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Application of central-limit theorems to turbulence and higher-order spectra

Published online by Cambridge University Press:  29 March 2006

J. L. Lumley  and
K. Takeuchi
J. L. Lumley
Affiliation:
Department of Aerospace Engineering, The Pennsylvania State University
K. Takeuchi
Affiliation:
Department of Civil Engineering, Stanford University
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Abstract

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Type
Research Article
Information
Journal of Fluid Mechanics , Volume 74 , Issue 3 , 6 April 1976 , pp. 433 - 468
Copyright
© 1976 Cambridge University Press

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References

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Brillinger, D. R. & Rosenblatt, M. 1967a Asymptotic theory of estimates of Kth order spectra. Advanced Seminar on Spectral Analysis of Time Series (ed. B. Harris). Wiley.
Brillinger, D. R. & Rosenblatt, M. 1967b Computation and interpretation of Kth order spectra. Advanced Seminar on Spectral Analysis of Time Series (ed. B. Harris). Wiley.
Frenkiel, F. N. & Klebanoff, P. S. 1967 Higher-order correlations in a turbulent field Phys. Fluids, 10, 507.Google Scholar
Hasselman, K., Munk, W. & Macdonald, G. 1963 Bispectrum of ocean waves. Time Series Analysis (ed. M. Rosenblatt). Wiley.
Kraichnan, R. H. 1959 The structure of isotropic turbulence at very high Reynolds numbers J. Fluid Mech. 5, 497.Google Scholar
Lumley, J. L. 1970 Stochastic Tools in Turbulence. Academic.
Lumley, J. L. 1971 Application of central-limit theorems to turbulence problems. Statistical Models and Turbulence, Lecture Notes in Physics, vol. 12 (eds M. Rosenblatt & C. Van Atta). Springer.
Lumley, J. L. & Wyngaard, J. C. 1967 A constant-temperature hot-wire anemometer J. Sci. Instr. 44, 363.Google Scholar
Nilsen, A. W. 1969 Analysis of the unsteady pressure in a turbulent jet. M.S. thesis, The Pennsylvania State University.
Novikov, E. A. 1965 Higher-order correlations in turbulent flow Izv. Atmos. Ocean Phys. 1, 788.Google Scholar
Novikov, E. A. 1966 Mathematical model for the intermittence of turbulent flow Soviet Phys. Doklady, 11, 497.Google Scholar
Novikov, E. A. & Stewart, R. W. 1964 The intermittency of turbulence and the spectrum of energy dissipation fluctuations Izv. Atmos. Ocean Phys. 3, 408.Google Scholar
Rosenblatt, M. 1956 A central limit theorem and a strong mixing condition Proc. Nat. Acad. Sci., U.S.A. 42, 43–47.Google Scholar
Rosenblatt, M. 1961 Some comments on narrow-band pass filters Quart. Appl. Math. 18, 387.Google Scholar
Rosenblatt, M. 1966 Remarks on higher-order spectra. Symp. on Multivariate Analysis. Academic.
Rosenblatt, M. & VAN NESS, X. 1965 Estimation of the bispectrum Ann. Math. Stat. 36, 1120.Google Scholar
Takeuchi, K. & Lumley, J. L. 1976 On the kurtosis of wind velocity derivatives in atmospheric boundary layers. (To be submitted for publication.)
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Von Frank, E. D. 1970 Turbulence characteristics in the mixing region of a perturbed and unperturbed round free jet. M.S. thesis, The Pennsylvania State University.
Wyngaard, J. C. & Lumley, J. L. 1967 A sharp cutoff spectral differentiator J. Appl. Meteor. 6, 592.Google Scholar
Yeh, T. T. & VAN ATTA, C. W. 1973 Spectral transfer of scalar and velocity fields in heated-grid turbulence J. Fluid Mech. 58, 233.Google Scholar