the Lagrangian-averaged Navier- Stokes-α equations. J. Stat. Phys. 113, 841-854.
29. Ilyin, A. A. & Titi, E. S. 2003 Attractors to the two-dimensional Navier-Stokes-α model: an α-dependence study. J. Dynam. Diff. Equat. 15, 751-778.
30. Kida, S. 1985 Three-dimensional periodic flows with high-symmetry. J. Phys. Soc. Jpn 54, 2132-2136.
31. Kraichnan, R. H. 1972 Some modern developments in the statistical theory of turbulence. In Statistical mechanics: new concepts, new problems, new applications (ed. S. A. Rice, K. F. Freed & J. C. Light), pp. 201-227.
32. Leonard, A. 1974 Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18, 237-248.
33. Leray, J. 1934 Essai sur le mouvement d'un fluide visqueux emplissant l'espace. Acta Math. 63, 193-248.
34. Marsden, J. E. & Shkoller, S. 2001 Global well-posedness for the Lagrangian averaged Navier-Stokes (LANS-α) equations on bounded domains. Phil. Trans. R. Soc. Lond. A 359, 1449-1468.
35. Marsden, J. E. & Shkoller, S. 2003 The anisotropic Lagrangian averaged Euler and Navier-Stokes equations. Arch. Ration. Mech. Analysis 166, 27-46.
36. Mohseni, K., Kosović, B., Shkoller, S. & Marsden, J. E. 2003 Numerical simulations of the Lagrangian averaged Navier-Stokes equations for homogeneous isotropic turbulence. Phys. Fluids 15, 524-544.
37. Nie, Q. & Tanveer, S. 1999 A note on third-order structure functions in turbulence. Proc. R. Soc. Lond. A 455, 1615-1635.
38. Putkaradze, V. & Weidman, P. 2003 Turbulent wake solutions of the Prandtl α equations. Phys. Rev. E 67, 036304.
39. Temam, R. 1984 Navier-Stokes equations: theory and numerical analysis. Studies in Mathematics and its Applications, vol. 2. Amsterdam: North-Holland.
40. Temam, R. 1988 In finite-dimensional dynamical systems in mechanics and physics. Applied Mathematical Sciences, vol. 68. Springer.