Anistropic spectrum of homogeneous turbulent shear flow in a Lagrangian renormalized approximation

Physics of Fluids

Volumn 15, Issue 8, 2003, Pages 2385-2397

  Yoshida, Kyo ^a   Ishihara, Takashi ^a   Kaneda, Yukio ^a  

^a NAGOYA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; REYNOLDS NUMBER; TURBULENT FLOW;

ANISOTROPIC VELOCITY;

SHEAR FLOW;

LAGRANGIAN ANALYSIS; REYNOLDS NUMBER; SHEAR FLOW; TURBULENT FLOW;

EID: 0041782611     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1588307     Document Type: Article

References (42)

1. A. N. Kolmogorov, "The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, " Dokl. Akad. Nauk SSSR 30, 301 (1941) [Proc. R. Soc. London, Ser. A 434, 9 (1991)].
2. X. Shen and Z. Wahrhaft, "The anisotropy of the small structure in high Reynolds number (r λ∼100) turbulent shear flow," Phys. Fluids 12, 2976 (2000).
3. L. Biferale and F. Toschi, "Anisotropic homogeneous turbulence: Hierarchy and intermittency of scaling exponents in the anisotropic sectors," Phys. Rev. Lett. 86, 4831 (2001).
4. T. Ishihara, K. Yoshida, and Y. Kaneda, "Anisotropic velocity correlation spectrum at small scales in a homogenous turbulent shear flow," Phys. Rev. Lett. 88, 154501 (2002), referred to as IYK.
5. J.L. Lumley, "Similarity and the turbulent energy spectrum," Phys. Fluids 10, 855 (1967).
6. J.C. Wyngaard and O. R. Cote, "Cospectral similarity in the atmospheric surface layer," Q. J. R. Meteorol. Soc. 98, 590 (1972), referred to as WC.
7. S.G. Saddoughi and S. V. Veeravalli, "Local isotropy in turbulent boundary layers at high Reynolds number," J. Fluid Mech. 268, 333 (1994), referred to as SV.
8. Y. Tsuji, "Anisotropy versus universality in shear flow turbulence," in Statistical Theories and Computational Approaches to Turbulence, Modern Perspectives and Applications to Global-Scale Flows, edited by Y. Kaneda and T. Gotoh (Springer, New York, 2002), pp. 138-158.
9. R.H. Kraichnan, "Lagrangian-history closure approximation for turbulence," Phys. Fluids 8, 575 (1965).
10. R.H. Kraichnan and J. R. Herring, "A strain-based Lagrangian-history turbulence theory," J. Fluid Mech. 88, 355 (1978 ).
11. Y. Kaneda, "Renormalized expansions in the theory of turbulence with the use of the Lagrangian position function," J. Fluid Mech. 107, 131 (1981), referred to as K81.
12. K. R. Sreenivasan, "On the universality of the Kolmogorov constant," Phys. Fluids 7, 2778 (1995).
13. I. Arad, B. Dhruva, S. Kurien, V. S. L'vov, I. Procaccia, and K. R. Sreenivasan, "Extraction of anisotropic contributions in turbulent flows," Phys. Rev. Lett. 81, 5330 (1998).
14. S. Kurien and K. R. Sreenivasan, "Anisotropic scaling contributions to high-order structure functions in high-Reynolds-number turbulence," Phys. Rev. E 62, 2206 (2000).
15. L. Biferale, I. Daumont, A. Lanotte, and F. Toschi, "Anomalous and dimensional scaling in anisotropic turbulence," Phys. Rev. E 66, 056306 (2002).
16. Y. Kaneda, T. Ishihara, M. Yokokawa, K. Itakura, and A. Uno, "Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a period box," Phys. Fluids 15, L21 (2003).
17. A. Praskovsky and S. Oncley, "Measurements of the Kolmogorov constant and intermittency exponent at very high Reynolds numbers," Phys. Fluids 6, 2886 (1994).
18. R. H. Kraichnan, "Stochastic modeling of isotropic turbulence," in New Perspectives in Turbulence, edited by L. Sirovich (Springer, Berlin, 1991), pp. 1-54.
19. R. H. Kraichnan, "Anomalous scaling of a randomly advected passive scalar," Phys. Rev. Lett. 72, 1016 (1994).
20. K. Gawedzki and A. Kupiainen, "Anomalous scaling of the passive scalar,:Phys. Rev. Lett. 75, 3834 (1995).
21. A. Fairhall, O. Gat, V. S. L'vov, and I. Procaccia, "Anomalous scaling in a model of passive scalar advection: Exact results," Phys. Rev. E 53, 3518 (1996).
22. M. Vergassola, "Anomalous scaling for passively advected magnetic fields," Phys. Rev. E 53, R3021 (1996).
23. O. Gat, I. Procaccia, and R. Zeitak, "Anomalous scaling in passive scalar advection: Monte Carlo Lagrangian trajectories," Phys. Rev. Lett. 80, 5536 (1998).
24. U. Frisch, A. Mazzino, A. Noullez, and M. Vergassola, "Lagrangian method for multiple correlations in passive scalar advection," Phys. Fluids 11, 2178 (1999).
25. I. Arad, L. Biferale, and I. Procaccia, "Nonperturbative spectrum of anomalous scaling exponents in the anisotropic sectors of passively advected magnetic fields," Phys. Rev. E 61, 2654 (2000).
26. K. Yoshida and Y. Kaneda, "Anomalous scaling of anisotropy of second-order moments in a model of a randomly advected solenoidal vector field," Phys. Rev. E 63, 016308 (2001).
27. H. Chen, J. R. Herring, M. Kerr, and R. H. Kraichnan, "Non-Gaussian statistics in isotropic turbulence," Phys. Fluids A 1, 1844 (1989).
28. V. V. Lebedev and V. S. L'vov, "Scaling of correlations of velocity gradients in hydrodynamic turbulence," Pis'ma Zh. Eksp. Teor. Fiz. 59, 1041 (1994) [JETP Lett. 59, 577 (1994)].
29. V. L'vov and I. Procaccia, "Exact resummations in the theory of hydrodynamic turbulence. I. The ball of locality and normal scaling," Phys. Rev. E 52, 3840 (1995).
30. V. L'vov and I. Procaccia, "Exact resummations in the theory of hydrodynamic turbulence. II. A ladder to anomalous scaling," Phys. Rev. E 52, 3858 (1995).
31. T. Gotoh, J. Nagaki, and Y. Kaneda, "Passive scalar spectrum in the viscous-convective range in two-dimensional steady turbulence," Phys. Fluids 12, 155 (2000).
32. J. R. Herring, "Approach of axisymmetric turbulence to isotropy," Phys. Fluids 17, 859 (1974).
33. D. C. Leslie, Developments in the Theory of Turbulence (Clarendon, Oxford, 1973), Chap, 15.
34. C. Cambon, D. Jeandel, and J. Mathieu, "Spectral modelling of homogeneous non-isotropic turbulence," J. Fluid Mech. 104, 247 (1981).
35. J.-P. Bertoglio, "A model of three-dimensional transfer in non-isotropic homogeneous turbulence," in Turbulence Shear Flows 3, edited by L.J.S. Bradbury, F. Durst, B. E. Launder, F. W. Schmidt, and J. H. Whitelaw (Springer, Heidelberg, 1982), pp. 253-261.
36. R. Rubinstein, "A relaxation approximation for time dependent second order effects in shear turbulence," Theor. Comput. Fluid Dyn. 8, 377 (1996).
37. A. Yoshizawa, Hydrodynamic and Magnetohydrodynamic Turbulent Flows (Kluwer Academic, Dordrecht, 1998). Chap. 6.
38. Y. Kaneda, "Inertial range structure of turbulent velocity and scalar fields in a Lagrangian renormalized approximation," Phys. Fluids 29, 701 (1986).
39. V. S. L'vov, I. Procaccia, and V. Tiberkevich, "Scaling exponents in anisotropic hydrodynamic turbulence," Phys. Rev. E 67, 026312 (2003).
40. R. H. Kraichnan, "The structure of isotropic turbulence at very high Reynolds numbers," J. Fluid Mech. 5, 497 (1959).
41. Y. Kaneda, T. Ishihara, and K. Gotoh, "Taylor expansions in powers of time of Lagrangian and Eulerian two-point two-time velocity correlations in turbulence," Phys. Fluids 11, 2154 (1999).
42. D. P. Laurie, "Periodizing transformations for numerical integration," J. Comput. Appl. Math. 66, 337 (1996).