Hostname: page-component-669899f699-chc8l Total loading time: 0 Render date: 2025-04-27T00:58:15.912Z Has data issue: false hasContentIssue false
  • English
  • Français

Simple Eulerian time correlation of full-and narrow-band velocity signals in grid-generated, ‘isotropic’ turbulence

Published online by Cambridge University Press:  29 March 2006

Geneviève Comte-Bellot  and
Stanley Corrsin
Geneviève Comte-Bellot
Affiliation:
École Centrale de Lyon
Stanley Corrsin
Affiliation:
The Johns Hopkins University
Get access Rights & Permissions [Opens in a new window]

Abstract

Space-time correlation measurements in the roughly isotropic turbulence behind a regular grid spanning a uniform airstream give the simplest Eulerian time correlation if we choose for the upstream probe signal a time delay which just ‘cancels’ the mean flow displacement. The correlation coefficient of turbulent velocities passed through matched narrow-band niters shows a strong dependence on nominal filter frequency (∼ wave-number at these small turbulence levels). With plausible scaling of the time separations, a scaling dependent on both wave-number and time, it is possible to effect a good collapse of the correlation functions corresponding to wave-numbers from 0·5 cm−1, the location of the peak in the three-dimensional spectrum, to 10 cm−1, about half the Kolmogorov wave-number. The spectrally local time-scaling factor is a ‘parallel’ combination of the times characterizing (i) gross strain distortion by larger eddies, (ii) wrinkling distortion by smaller eddies, (iii) convection by larger eddies and (iv) gross rotation by larger eddies.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 48 , Issue 2 , 28 July 1971 , pp. 273 - 337
Copyright
© 1971 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.)

Article purchase

Temporarily unavailable

References

Anderson, O. K. 1966 On the distortion of measured correlation functions caused by the frequency response of the measuring system DISA Information, 3, 21–27.Google Scholar
Baldwin, L. V. & Mickelsen, W. R. 1962 Turbulent diffusion and anemometer measurements J. Eng. Mech. Div., Proc. Am. Soc. Civil Engrs, 88, 37–69.Google Scholar
Baldwin, L. V. & Walsh, T. J. 1961 Turbulent diffusion in the core of fully developed pipe flow A.I.Ch.E. J. 7, 53–61.Google Scholar
Bass, J. 1954 Space and time correlations in a turbulent fluid. University of California, Publications in Statistics, 2 (3) 55–84.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor, G. K. & Stewart, R. W. 1950 Anisotropy of the spectrum of turbulence at small wave-numbers Quart. J. Mech. Appl. Math. 3, 1–8.Google Scholar
Batchelor, G. K. & Townsend, A. A. 1948 Decay of turbulence in the final period. Proc. Roy. Soc A 194, 527–543.Google Scholar
Batchelor, G. K. & Townsend, A. A. 1956 Turbulent diffusion. Surveys in Mechanics (ed. G. K. Batchelor and R. M. Davies), 352–399. Cambridge University Press.
Burgers, J. 1951 On turbulent fluid motion. Hydrodynamics Lab., CALTECH, Rept. E-34.1.Google 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.Google Scholar
Corrsin, S. 1958 Local isotropy in turbulent flow. NACA Res. Mem. 58 B11.Google Scholar
Corrsin, S. 1959 Outline of some topics in homogeneous turbulent flow J. Geophys. Res. 64, 2134–2150.Google Scholar
Corrsin, S. 1962a Theories of turbulent dispersion. Proc. Intern. Colloq. on Turbulence (Marseille 1961), Centr. Nat. Rech. Sci. 27–52.Google Scholar
Corrsin, S. 1962b Discussion of Baldwin & Mickelsen (1962). J. Eng. Mech. Div., Proc. Am. Soc. Civil Engrs, 88, 151–153.Google Scholar
Corrsin, S. 1963a Estimates of the relations between Eulerian and Lagrangian scales in large Reynolds number turbulence J. Atmos. Sci. 20, 115–119.Google Scholar
Corrsin, S. 1963b Turbulence: experimental methods. Handbuch der Physik 8 (ed. S. Flügge and C. Truesdell), no. 2, 524–590. Springer.
Corrsin, S. 1964 The isotropic turbulent mixer. Part 2. Arbitrary Schmidt numbers A.I.Ch.E. J. 10, 870–877.Google Scholar
Deissler, R. G. 1961 Analysis of multipoint-multitime correlations and diffusion in decaying homogeneous turbulence. NASA, Tech. Rept. R-96.Google Scholar
Dryden, H. L., Schubauer, G. B., Mock, W. C. & Skramstad, H. K. 1937 Measurements of intensity and scale of wind tunnel turbulence and their relation to the critical Reynolds number of spheres. NACA Rept. 581.Google Scholar
Favre, A. 1948 Mesures statistiques de la correlation dans le temps. Proc. 7th Int. Cong. for Appl. Mech., London, 2, 44–55.Google Scholar
Favre, A. 1965 Review on space-time correlations in turbulent fluids. J. Appl. Mech. 32 E, 241–257.Google Scholar
Favre, A., Gaviglio, J. & Dumas, R. 1951 Mesures de la correlation dans le temps et l'’space et spectres de la turbulence en soufflerie. Colloque Intern. de Mecanique, Poitiers 1950 Publ. Sci. et Tech. Ministere Air 251, 293–309.Google Scholar
Favre, A., Gaviglio, J. & Dumas, R. 1952 Appareils de mesures de la correlation dans le temps et l'’space. Quelques mesures de correlation dans le temps et l'’space en soufflerie. Proc. 8th Int. Cong. for Appl. Mech., Istanbul, 304–314, 314–324.Google Scholar
Favre, A., Gaviglio, J. & Dumas, R. 1954 Correlation dans le temps et l'’space, avec filtre de bande, en aval d'’ne grille de turbulence La Recherche Aeronautique, 40, 7–14.Google Scholar
Favre, A., Gaviglio, J. & Fohr, J. P. 1964 Repartition spectrale de correlations spatiotemporelles de vitesse, en couche limite turbulente. Proc. 11th Int. Cong. for Appl. Mech., Munich, 878–888.Google Scholar
Fisher, M. J. & Davies, P. O. A. L. 1964 Correlation measurements in a non-frozen pattern of turbulence J. Fluid Mech. 18, 97–116.Google Scholar
Frenkiel, F. N. & Klebanoff, P. S. 1966 Space-time correlations in turbulence. Dynamics of Fluids and Plasmas (ed. S. I. Pai), 257–274. Academic.
Heisenberg, W. 1948 On the statistical theory of turbulence Z. Phys. 124, 628–657. (Trans. NACA TM 1431.)Google Scholar
Heskestad, G. 1965 A generalized Taylor hypothesis with application for high Reynolds number turbulent shear flows. J. Appl. Mech., Trans. ASME E 32, 735–739.Google Scholar
Howells, I. D. 1960 An approximate equation for the spectrum of a conserved scalar quantity in a turbulent fluid J. Fluid Mech. 9, 104–106.Google Scholar
Inoue, E. 1950 On the turbulent diffusion in the atmosphere 1 J. Met. Soc. Japan, 28, 441–455.Google Scholar
Inoue, E. 1951 On the turbulent diffusion in the atmosphere 2 J. Met. Soc. Japan, 29, 246–252.Google Scholar
KampÉ De Feriet, J. 1939 Les fonctions aleatoires stationnaries et la theorie statistique de la turbulence homogene Ann. Soc. Sci. Bruxelle, 59, 145–194.Google Scholar
KampÉ De Feriet, J. 1953 Fonctions aléatoires et théorie statistique de la turbulence. Théorie des Fonctions Aléatoires (A. Blanc-Lapierre and R. Fortet), ch. 14. Paris: Masson.
KÁrmÁn, T. Von & Howarth, L. 1938 On the statistical theory of isotropic turbulence. Proc. Roy. Soc A 164, 192–215.Google Scholar
Kellogg, R. M. 1965 Evolution of a spectrally local disturbance in a grid-generated turbulent flow. Ph.D. dissertation, Johns Hopkins University.
Kolmogorov, A. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers C. R. Akad. Sci. SSSR 30, 301–305.Google Scholar
Kovasznay, L. S. G. 1948 Spectrum of locally isotropic turbulence J. Aero. Sci. 15, 745–753.Google Scholar
Kraichnan, R. H. 1959 The structure of isotropic turbulence at very high Reynolds numbers J. Fluid Mech. 5, 497–543.Google Scholar
Kraichnan, R. H. 1964a Decay of isotropic turbulence in the direct interaction approximation Phys. Fluids, 7, 1030–1048.Google Scholar
Kraichnan, R. H. 1964b Kolmogorov's hypothesis and Eulerian turbulence theory Phys. Fluids, 7, 1723–1734.Google Scholar
Kraichnan, R. H. 1966 Isotropic turbulence and inertial-range structure Phys. Fluids, 9, 1728–1752.Google Scholar
Kraichnan, R. H. 1967 Invariance principles and approximation in turbulence dynamics. Dynamics of Fluids and Plasmas, 239–255. Academic.
Liepmann, H. W. 1951 Aspects of the turbulence problem ZAMP 3, 321–426.Google Scholar
Lin, C. C. 1953 On Taylor's hypothesis and the acceleration terms in the Navier-Stokes equations Quart. Appl. Math. 10, 295–306.Google Scholar
Loitsianskii, L. G. 1939 Some basic laws of isotropic turbulent flow. Cent. Aero. Hydrodyn. Inst. Moscow, Rept. 440. (Trans. NACA TM 1079.)Google Scholar
Lumley, J. L. & Panofsky, H. A. 1964 The Structure of Atmospheric Turbulence. Interscience.
Lumley, J. L. 1965 Interpretation of time spectra measured in high-intensity shear flows Phys. Fluids, 8, 1056–1062.Google Scholar
Lumley, J. L. 1970 Stochastic Tools in Turbulence. Academic.
Macphail, D. C. 1940 An experimental verification on the isotropy of turbulence produced by a grid J. Aero. Sci. 8, 73–75.Google Scholar
Meecham, W. C. 1958 Relatian between time symmetry and reflection symmetry of turbulent fluids Phys. Fluids, 1, 408–410.Google Scholar
Nayar, B. M., Siddon, T. E. & Chu, W. T. 1969 Properties of the turbulence in the transition region of a round jet. Toronto, Inst. Aerosp. Studies, Tech. Note 131.Google Scholar
O'’rien, E. E. & Francis, G. C. 1962 A consequence of the zero fourth cumulant approximation J. Fluid Mech. 13, 369–382.Google Scholar
Obukhov, A. M. 1941 On the energy distribution in the spectrum of a turbulent flow. Izvest. Akad. Nauk, Ser. Geogr. i. Geofiz. 453–463. (C.R. Acad. Sci. SSSR 32 (1), 19–21, précis.)Google Scholar
Ogura, Y. 1963 A consequence of the zero-fourth cumulant approximation in the decay of isotropic turbulence J. Fluid Mech. 16, 33–40.Google Scholar
Onsager, L. 1945 The distribution of energy in turbulence. (Abstract only.) Phys. Rev. 68, 286.Google Scholar
Onsager, L. 1949 Statistical hydrodynamics. Nuovo Cimento (9) (suppl.), 279–287.Google Scholar
Rice, S. O. 1944 Mathematical analysis of random noise Bell. Syst. Tech. J. 23, 1–51. (Also 1954 Selected Papers on Noise and Stochastic Processes, ed. N. Wax. Dover.)Google Scholar
Rice, S. O. 1945 Mathematical analysis of random noise Bell. Syst. Tech. J. 24, 52–162.Google Scholar
Saffman, P. 1967 Note on decay of homogeneous turbulence Phys. Fluids, 10, 1349.Google Scholar
Simmons, L. F. G. & Salter, C. 1934 Experimental investigation and analysis of the velocity variations in turbulent flow. Proc. Roy. Soc A 145, 212–234.Google Scholar
Simmons, L. F. G. & Salter, C. 1938 An experimental determination of the spectrum of turbulence. Proc. Roy. Soc A 165, 73–89.Google Scholar
Stewart, R. W. & Townsend, A. A. 1951 Similarity and self-preservation in isotropic turbulence. Phil. Trans A 243, 359–386.Google Scholar
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. London Math. Soc. (2) 20, 196–212.Google Scholar
Taylor, G. I. 1935 Statistical theory of turbulence. Proc. Roy. Soc A 151, 421–478.Google Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. Roy. Soc A 164, 476–490.Google Scholar
Townsend, A. A. 1947 The measurement of double and triple correlation derivatives in isotropic turbulence Proc. Camb. Phil. Soc. 43, 560–570.Google Scholar
Townsend, A. A. 1954 The diffusion behind a line source in homogeneous turbulence. Proc. Roy. Soc A 224, 487–512.Google Scholar
Uberoi, M. S. & Corrsin, S. 1953 Diffusion of heat from a line source in isotropic turbulence. NACA Rept. 1142.Google Scholar
WeizsÄcker, C. F. Von 1948 Das spectrum der turbulenz bei grossen Reynoldsschen zahlen Z. Phys. 124, 614–627.Google Scholar
Wiener, N. 1930 Generalized harmonic analysis Acta Math. 55, 117–258.Google Scholar
Wyld, H. W. 1961 Formulation of the theory of turbulence in an incompressible fluid Ann. Phys. 14, 143–165.Google Scholar