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Bispectral measurements in turbulence

Published online by Cambridge University Press:  11 April 2006

K. S. Lii ,
M. Rosenblatt  and
C. Van Atta
K. S. Lii
Affiliation:
University of California, La Jolla
M. Rosenblatt
Affiliation:
University of California, La Jolla
C. Van Atta
Affiliation:
University of California, La Jolla
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Abstract

A bispectral analysis of high Reynolds number turbulent velocity-derivative data is carried out. The computations suggest that contributions of wavenumber triplets to the rate of vorticity production and spectral transfer are non-local in wavenumber space and comparable over the whole range of wavenumbers studied. Statistical resolvability of the bispectral estimates is obtained. An appendix on the asymptotic behaviour of bispectral estimates is given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 77 , Issue 1 , 9 September 1976 , pp. 45 - 62
Copyright
© 1976 Cambridge University Press

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References

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor, G. K. & Townsend, A. A. 1956 Turbulent diffusion. In Surveys in Mechanics, pp. 352–399. Cambridge University Press.
Betceov, R. 1956 An inequality concerning the production of vorticity in isotropic turbulence. J. Fluid Mech. 1, 497–504.Google Scholar
Brillinoer, D. R. & Rosenblatt, M. 1967 Computation and interpretation of κth order spectra. In Spectral Analysis of Time Series (ed. B. Harris), pp. 189–232. Wiley.
Cartwright, D. E. 1968 A unified analysis of tides and surges round North and East Britain. Phil. Trans. A 263, 1–55.Google Scholar
Hasselman, K., Munk, W. & Macdonald, G. 1963 Bispectra of ocean waves. In Time Series Analysis (ed. M. Rosenblett), pp. 125–139. Wiley.
Haugen, D. A., Karrar, J. C. & Bradley, E. F. 1971 An experimental study of Reynolds stress and heat flux in the atmospheric boundary layer. Quart. J. Roy. Met. Soc. 97, 1968.Google Scholar
Huber, P. J., Kleiner, B., Gasser, TH. & Dumermuth, G. 1971 Statistical methods for investigating phase relations in stationary stochastic processes. I.E.E.E. Trans. Audio Electroacowt.Google Scholar
Kármán, T. Von 1937 The fundamentals of the statistical theory of turbulence. J. Aero. Sci. 4, 131–138.Google Scholar
Kraichnan, R. H. 1959 The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mffih. 5, 497–542.Google Scholar
Kraichnan, R. H. 1971 Inertial-range transfer in two-and three-dimensional turbulence. J. Fluid Mech. 47, 525–535.Google Scholar
Lumley, J. L. & Takeuojii, K. 1976 Application of central-limit theorems to turbulence and higher-order spectra. J. Fluid Mech. 74, 433–468.Google Scholar
Roden, G. I. & Bendiner, D. J. 1973 Bispectra and cross-spectra of temperature, salinity, sound velocity and density functions with depth off Northeastern Japan. J. Phys. Ocean. 3, 308–317.Google Scholar
Rosenblatt, M. 1971 Curve estimates. Ann. Math. Stat. 42, 1815–1842.Google Scholar
Rosenblatt, M. 1974 Random Processes. Springer.
Taylor, G. I. 1938 Production and dissipation of vorticity in a turbulent fluid. Proc. Roy. Soc. A 144, 15–23.Google Scholar
Van Atta, C. W. & Yeh, T. T. 1973 The structure of internal intermittency in turbulent flows at large Reynolds number: experimental scale similarity. J. Fluid Mech. 59, 537–559.Google Scholar
Van Atta, C. W. & Ych, T. T. 1975 Evidence for scale similarity of internal intermittency in turbulent flows at large Reynolds numbers. J. Fluid Meoh. 71, 417–440.Google Scholar
Wyngaard, J. C. & Lumley, J. L. 1967 A sharp cutoff spectral differentiator. J. Appl. Met. 6, 952.Google Scholar
Wyngaard, J. C. & Pao, Y. H. 1972 Some measurements of the fine structure of large Reynolds number turbulence. In Statistical Models and Turbulence, Lecture Notes in Physics, vol. 12 (ed. M. Rosenblatt & C. Van Atta), pp. 384–401. Springer.
Yeh, T. T. & Van Atta, C. W. 1973 Spectral transfer of scalar and velocity fields in heated-grid turbulence. J. Fluid Mech. 58, 233–261.Google Scholar