Skip to main content
×
Home
    • Aa
    • Aa

Isotropy of the small scales of turbulence at low Reynolds number

  • J. Kim (a1) and R. A. Antonia (a2)
Abstract

Spectral local isotropy tests are applied to direct numerical simulation data, mainly at the centreline of a fully developed turbulent channel flow. Despite the small Reynolds number of the simulation, the high-wavenumber behaviour of velocity and vorticity spectra is consistent with local isotropy. This consistency is verified by the relationship between streamwise wavenumber spectra and spanwise wavenumber spectra. The high-wavenumber behaviour of the pressure spectrum is also consistent with local isotropy and compares favourably with the calculation of Batchelor (1951), which assumes isotropy and joint normality of the velocity field at two points in space. The latter assumption is validated by the shape but not the magnitude of the quadruple correlation of the streamwise velocity fluctuation at small separations. There is only partial support for local spectral isotropy away from the centreline as the magnitude of the mean strain rate increases.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

Antonia, R. A., Anselmet, F. & Chambers, A. J. 1986 Assessment of local isotropy using measurements in a turbulent plane jet. J. Fluid Mech. 163, 365391.

Antonia, R. A., Browne, L. W. B. & Shah, D. A. 1988 Characteristics of vorticity fluctuations in a turbulent wake. J. Fluid Mech. 189, 349365.

Antonia, R. A., Kim, J. & Browne, L. W. B. 1991 Some characteristics of small-scale turbulence in a turbulent duct flow. J. Fluid Mech. 233, 369388.

Antonia, R. A., Shah, D. A. & Browne, L. W. B.1987Spectra of velocity derivatives in a turbulent wake. Phys. Fluids30, 34553462.

Antonia, R. A., Shah, D. A. & Browne, L. W. B.1988Dissipation and vorticity spectra in a turbulent wake. Phys. Fluids31, 18051807.

Antonia, R. A., Teitel, M., Kim, J. & Browne, L. W. B. 1992 Low Reynolds number effects in a fully developed turbulent channel flow. J. Fluid Mech. 236, 579605.

Batchelor, G. K.1951Pressure fluctuations in isotropic turbulence. Proc. Camb. Phil. Soc.47, 359374.

Champagne, F. H.1978The fine-scale structure of the turbulent velocity field. J. Fluid Mech.86, 67108.

Champagne, F. H., Harris, V. G. & Corrsin, S. 1970 Experiments on nearly homogeneous turbulent shear flow. J. Fluid Mech. 41, 81139.

Domaradzky, J. A. & Rogallo, R. S.1991Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence. Phys. Fluids A 2, 413426.

Fung, J. C. H., Hunt, J. C. R., Malik, N. A. & Perkins, R. A. 1992 Kinematic simulation of homogeneous turbulence by unsteady random Fourier modes. J. Fluid Mech. 236, 281318.

George, W. K., Beutcher, P. D. & Arndt, R. E. A. 1984 Pressure spectra in turbulent free shear flows. J. Fluid Mech. 148, 155191.

Heisenberg, W.1948Zur Statischen Theorie der Turbulenz. Z. Phys.124, 628657.

Hunt, J. C. R. & Vasilicos, J. C.1991Kolmogorov's contributions to the physical and geometrical understanding of small-scale turbulence and recent developments. Proc. R. Soc. Lond. A 434, 183210.

Jones, B. G., Adrian, R. J., Nithianandan, C. K. & Planchon, H. P.1979Spectra of turbulent static pressure fluctuations in jet mixing layers. AIAA J.17, 449457.

Kim, J. 1989 On the structure of pressure fluctuations in simulated turbulent channel flow. J. Fluid Mech. 205, 421451.

Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.

Mestayer, P. 1982 Local isotropy and anisotropy in a high-Reynolds-number turbulent boundary layer. J. Fluid Mech. 125, 475503.

Mestayer, P. & Chambaud, P.1979Some limitation to measurements of turbulence micro-structure with hot and cold-wires. Boundary-Layer Met.16, 311329.

Phillips, O. M.1991The Kolmogorov spectrum and its oceanic cousins: a review. Proc. R. Soc. Lond. A 434, 125138.

Sanada, T.1992Comment on the dissipation-range spectrum in turbulent flows. Phys. Fluids A 4, 10861087.

Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to Rθ = 1410. J. Fluid Mech. 187, 6198.

Sreenivasan, K. R.1991On local isotropy of passive scalars in turbulent shear flows. Proc. R. Soc. Lond. A 434, 165182.

Uberoi, M. S.1953Quadruple velocity correlations and pressure fluctuations in isotropic turbulence. J. Aero. Sci.20, 197204.

Van Atta, C. W. 1977 Second-order spectral local isotropy in turbulent scalar fields. J. Fluid Mech.80, 609615.

Van Atta, C. W.1991Local isotropy of the smallest scales of turbulent scalar and velocity fields. Proc. R. Soc. Lond. A 434, 139147.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 19 *
Loading metrics...

Abstract views

Total abstract views: 68 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th September 2017. This data will be updated every 24 hours.