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Anisotropic pressure correlation spectra in turbulent shear flow

  • Yoshiyuki Tsuji (a1) and Yukio Kaneda (a2)
Abstract

We measured the correlation spectrum of pressure fluctuations in a driving mixing layer with a Taylor-scale Reynolds number up to by a newly developed pressure probe with spatial and temporal resolutions that are sufficient to analyse inertial-subrange statistics. The influence of the mean velocity gradient tensor in the mixing layer, which is almost constant near its centreline, is studied using an idea similar to that underlying the linear response theory developed in statistical mechanics for systems at or near thermal equilibrium. If we write the spectrum as , where is the isotropic Kolmogorov spectrum in the absence of mean shear, then for small the deviation due to the shear is approximately linear and is determined by a few non-dimensional universal constants in addition to , and the mean energy dissipation rate. We also measured the pressure–velocity and velocity–velocity correlation spectra. Deviations from isotropy due to shear are shown to be approximately proportional to at large .

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Corresponding author
Email address for correspondence: c42406a@nucc.cc.nagoya-u.ac.jp
References
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1. Arad, I., Dhruva, B., Kurien, S., L’vov, V. S., Procaccia, I. & Sreenivasan, K. R. 1998 Extraction of anisotropic contribution in turbulent flows. Phys. Rev. Lett. 81, 53305333.
2. Arad, I., L’vov, V. S. & Procaccia, I. 1999 Correlation functions in isotropic and anisotropic turbulence: the role of the symmetry group. Phys. Rev. E 59, 67536765.
3. Batchelor, G. K. 1951 Pressure fluctuations in isotropic turbulence. Proc. Camb. Phil. Soc. 47, 359374.
4. Bell, J. H. & Mehta, R. D. 1990 Development of a two-stream mixing layer from tripped and untripped boundary layers. AIAA J. 28, 20342042.
5. Biferale, L. & Procaccia, I. 2005 Anisotropy in turbulent flows and in turbulent transport. Phys. Rep. 414, 43164.
6. Borue, V. & Orszag, S. A. 1996 Numerical study of three-dimensional Kolmogorov flow at high Reynolds numbers. J. Fluid Mech. 306, 293323.
7. Browne, L. W. B., Antonia, R. A. & Chua, L. P. 1989 Calibration of x-probes for turbulent flow measurements. Exp. Fluids 7, 201208.
8. Cao, N., Chen, S. & Doolen, G. D. 1999 Statistics and structures of pressure in isotropic turbulence. Phys. Fluids 11, 22352250.
9. Casciola, C. M., Gualtieri, P., Jacob, B. & Piva, R. 2005 Scaling properties in the production range of shear dominated flows. Phys. Rev. Lett. 95, 024503.
10. Casciola, C. M., Gualtieri, P., Jacob, B. & Piva, R. 2007 The residual anisotropy at small scales in high shear turbulence. Phys. Fluids 19, Art. 101704.
11. Champagne, F. H., Pao, Y. H. & Wygnanski, I. J. 1976 On the two-dimensional mixing region. J. Fluid Mech. 74, 209250.
12. Corrsin, S. 1958 Local isotropy in turbulent shear flow. NACA R & M 58B11.
13. Frish, U. 1995 Turbulence. Cambridge University Press.
14. George, W. & Hussein, H. J. 1991 Locally axisymmetric turbulence. J. Fluid Mech. 233, 123.
15. George, W. K., Beuther, P. D. & Arndt, R. E. A. 1984 Pressure spectra in turbulent free shear flows. J. Fluid Mech. 148, 155191.
16. Gotoh, T. & Fukayama, D. 2001 Pressure spectrum in homogeneous turbulence. Phys. Rev. Lett. 86, 37753778.
17. Gotoh, T. & Rogallo, R. S. 1999 Intermittency and scaling of pressure at small-scales in forced isotropic turbulence. J. Fluid Mech. 396, 257285.
18. Heisenberg, W. 1948 Zür statistischen theorie der turbulenz. Z. Phys. 124, 628657.
19. Hill, R. J. 2002 Scaling of acceleration in locally isotropic turbulence. J. Fluid Mech. 452, 361370.
20. Hinze, J. O. 1975 Turbulence. McGraw-Hill.
21. Inoue, E. 1951 The application of the turbulence theory to the large-scale atmospheric phenomena. Geophys. Mag. 23, 114.
22. Ishida, T. & Kaneda, Y. 2007 Small-scale anisotropy in magnetohydrodynamic turbulence under a strong uniform magnetic field. Phys. Fluids 19, 075104, 10 pages.
23. Ishihara, T., Kaneda, Y., Yokokawa, M., Itakura, K. & Uno, A. 2003 Spectra of energy dissipation, enstropy and pressure by high-resolution direct numerical simulations of turbulence in a periodic box. J. Phys. Soc. Japan 72, 983986.
24. Ishihara, T., Kaneda, Y., Yokokawa, M., Itakura, K. & Uno, A. 2007 Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics. J. Fluid Mech. 592, 335366.
25. Ishihara, T., Yoshida, K. & Kaneda, Y. 2002 Anisotropic velocity correlation spectrum at small-scales in a homogeneous turbulent shear flow. Phys. Rev. Lett. 88, 154501–1–4.
26. Jacob, B., Casciola, C. M., Talamelli, A. & Alfredsson, P. H. 2008 Scaling of mixed structure functions in turbulent boundary layers. Phys. Fluids 20, art. 045101.
27. Jones, B. G., Adrian, R. J., Nithiandan, C. K. & Planchon, H. P. 1979 Spectra of turbulent static pressure fluctuation in jet mixing layers. AIAA J. 17, 449457.
28. Kaneda, Y. & Ishihara, T. 2009 Universality in statistics at small scales of turbulence -a study by high resolution DNS. In Notes Numerical Fluid Mechanics and Multidisciplinary Design (ed. Deville, M., Le, T.-H. & Sagaut, P. ). 105. pp. 5576. Springer.
29. Kaneda, Y. & Morishita, K. 2011 Small-scale statistics and structure of Turbulence – in the light of high resolution direct numerical simulation –. In The Nature of Turbulence (ed. Davidson, P., Kaneda, Y. & Sreenivasan, K.R. ). Cambridge Unversity Press, (submitted).
30. Kaneda, Y. & Yoshida, K. 2004 Small-scale anisotropy in stably stratified turbulence. New J. Phys. 6, 34.
31. Kim, J. & Antonia, R. A. 1993 Isotropy of the small-scales of turbulence at low Reynolds number. J. Fluid Mech. 251, 219238.
32. Klebanoff, P. S. 1954 Characteristics of turbulence in a boundary later with zero pressure gradient. NACA Technical Note 3178.
33. Kobashi, Y. 1957 Measurements of pressure fluctuation in the wake of cylinder. J. Phys. Soc. Japan 12, 533543.
34. Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 299303.
35. Kraichnan, R. H. 1956a Pressure field within homogeneous anisotropic turbulence. J. Acoust. Soc. Am. 28, 6472.
36. Kraichnan, R. H. 1956b Pressure fluctuation in turbulent flow over a flat plate. J. Acoust. Soc. Am. 28, 378390.
37. Kubo, R. 1966 The fluctuation-dissipation theorem. Rep. Prog. Phys. 29, 255284.
38. Kurien, S., L’vov, V. S., Procaccia, I. & Sreenivasan, K. R. 2000 Scaling structure of the velocity statistics in atmospheric boundary layers. Phys. Rev. E 61, 407421.
39. La Porta, A., Voth, G. A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2001 Fluid particle accelerations in fully developed turbulence. Nature 409, 10171019.
40. Lumley, J. L. 1965 Interpretation of time spectra measured in high-intensisty shear flows. Phys. Fluids 8, 10561062.
41. Lumley, J. L. 1967 Similarity and the turbulence energy spectrum. Phys. Fluids 10, 855858.
42. Monin, M. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics, Vol. 2. The MIT Press.
43. Nakano, H. 1993 Linear response theory: a historical perspective. Intl J. Mod. Phys. 7, 23972467.
44. Nelkin, M. 1994 Universality and scaling in fully developed turbulence. Adv. Phys. 43, 143181.
45. Obukhoff, A. M. & Yaglom, A. M. 1951 The microstructure of turbulent flow. NACA Tech. Mem. 1350.
46. Ott, S. & Mann, J. 2000 An experimental investigation of the relative diffusion of particle pairs in three-dimensional turbulent flow. J. Fluid Mech. 422, 207223.
47. Perry, A. E. & Li, J. D. 1990 Experimental support for the attached-eddy hypothesis in zero-pressure-gradient turbulent boundary layers. J. Fluid Mech. 218, 405438.
48. Rogers, M. M. & Moser, R. D. 1994 Direct simulation of a self-similar turbulent mixing layer. Phys. Fluids 6, 903923.
49. Saddoughi, S. G. & Veeravalli, S. V. 1994 Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333372.
50. Shen, X. & Warhaft, Z. 2000 The anisotropy of the small-scale structure in high Reynolds number turbulent shear flow. Phys. Fluids 12, 29762989.
51. Smyth, W. D. & Moum, J. N. 2000 Anisotropy of turbulence in stably stratified mixing layers. Phys. Fluids 12, 13431362.
52. Sreenivasan, K. R. & Antonia, R. A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435472.
53. Sreenivasan, K. R. & Dhruva, B. 1998 Is there scaling in high-Reynolds-number turbulence? Progr. Theor. Phys. Suppl. 130, 103120.
54. Sreenivasan, K. R. & Stolovitzky, G. 1996 Statistical dependence of inertila range properties on large scales in a high-Reynolds-number shear flow. Phys. Rev. Lett. 77, 22182221.
55. Staicu, A., Vorselaars, B. & van de Water, W. 2003 Turbulence anisotropy and the SO(3) description. Phys. Rev. E 68, 046303–1–12.
56. Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.
57. Toyoda, K., Okamoto, T. & Shirahama, Y. 1993 Eduction of vortical structures by pressure measurements in noncircular jet. Fluid Mech. Appl. 21, 125136.
58. Tsuji, Y. 2002 Anisotropy versus universality in shear flow turbulence. In Statistical Theories and Computational Approaches to Turbulence (ed. Kaneda, Y. & Gotoh, T. ). pp. 138158. Springer.
59. Tsuji, Y. 2003 Large-scale anisotropy effect on small-scale statistics over rough wall turbulent boundary layers. Phys. Fluids 12, 38163828.
60. Tsuji, Y. 2007 Lagrangian acceleration measurement in fully developed turbulence. In Turbulent Shear Flow Phenomena 5, TU Munchen, Garching, Germany, 27–29 August, 2007, pp. 537–541.
61. Tsuji, Y., Fransson, J. H. M., Alfredsson, P. H. & Johansson, A. V. 2007 Pressure statistics and their scaling in high-Reynolds-number turbulent boundary layers. J. Fluid Mech. 585, 140.
62. Tsuji, Y. & Ishihara, T. 2003 Similarity scaling of pressure fluctuation in turbulence. Phys. Rev. E 68, 026309.
63. Vedula, P. & Yeung, P. K. 1999 Similarity scaling of acceleration and pressure statistics in numerical simulation of isotropic turbulence. Phys. Fluids 11, 12081220.
64. Warhaft, Z. 2000 Passive scalars in turbulent flow. Annu. Rev. Fluid Mech. 32, 203240.
65. Wygnanski, I. & Fiedler, H. E. 1970 Two-dimensional mixing region. J. Fluid Mech. 41, 327361.
66. Wyngaard, J. C. & Cote, O. R. 1972 Cospectral similarity in the atomospheric surface layer. J. R. Met Soc. 98, 590603.
67. Yoshida, K., Ishihara, T. & Kaneda, Y. 2003 Anisotropic spectrum of homogeneous turbulent shear flow in a Lagrangian renormalized approximation. Phys. Fluids 15, 23852397.
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