Multi-scale gradient expansion of the turbulent stress tensor

Journal of Fluid Mechanics

Volumn 549, Issue , 2006, Pages 159-190

  Eyink, Gregory L ^a  

^a Johns Hopkins University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CASCADES (FLUID MECHANICS); GRADIENT METHODS; SHEAR STRESS; STRAIN; TENSILE STRESS; TENSORS; VORTEX FLOW;

LARGE-SCALE VELOCITY; MULTI-SCALE GRADIENT EXPANSION; TURBULENT STRESS TENSOR;

TURBULENCE;

APPROXIMATION THEORY; CASCADES (FLUID MECHANICS); GRADIENT METHODS; SHEAR STRESS; STRAIN; TENSILE STRESS; TENSORS; TURBULENCE; VORTEX FLOW;

TURBULENCE;

EID: 33645798894     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112005007895     Document Type: Article

References (48)

1. Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. National Bureau of Standards.
2. André, J. C. & Lesieur, M. 1977 Influence of helicity on the evolution of isotropic turbulence at high Reynolds number. J. Fluid Mech. 81, 187-207.
3. Ashurst, W. T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence. Phys. Fluids 30, 2343-2353.
4. Betchov, R. 1956 An inequality concerning the production of vorticity in isotropic turbulence. J. Fluid Mech. 1, 497-504.
5. Borue, V. & Orszag, S. A. 1998 Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 1-31.
6. Brissaud, A., Frisch, U., Leorat, J., Lesieur, M. & Mazure, A. 1973 Helicity cascades in fully developed isotropic turbulence. Phys. Fluids 16, 1366-1367.
7. Burton, G. C., Dahm, W. J. A., Powell, K. G. & Dowling, D. R. 2002 A new multifractal subgrid scale model for large eddy simulation. AIAA Paper 2002-0983, 40th AIAA Aerospace Sciences Meeting, January, 2002, Reno, NV.
8. Cantwell, B. 1992 Exact solution of a restricted Euler equation for the velocity gradient tensor. Phys. Fluids A 4, 782-793.
9. Carati, D., Winckelmans, G. S. & Jeanmart, H. 2001 On the modelling of the subgrid-scale and filtered-scale stress tensors in large-eddy simulation. J. Fluid Mech. 441, 119-138.
10. Chapman, S. & Cowling, T. 1939 Mathematical Theory of Non-Uniform Gases. Cambridge University Press.
11. Chen, Q., Chen, S. & Eyink, G. 2003a The joint cascade of energy and helicity in three-dimensional turbulence. Phys. Fluids 15, 361-374.
12. Chen, S., Ecke, R. E., Eyink, G. L., Wang, X. & Xiao, Z. 2003b Physical mechanism of the two-dimensional enstrophy cascade. Phys. Rev. Lett. 91, 214501.
13. Chertkov, M., Pumir, A. & Shraiman, B. I. 1999 Lagrangian tetrad dynamics and the phenomenology of turbulence. Phys. Fluids 11, 2394-2410.
14. Constantin, P., E, W & Titi, E. S. 1994 Onsager's conjecture on the energy conservation for solutions of Euler's equation. Commun. Math. Phys. 165, 207-209.
15. Crow, S. C. 1968 Viscoelastic properties of fine-grained incompressible turbulence. J. Fluid Mech. 33, 1-20.
16. Domaradzki, J. A. & Adams, N. A. 2002 Direct modelling of subgrid scales of turbulence in large eddy simulations. J. Turb. 3, 024.
17. Domaradzki, J. A. & Saiki, E. M. 1997 A subgrid-scale model based on the estimation of unresolved scales of turbulence. Phys. Fluids 9, 2148-2164.
18. Enskog, D. 1917 Kinetische theorie der Vorange in massig verdunnten Gasen. I Allgemeiner Teil. Almqvist & Wiksell.
19. Eyink, G. L. 1995 Local energy flux and the refined similarity hypothesis. J. Stat. Phys. 78, 335-351.
20. Eyink, G. 1996 Turbulence noise. J. Stat. Phys. 83, 955-1019.
21. Eyink, G. L. 2001 Dissipation in turbulent solutions of 2D Euler equations. Nonlinearity 14, 787-802.
22. Eyink, G. L. 2005 Locality of turbulent cascades. Physica D 207, 91-116.
23. Eyink, G. L. 2006 A turbulent constitutive law for the two-dimensional inverse energy cascade. J. Fluid Mech. 549, 191-214.
24. Germano, M. 1992 Turbulence: The filtering approach. J. Fluid Mech. 238, 325-336.
25. Gorkov, L. P. 1959 Microscopic derivation of the Ginzburg-Landau equations in the theory of superconductivity. Sov. Phys. J. Expl. Theor. Phys. 9, 1364 (Zh. Eksp. Teor. Fiz. 36, 1918).
26. Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417-1423.
27. Kraichnan, R. H. 1970 Convergents to turbulence functions. J. Fluid Mech. 41, 189-217.
28. Kraichnan, R. H. 1971 Inertial-range transfer in two- and three-dimensional turbulence. J. Fluid Mech. 47, 525-535.
29. Kraichnan, R. H. 1973 Helical turbulence and absolute equilibrium. J. Fluid Mech. 59, 745-752.
30. Kraichnan, R. H. 1974 On Kolmogorov's inertial-range theories. J. Fluid Mech. 62, 305-330.
31. Leonard, A. 1974 Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18, 237-248.
32. Leonard, A. 1997 Large-eddy simulation of chaotic convection and beyond. AIAA Paper 97-0204, 35th Aerospaces Sciences Meeting and Exhibit, 6-10 Jan, Reno, Nevada.
33. Lindenberg, K., West, B. J. & Kottalam, J. 1987 Fluctuations and dissipation in problems of geophysical fluid dynamics. In Irreversible Phenomena and Dynamical Systems Analysis in Geosciences, NATO ASI Ser. C (ed. C. Nicolis & G. Nicolis). Reidel.
34. Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 1-32.
35. Misra, A. & Pullin, D. I. 1997 A vortex-based subgrid scale stress model for large-eddy simulation. Phys. Fluids 9, 2443-2454.
36. Moffatt, H. K. 1969 The degree of knottedness of tangled vortex lines. J. Fluid Mech. 35, 117-129.
37. Moreau, J. J. 1961 Constantes d'un îlot tourbillonnaire en fluide parfait barotrope. C. R. Acad. Sci. Paris 252, 2810-2812.
38. Neu, J. C. 1984 The dynamics of a columnar vortex in an imposed strain. Phys. Fluids 27, 2397-2402.
39. Piomelli, U., Cabot, W. H., Moin, P. & Lee, S. 1991 Sub-grid scale backscatter in turbulent and transitional flows. Phys. Fluids A 3, 1766-1771.
40. Scotti, A. & Meneveau, C. 1999 A fractal model for large eddy simulation of turbulent flows. Physica D 127, 198-232.
41. Tao, B., Katz, J. & Meneveau, C. 2002 Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements. J. Fluid Mech. 467, 35-78.
42. Taylor, G. I. 1938 Production and dissipation of vorticity in a turbulent fluid. Proc. R. Soc. Lond. A 164, 15-23.
43. Tewordt, L. 1965 Generalized Ginzburg-Landau theory of superconducting alloys. Phys. Rev. 137, A1745-A1749.
44. Van der Bos, F., Tao, B., Meneveau, C. & Katz, J. 2002 Effects of small-scale turbulent motions on the filtered velocity gradient tensor as deduced from holographic PIV measurements. Phys. Fluids 14, 2456-2474.
45. Vieillefosse, P. 1982 Local interaction between vorticity and shear in a perfect incompressible fluid. J. Phys. Paris 43, 837-842.
46. Vieillefosse, P. 1984 Internal motion of a small element of fluid in an inviscid flow. Physica A 125, 150-162.
47. Vreman, B., Geurts, B., & Kuerten, H. 1994 Realizability conditions for the turbulent stress tensor in large eddy simulation. J. Fluid Mech. 278, 351-362.
48. Yeo, W. & Bedford, K. 1988 Closure-free turbulence modeling based upon a conjunctive higher-order averaging procedure. In Computational Methods in Flow Analysis (ed. H. Niki & M. Kawahara), pp. 844-851. Okayama University of Science.