Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-19T12:14:53.143Z Has data issue: false hasContentIssue false
  • English
  • Français

Is grid turbulence Saffman turbulence?

Published online by Cambridge University Press:  11 December 2009

P.-Å. KROGSTAD  and
P. A. DAVIDSON
P.-Å. KROGSTAD*
Affiliation:
Norwegian University of Science and Technology, N-7491 Trondheim, Norway
P. A. DAVIDSON
Affiliation:
University of Cambridge, Cambridge CB2 1PZ, UK
*
†Email address for correspondence: per.a.krogstad@ntnu.no
Get access Rights & Permissions [Opens in a new window]

Abstract

There has been a longstanding debate as to whether the large scales in grid turbulence should be classified as of the Batchelor or Saffman type. In the former, the integral scales, u and ℓ, satisfy u2ℓ5 ≈ constant, while in Saffman turbulence we have u2ℓ3 = constant. For strictly homogeneous turbulence the energy decay rates in these two types of turbulence differ, with u2 ~ t−10/7 in Batchelor turbulence and u2 ~ t−6/5 in Saffman turbulence. We present high-resolution measurements of grid turbulence taken in a large wind tunnel. The particularly large test section allows us to measure energy decay exponents with high accuracy. We find that the turbulence behind the grid is almost certainly of the Saffman type, with u2ℓ3 = constant. The measured energy decay exponent, however, is found to lie slightly below the theoretical prediction of u2 ~ t−1.2. Rather we find u2 ~ t−n, with n = 1.13±0.02. This discrepancy is shown to arise from a weak temporal decay of the dimensionless energy dissipation coefficient, εℓ/u3, which is normally taken to be constant in strictly homogeneous turbulence, but which varies very slowly in grid turbulence.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 642 , 10 January 2010 , pp. 373 - 394
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Batchelor, G. K. & Proudman, I. 1956 The large-scale structure of homogeneous turbulence. Phil. Trans. R. Soc. A 248, 369–405.Google Scholar
Bennett, J. C. & Corrsin, S. 1978 Small Reynolds number nearly isotropic turbulence in a straight duct and a contraction. Phys. Fluids 21, 2129–2140.CrossRefGoogle Scholar
Comte-Bellot, G. & Corrsin, S. 1966 The use of a contraction to improve the isotropy of grid-generated turbulence. J. Fluid Mech. 25, 657–682.CrossRefGoogle Scholar
Davidson, P. A. 2004 Turbulence, An Introduction for Scientists and Engineers. Oxford University Press.Google Scholar
Davidson, P. A. 2009 On the role of angular momentum conservation in homogenous turbulence. J. Fluid Mech. 632, 329–358.CrossRefGoogle Scholar
Ishida, T., Davidson, P. A. & Kaneda, Y. 2006 On the decay of isotropic turbulence. J. Fluid Mech. 564, 455–475.CrossRefGoogle Scholar
Kistler, A. L. & Vrebalovich, T. 1966 Grid turbulence at large Reynolds numbers. J. Fluid Mech. 26, 37–47.CrossRefGoogle Scholar
Lavoie, P., Djenedi, L. & Antonia, R. A. 2007 Effects of initial conditions in decaying turbulence generated by passive grids. J. Fluid Mech. 585, 395–420.CrossRefGoogle Scholar
Maxey, M. R. 1987 The velocity skewness measured in grid turbulence. Phys. Fluids 30, 935–938.CrossRefGoogle Scholar
Mohamed, M. S. & LaRue, J. C. 1990 The decay power law in grid-generated turbulence. J. Fluid Mech. 219, 195–214.CrossRefGoogle Scholar
Pearson, B. R., Krogstad, P.-Å. & van de Water, W. 2002 Measurements of the turbulent energy dissipation rate. Phys. Fluids 14, 1288–1290.CrossRefGoogle Scholar
Pullin, D. I. & Saffman, P. J. 1998 Vortex dynamics in turbulence. Annu. Rev. Fluid Mech. 30, 31–51.CrossRefGoogle Scholar
Saffman, P. J. 1967 The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27, 581–593.CrossRefGoogle Scholar
Townsend, A. A. 1947 The measurement of double and triple correlation derivatives in isotropic turbulence. Proc. Cam. Phil. Soc. 43, 560–572.CrossRefGoogle Scholar
Warhaft, Z. & Lumley, J. L. 1978 An experimental study of the decay of temperature fluctuations in grid generated turbulence. J. Fluid Mech. 88, 659–684.CrossRefGoogle Scholar