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Numerical study of small-scale intermittency in three-dimensional turbulence

Published online by Cambridge University Press:  20 April 2006

Eric D. Siggia
Eric D. Siggia
Affiliation:
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, and National Center for Atmospheric Research, P.O. Box 3000, Boulder, Colorado 80307
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Abstract

Intermittency effects, in magnitude comparable to the early Batchelor & Townsend (1949) experiments, are studied for stationary, homogeneous, isotropic turbulence by means of a direct spectral simulation on a 643 lattice. The turbulence is kept stationary by a coupling to modes external to the spectral code that model the straining effects of large scales on smaller ones. The rate of energy input and viscosity are free parameters. The interrelations of intermittency and parametrizations of the large scales are discussed. Small-scale universality and a local cascade are necessary if comprehensive models of the large scales are to prove tractable. An iterative method to determine the otherwise arbitrary parameters in such a scheme is proposed but not implemented.

The equations for energy and vorticity balance are checked as a function of wave-number. The nonlinear (e.g. vortex stretching) terms in the spectral simulation account for nearly 95% of the vorticity production with the external forcing supplying the rest. The non-dimensionalized one-dimensional energy spectrum agrees well with experiments in the dissipation range at Rλ ∼ 100. The locality of the energy cascade in wavenumber is also examined.

First- and second-derivative flatness factors of order 4·5-5·0 and 9·0 respectively are found under stationary conditions with bursts to higher values. Resolution and other systematic errors are explored by extensive runs with a 323 code; de-aliasing all higher-order derivative statistics; and recomputing selected averages after zeroing in succession the highest- and lowest-wavenumber bands. The latter analysis is of some relevance to the experimental problem of gauging how a finite-length hot wire biases a flatness measurement. A host of other higher-order derivative statistics are computed, including the vorticity/rate of strain correlations. Three-dimensional plots of the vorticity reveal persistent and extended tubes, sheets and blobs.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 107 , June 1981 , pp. 375 - 406
Copyright
© 1981 Cambridge University Press

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References

Batchelor, G. K. & Townsend, A. A. 1949 Proc. Roy. Soc. A 199, 238.
Betchov, R. 1956 J. Fluid Mech. 1, 497.
Champagne, F. 1978 J. Fluid Mech. 86, 67.
Clark, R. A., Ferziger, J. H. & Reynolds, W. S. 1979 J. Fluid Mech. 91, 1.
Frisch, U., Sulem, P. L. & Nelkin, M. 1978 J. Fluid Mech. 87, 719.
Kolmogorov, A. N. 1941 C. r. Acad. Sci. U.S.S.R. 30, 301, 538.
Kraichnan, R. H. 1974 J. Fluid Mech. 62, 305.
Kraichnan, R. H. 1976 J. Atmos. Sci. 33, 1521.
Kuo, A. Y.-S. & Corrsin, S. 1971 J. Fluid Mech. 50, 285.
Kuo, A. Y.-S. & Corrsin, S. 1972 J. Fluid Mech. 56, 447.
Mandelbrot, B. 1976 In Proceedings Journées Mathématiques sur la Turbulence (ed. R. Teman). Springer.
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Dynamics, vol. 2. Massachusetts Institute of Technology Press.
Orszag, S. A. & Patterson, G. S. 1972 In Statistical Models and Turbulence (ed. M. Rosenblatt & C. Van Atta), p. 127. Springer.
Patterson, G. S. & Orszag, S. A. 1971 Phys. Fluids 14, 2538.
Saffman, P. G. 1968 In Topics in Nonlinear Physics (ed. N. Zabusky), p. 485. Springer.
Siggia, E. D. 1977 Phys. Rev. A 15, 1730.
Siggia, E. D. 1978 Phys. Rev. A 17, 1166.
Siggia, E. D. 1981 Phys. Fluids. (Submitted.)
Siggia, E. D. & Patterson, G. S. 1978 J. Fluid Mech. 86, 567.
Van Atta, C. W. & Antonia, R. A. 1980 Phys. Fluids 23, 252.
Wilson, K. G. & Kogut, J. 1974 Phys. Rev. C 12, 76.
Wyngard, J. C. 1968 J. Sci. Inst. 1, 1105.
Wyngaard, J. C. 1969 J. Sci. Inst. 2, 983.
Wyngaard, J. C. 1971 J. Phys. Fluids 14, 2052.