A generalized Heisenberg model for turbulent spectral dynamics

Theoretical and Computational Fluid Dynamics

Volumn 17, Issue 4, 2004, Pages 249-272

  Rubinstein, Robert ^a   Clark, Timothy T ^b  

^a NASA LANGLEY RESEARCH CENTER   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

Heisenberg model; Isotropic turbulence; Turbulence closures

Indexed keywords

EID: 4344580197     PISSN: 09354964     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00162-004-0104-x     Document Type: Article

References (52)

1. Bailly, C., Juvé, D.: A stochastic approach to compute subsonic noise using linearized Euler's equations. AIAA. paper 99-1872 (1999)
2. Batchelor, G. K.: Statistical theory of turbulence, p. 132, Cambridge University Press, Cambridge (1953)
3. Bertoglio, J. P., Shao, L., Parpais. S.: A simplified spectral model for inhomogeneous and nonequilibrium turbulence. AIAA Paper 94-2385 (1994)
4. Besnard, D. C., Harlow, F. H., Rauenzahn, R. M., Zemach, C.: Spectral transport model for turbulence. Theor. Comput. Fluid Dyn. 8, 1-35 (1996)
5. Bowman, J. C., Krommes, J. A.: The realizable Markovian closure and realizable test-field model. II. Application to anisotropic drift-wave dynamics. Phys. Plasmas 4, 3895-3909 (1997)
6. Cadiou, A.: One-point multi-scale turbulence closures derived from a spectral description, APTF R/99-11, Dept of Applied Physics, TU Delft, Netherlands (1999)
7. Cambon, C., Mansour, N. N., Godeferd, F. S.: Energy transfer in rotating turbulence. J. Fluid Mech. 337, 303-332 (1996)
8. Canuto, V. M., Dubovikov, M. S.: A dynamical model for turbulence: I. General formalism. Phys. Fluids 8, 571-613 (1996)
9. Canuto, V. M., Dubovikov, M. S.: A dynamical model for turbulence: II. Shear-driven flows. Phys. Fluids 8, 587-598 (1997)
10. Canuto, V. M., Dubovikov, M. S., Dienstfrey, A.: A dynamical model for turbulence: IV. Buoyancy-driven flows. Phys. Fluids 9, 2118-2131 (1997)
11. Canuto, V. M., Dubovikov, M. S.: A dynamical model for turbulence: V. The effect of rotation. Phys. Fluids 9, 2132-2140 (1997)
12. Canuto, V. M., Dubovikov, M. S., Yu, G.: A dynamical model for turbulence: IX. Reynolds stresses for shear-driven flows. Phys. Fluids 11, 678-691 (1999)
13. Canuto, V. M., Goldman, I.: Analytical model for large-scale turbulence. Phys. Rev. Lett. 54, 430-433 (1985)
14. Clark, T. T.: Two-point closures and statistical equilibrium-implications for engineering turbulence models. In Modeling complex turbulent flows, M. Salas, J. N. Hefner, L. Sakell, eds., pp. 183-202, Kluwer, Dordrecht (1999)
15. Clark, T. T., Zemach, C.: A spectral model applied to homogeneous turbulence. Phys. Fluids 7, 1674-1694 (1995)
16. Clark, T. T., Zemach, C.: Symmetries and the approach to statistical equilibrium in isotropic turbulence. Phys. Fluids 10, 2846-2858 (1998)
17. Connaughton, C., Nazarenko, S.: preprint arXiv:physics/0304044
18. Domaradzki, A.: Nonlocal triad interactions and the dissipation range of isotropic turbulence. Phys. Fluids A 4, 2037-2045 (1992)
19. Falkovich, G.: Bottleneck phenomenon in developed turbulence. Phys. Fluids 6, 1411-1414 (1994)
20. Gotoh, T.: private communication (2003)
21. Godeferd, F. S., Cambon, C.: Detailed investigation of energy transfers in homogeneous stratified turbulence. Phys. Fluids 6, 2084-2100 (1994)
22. Grégoire, O., Souffland, D., Gauthier, S., Schiestel, R.: A two-time scale turbulence model for compressible flow: turbulence dominated by mean deformation interaction. Phys. Fluids 11, 3793-3807 (1999)
23. Hanjalić, K., Launder, B. E., Schiestel, R.: Multiple time-scale concepts in turbulent transport modeling. In Second International Symposium on Turbulent Shear flows, Selected Papers, pp. 36-49, Springer, Berlin Heidelberg New York (1980)
24. Herring, J. R.: Some contributions of two-point closure to turbulence. In Frontiers in Fluid Mechanics, S. H. Davis, J. L. Lumley, eds., pp. 68-87, Springer, Berlin Heidelberg New York (1985)
25. Hinze, J. O.: Turbulence, McGraw-Hill, pp. 230-241, New York (1975)
26. Kaneda, Y.: Renormalized expansions in the theory of turbulence with the use of the Lagrangian position function. J. Fluid. Mech. 107, 131-145 (1981)
27. Kaneda, Y.: private communication 2001
28. Kaneda, Y., Ishihara, T., Yokokawa, M., Itakura, K., Uno, A.: Energy dissipation rate and energy spectrum in high resolution direct numerical simulation of turbulence in a periodic box. Phys. Fluids 15, L21-L24 (2003)
29. Kraichnan, R. H.: The structure of turbulence at very high Reynolds number. J. Fluid Mech. 5, 497-543 (1959)
30. Kraichnan, R. H.: Direct interaction approximation for shear and thermally-driven turbulence. Phys. Fluids 7, 1049-1062 (1964)
31. Kraichnan, R. H.: Lagrangian-history closure approximation for turbulence. Phys. Fluids 8, 575-598 (1965)
32. Kraichnan, R. H.: An almost-Markovian Galilean-invariant turbulence model. J. Fluid Mech. 47, 513-524 (1971)
33. Kraichnan, R. H.: Eddy viscosity in two and three dimensions. J. Atmos. Sci. 33, 1521-1536 (1976)
34. Kraichnan, R. H.: An interpretation of the Yakhot-Orszag turbulence theory. Phys. Fluids 30, 2400-2405 (1987)
35. Kraichnan, R. H.: Kolmogorov's constant and local interactions. Phys. Fluids 30, 1583-1585 (1987)
36. Kraichnan, R. H., Spiegel, E. A.: A model for energy transfer in isotropic turbulence. Phys. Fluids 5, 583-588 (1962)
37. Lesieur, M.: Turbulence in fluids, Kluwer, Dordrecht (1990)
38. Lesieur, M., Rogallo, R.: Large-eddy simulation of passive scalar diffusion in isotropic turbulence. Phys. Fluids A 1, 718-722 (1989)
39. Leslie, D. C.: Developments in the theory of turbulence, Oxford University Press, Oxford (1972)
40. Monin, A. S., Yaglom, A. M.: Statistical hydrodynamics, MIT, pp. 212-235, Cambridge (1975)
41. Orszag, S. A.: Lectures on the statistical theory of turbulence. In Fluid Dynamics, R. Balian, J.-L. Preube, eds., Gordon and Breach, London (1973)
42. Ossia, S., Lesieur, M.: Energy backscatter in large-eddy simulations of three-dimensional incompressible isotropic turbulence. J. Turbul. 1, 1-11 (2000)
43. Ritz, Ch. P., Powers, E. J., Miksad, R. W., Solis, R. S.: Nonlinear spectral dynamics of a transitioning flow. Phys. Fluids 31, 3577-3588 (1988)
44. Rubinstein, R., Rumsey, C. L., Salas, M. D., Thomas, J. L.: Turbulence modeling workshop, ICASE Interim Report 37, NASA/CR-2001-21-841 (2001)
45. Rubinstein, R., Zhou, Y.: The frequency spectrum of sound radiated by isotropic turbulence. Phys. Lett. A 267, 379-383 (2000)
46. Schiestel, R.: Multiple time scales modeling of turbulent flows in one point closures. Phys. Fluids 30, 722-731 (1987)
47. Schilling, O.: private communication (2002)
48. Ulitsky, M., Collins, L. R.: On constructing realizable, conservative mixed scalar equations using the eddy-damped quasi-normal Markovian theory. J. Fluid Mech. 412, 303-329 (2000)
49. Yakhot, V., Orszag, S. A.: Renormalization group analysis of turbulence I. Basic theory. J. Sci. Comput. 1, 3-51 (1986)
50. Zhou, Y.: Interacting scales and energy transfer in isotropic turbulence. Phys. Fluids A 5, 2511-2524 (1993)
51. Zhou, Y., Rubinstein, R., Eliason, D., Cabot, W.: Computing turbulent flows driven by Rayleigh-Taylor and Richtmyer-Meshkov instabilities. Astron. Astrophys. 405, 379-386 (2003)
52. Zhou, Y., Vahala, G.: Local interactions in renormalization methods for Navier-Stokes turbulence. Phys. Rev. A 46, 1136-1139 (1992)