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Spectral transfer of scalar and velocity fields in heated-grid turbulence

Published online by Cambridge University Press:  29 March 2006

T. T. Yeh  and
C. W. Atta
T. T. Yeh
Affiliation:
Institute for Pure and Applied Physical Sciences and Department of Applied Mechanics and Engineering Science, University of California, San Diego
C. W. Atta
Affiliation:
Institute for Pure and Applied Physical Sciences and Department of Applied Mechanics and Engineering Science, University of California, San Diego
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Abstract

For locally isotropic, homogeneous fluid turbulence, a digital Fourier analysis method of measuring directly the net scalar and velocity spectral transfer Tn(k) of scalar and kinetic energy to a pa;rticular wavenumber from all other wave-numbers is described and applied to heated-grid turbulence. The technique uses the imaginary part of a particular cross-spectrum to obtain the one-dimensional net spectral transfer function Ln(k1) of velocity and scalar turbulence, and is a refinement of that used previously by Van Atta & Chen for measuring the velocity kinetic energy transfer.

The detailed spectral transfer Tn(k, k′) from one wavenumber to any other is related to the imaginary part of a particular three-dimensional bispectrum. Tn(k, k′) can be, in principle, computed from a particular two-dimensional triple correlation. Unlike Tn(k), which can be obtained from Ln(k1), Tn(k, k′) cannot be determined from the measurable one-dimensional bippectrum B1, n, n (k1, k1′) nor the one-dimensional transfer spectrum Ln(k1, k1′).

The measured net transfer spectra Tn(k) have been used to determine the extent of validity for heated-grid turbulence of the dynamical equations for the three-dimensional power spectra of temperature and velocity in locally isotropic turbulence. The measured temperature transfer spectrum is also compared with those obtained from the power spectra of velocity and temperature by using various simple hypotheses.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 58 , Issue 2 , 17 April 1973 , pp. 233 - 261
Copyright
© 1973 Cambridge University Press

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References

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor, G. K. 1959 J. Fluid Mech. 5, 113.
Batcrleor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Brillinger, R. R. 1965 Ann. Math. Statist. 36, 1351.
Comte-Bellot, G. & Corrsin, S. 1971 J. Fluid Mech. 48, 273.Google Scholar
Cooley, J. W. & Tukey, J. W. 1965 Math. Comp. 19, 297.
Corrsin, S. 1947 Rev. Sci. Inst. 18, 469.
Corrsin, S. 1949 N.A.C.A. Tech. Note, no. 1864.
Corrsin, S. 1951 J. Appl. Phys. 22, 469.
Corrsin, S. 1961 J. Fluid. Mech. 11, 401.Google Scholar
Corrsin, S. 1964 Phys. Fluids, 7, 1156.
Corrsin, S. & Uberoi, M. S. 1951 N.A.C.A. Rep. no. 1040.
Ellison, T. H. 1962 Me'caniipue de la Turbulence p. 113. Paris: C.N.R.S.
Frenkiel, F. N. & Klebanoff, P. S. 1967 Phys. Fluids, 10, 507.
Gibson, C. H. & Schwarz, W. H. 1963 J. Fluid Mech. 16, 357.Google Scholar
Haubrich, R. A. 1965 J. Geophys. Res. 70, 1415.
Heisenberg, W. 1948 Proc. Roy. SOC. A 195, 402.
Hinze, J. O. 1959 Turbulence. MoGraw-Hill.
Kidron, I. 1966 DISA Inf. 4, 25.
Kistler, A. L., O'Brien, V. & Corrsin, S. 1956 J. Aero. Sci. 96.
Kovasznay, L. S. G. 1948 J. Aero. SOC. 15, 745.
Kraichnan, R. 1964 Phys. Fluids, 7, 1030.
Lin, C. C. 1953 Quart. Appl. Math. 10, 295.
Lumley, J. L. 1965 Phys. Fluids, 8, 1056.
Mills, R. R., Kistler, A. L., O'Brien, V. & Corrsin, S. 1958 N.A.C.A. Tech. Note. no. 4288.
Monin, A. S. & Yaglom, A. M. 1967 Statistical Hydrodynamics. Part 2, Mechanics of Turbulence (in Russian). Mosoow : Science Publishers.
Obukov, A.M. 1941 C. r. Acad. Sci. U.S.S.R. 32, 19.
Obukov, A. M. 1949 Izv. A W. Nuuk. 13, 58.
Onsager, L. 1945 Phys. Rev. 68, 286.
Onsager, L. 1949 Nuovo Cimento, Suppl. 6, 279.
Pao, Y. H. 1965 Phys. Fluids, 8, 1063.
Robertson, H. P. 1940 Proc. Comb. Phil. SOC. 36, 209.
Rosenblatt, M. & Van Ness, J. W. 1965 Ann. Math. Statist. 36, 1120.
Stewart, R. W. 1951 Proc. Camb. Phil. SOC. 47, 146.
Stewart, R. W. & Townsend, A. A. 1951 Phil. Trans. A 243, 359.
Townsend, A. A. 1947 Proc. Camb. Phil. Soc. 44, 560.
Uberoi, M. S. 1963 Phys. Fluids, 6, 1048.
Uberoi, M. S. & Corrsin, S. 1953 N.A.C.A. Rep. no. 1142.
Van Atta, C. W. & Chen, W. Y. 1968 J. Fluid Mech. 34, 497.
Van Atta, C. W. & Chen, W. Y. 1969 J. Fluid Mech. 38, 743.
Van Atta, C. W. & Yeh, T. T. 1970 J. Fluid Mech. 41, 169.
Von K'rmán, T. 1948 Proc. Natn. Acad. Sci. 34, 530.
Yeh, T. T. 1971 Ph.D. thesis, University of California, San Diego.