Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-16T10:32:53.612Z Has data issue: false hasContentIssue false
  • English
  • Français

On the fine structure of turbulent flows

Published online by Cambridge University Press:  28 March 2006

R. Betchov
R. Betchov
Affiliation:
Department of Aeronautics, The Johns Hopkins University
Get access Rights & Permissions [Opens in a new window]

Abstract

The turbulence produced by a multiplicity of small air jets has been investigated and comparisons are made with other turbulent flows. The eddy Reynolds number is large (Rλ = 250).

The energy spectrum was measured, as well as the skewness and kurtosis of ∂u/∂x. The effect of the finite length of the hot wire is considered and the corrected results indicate that the spectrum follows the law of Kolmogoroff in an intermediate range and appers to fall off with the (−6)-power of the frequency in the viscous range. This range is limited at the upper end of the frequency range by electrical noise. Special precautions reduced this noise to the level of thermal agitation in the hot wire.

The ultimate limit to spectral analysis is imposed by the molecular agitation of the gas. This limit is evaluated and compared with the spectrum of turbulence. It appears that the spectrum of ∂3u/∂x3 merges with the spectrum of molecular agitation without a distinctive separation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 3 , Issue 2 , November 1957 , pp. 205 - 216
Copyright
© 1957 Cambridge University Press

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

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor, G. K. & Townsend, A. A. 1949 The nature of turbulent motion at large wave-numbers, Proc. Roy. Soc. A, 199, 238.Google Scholar
Betchov, R. 1948 L'influence de la conduction thermique sur les anemometres à fil chaud, Proc. Kon. Akad. Wet. 51, 721.Google Scholar
Betchov, R. 1956 An inequality concerning the production of vorticity in isotropic turbulence, J. Fluid Mech. 1, 497.Google Scholar
Crane, H. L. & Chilton, R. G. 1956 Measurements of atmospheric turbulence over a wide range of wave-length for one meteorological condition, Nat. Adv. Comm. Aero., Wash., Tech. Note no. 3702.Google Scholar
Corrsin, S. 1944 Investigation of the behavior of parallel two-dimensional air jets, Nat. Adv. Comm. Aero., Wash., Rep. ACR 4H24.Google Scholar
Corrsin, S. & Uberoi, M. S. 1951 Spectra and diffusion in a round turbulent jet, Nat. Adv. Comm. Aero., Wash., Rep. no. 1040.Google Scholar
Gödecke, K. 1935 Messungen der atmosphärischen Turbulenz in Bodennähe, Ann. Hydr., Berl., 63, 400.Google Scholar
Klebanoff, P. S. & Diehl, Z. W. 1951 Some features of artificially fully developed turbulent boundary layers with zero pressure gradients, Nat. Adv. Comm. Aero., Wash., Tech. note no. 2475.Google Scholar
Kovásznay, L. S. G. & Uberoi, M. S. 1953 On mapping and measurements of random fields, Quart. Appl. Math. 10, 375.Google Scholar
Laufer, J. 1950 Investigation of turbulent flow in a two-dimensional channel, Nat. Adv. Comm. Aero., Wash., Tech. note no. 2123.Google Scholar
Laufer, J. 1953 The structure of turbulence in fully developed pipe flow, Nat. Adv. Comm. Aero., Wash., Tech. Note no. 2954.Google Scholar
Liepmann, H. W., Laufer, J. & Liepmann, K. 1951 On the spectrum of isotropic turbulence, Nat. Adv. Comm. Aero., Wash., Tech. Note no. 2473.Google Scholar
Stewart, R. W. & Townsend, A. A. 1951 Similarity and self-preservation in isotropic turbulence, Phil. Trans. A, 243, 359.Google Scholar
Townsend, A. A. 1951 On the fine-scale structure of turbulence, Proc. Roy. Soc. A, 208, 534.Google Scholar