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Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence

Published online by Cambridge University Press:  20 April 2006

Robert M. Kerr
Robert M. Kerr
Affiliation:
NASA Ames Research Center, M.S. 202A-1, Moffett Field, CA 94035
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Abstract

In a three-dimensional simulation higher-order derivative correlations, including skewness and flatness (or kurtosis) factors, are calculated for velocity and passive scalar fields and are compared with structures in the flow. Up to 1283 grid points are used with periodic boundary conditions in all three directions to achieve Rλ to 82.9. The equations are forced to maintain steady-state turbulence and collect statistics. The scalar-derivative flatness is found to increase much faster with Reynolds number than the velocity-derivative flatness, and the velocity- and mixed-derivative skewnesses do not increase with Reynolds number. Separate exponents are found for the various fourth-order velocity-derivative correlations, with the vorticity-flatness exponent the largest. This does not support a major assumption of the lognormal and β models, but is consistent with some aspects of structural models of the small scales. Three-dimensional graphics show strong alignment between the vorticity, rate-of-strain, and scalar-gradient fields. The vorticity is concentrated in tubes with the scalar gradient and the largest principal rate of strain aligned perpendicular to the tubes. Velocity spectra, in Kolmogorov variables, collapse to a single curve and a short $-\frac{5}{3}$ spectral regime is observed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 153 , April 1985 , pp. 31 - 58
Copyright
© 1985 Cambridge University Press

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References

Antonia, R. A. & Chambers, A. J. 1980 On the correlation between turbulent velocity and temperature derivatives in the atmospheric surface layer. Boundary-Layer Met. 18, 399–410.Google Scholar
Antonia, R. A., Chambers, A. J., Friehe, C. A. & Van Atta, C. W. 1979 Temperature ramps in the atmospheric surface layer. J. Atmos. Sci. 36, 99–108.Google Scholar
Antonia, R. A., Satyaprakash, B. R. & Hussain, A. K. M. F. 1982 Statistics of fine-scale velocity in turbulent plane and circular jets. J. Fluid Mech. 119, 55–89.Google Scholar
Antonia, R. A. & Van Atta, C. W. 1978 Structure functions of temperature fluctuations in turbulent shear flows. J. Fluid Mech. 84, 561–580.Google Scholar
Aref, H. & Siggia, E. D. 1980 Vortex dynamics of the two-dimensional turbulent shear layer. J. Fluid Mech. 100, 705–738.Google Scholar
Batchelor, G. K. 1952 The effect of homogeneous turbulence on material lines and surfaces. Proc. R. Soc. Lond. A 213, 349–366.Google Scholar
Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113–133.Google Scholar
Batchelor, G. K., Howells, I. D. & Townsend, A. A. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 2. The case of large conductivity. J. Fluid Mech. 5, 134–139.Google Scholar
Betchov, R. 1956 An inequality concerning the production of vorticity in isotropic turbulence. J. Fluid Mech. 1, 497–504.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structures in turbulent mixing layers. J. Fluid Mech. 64, 775–816.Google Scholar
Champagne, F. H., Friehe, C. A., LaRue, J. C. & Wyngaard, J. C. 1977 Flux measurements, flux estimation techniques and fine-scale turbulence measurements in the unstable surface layer over land. J. Atmos. Sci. 34, 515.Google Scholar
Clay, J. P. 1973 Turbulent mixing of temperature in water, air and mercury. Ph.D. thesis. University of California at San Diego.
Corrsin, S. 1951 On the spectrum of isotropic temperature fluctuations in isotropic turbulence. J. Appl. Phys. 22, 469–473.Google Scholar
Corrsin, S. 1962 Turbulent dissipation fluctuations. Phys. Fluids 5, 1301–1302.Google Scholar
Frenkiel, F. M. & Klebanoff, P. S. 1975 On the lognormality of the small-scale structure of turbulence. Boundary-Layer Met. 8, 173.Google Scholar
Frisch, U., Sulem, P. L. & Nelkin, M. 1979 A simple model of intermittent fully-developed turbulence. J. Fluid Mech. 87, 719–736.Google Scholar
Gibson, C. H., Stegen, G. R. & Williams, R. B. 1970 Statistics of the fine structure of turbulent velocity and temperature fields measured at high Reynolds number. J. Fluid Mech. 41, 153–167.Google Scholar
Gibson, C. H. 1968 Fine structure of scalar fields mixed by turbulence. II. Spectral theory. Phys. Fluids 11, 2316–2327.Google Scholar
Herring, J. R. & Kerr, R. M. 1982 Comparison of direct numerical simulations with predictions of two-point closures for isotropic turbulence convecting a passive scalar. J. Fluid Mech. 118, 205–219.Google Scholar
Hill, R. J. 1978 Models of the scalar spectrum for turbulent advection. J. Fluid Mech. 88, 541–562.Google Scholar
Kerr, R. M. 1981 Theoretical investigation of a passive scalar such as temperature in isotropic turbulence. Ph.D. thesis; Cooperative Thesis no. 64. Cornell University and National Center for Atmospheric Research.
Kerr, R. M. 1983 Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence. NASA Technical Memo 84407.
Kolmogorov, A. N. 1941 Local structure of turbulence in an incompressible fluid at very high Reynolds numbers. C.R. Acad. Sci. UUSR 30, 301–305.Google Scholar
Kolmogorov, A. N. 1962 A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13, 82–85.Google Scholar
Kuo, A. Y. & Corrsin, S. 1971 Experiments on internal intermittency and fine-structure distribution functions in fully turbulent fluid. J. Fluid Mech. 50, 285–319.Google Scholar
Larcheveque, M., Chollet, J. P., Herring, J. R., Lesieur, M., Newman, G. R. & Schertzer, D. 1980 Two-point closure applied to a passive scalar in decaying isotropic turbulence. In Turbulent Shear Flows 2 (ed. J. S. Bradbury, F. Durst, B. E. Launder, F. W. Schmidt & J. H. Whitelaw), pp. 50–60. Springer.
Lundgren, T. S. 1982 Strained spiral vortex model for turbulent fine structure. Phys. Fluids 25, 2193–2203.Google Scholar
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, vol. 2. Massachusetts Institute of Technology Press.
Nelkin, M. 1981 Do the dissipation fluctuations in high-Reynolds-number turbulence define a universal exponent?. Phys. Fluids 24, 556.Google Scholar
Nelkin, M. & Bell, T. L. 1978 One-exponent scaling for very high-Reynolds-number turbulence. Phys. Rev. A 17, 363–369.Google Scholar
Orszag, S. A. 1971 Numerical simulation of incompressible flows within simple boundaries: accuracy. J. Fluid Mech. 49, 75–112.Google Scholar
Orszag, S. A. & Patterson, G. S. 1972 Numerical simulation of turbulence. In Statistical Models and Turbulence (ed. M. Rosenblatt & C. Van Atta), Lecture Notes in Physics vol. 12, pp. 127–147. Springer.
Pao, Y-H. 1965 Structure of turbulent velocity and scalar fields at large wavenumbers. Phys. Fluids 8, 1063–1075.Google Scholar
Park, J. T. 1976 Inertial subrange turbulence measurements in the marine boundary layer. Ph.D. thesis. University of California, San Diego.
Patterson, G. S. & Orszag, S. A. 1971 Spectral calculations of isotropic turbulence: efficient removal of aliasing interactions. Phys. Fluids 14, 2538–2541.Google Scholar
Rogallo, R. S. 1981 Numerical experiments in homogeneous turbulence. NASA TM 81315.
Saffman, P. G. 1968 Lectures in homogeneous turbulence. In Topics in Nonlinear Physics (ed. N. Zabusky), pp. 485–614. Springer.
Siggia, E. D. 1981a Numerical study of small scale intermittency in three-dimensional turbulence. J. Fluid Mech. 107, 375–406.Google Scholar
Siggia, E. D. 1981b Invariants for the one-point vorticity and strain rate correlation functions. Phys. Fluids 24, 1934–1936.Google Scholar
Siggia, E. D. & Patterson, G. S. 1978 Intermittency effects in a numerical simulation of stationary three-dimensional turbulence. J. Fluid Mech. 86, 567–592.Google Scholar
Sreenivasan, K. R. & Tavoularis, S. 1980 On the skewness of the temperature derivative in turbulent flows. J. Fluid Mech. 101, 783–795.Google Scholar
Sreenivasan, K. R., Tavoularis, S., Henry, R. & Corrsin, S. 1980 Temperature fluctuations and scales in grid-generated turbulence. J. Fluid Mech. 100, 597–621.Google Scholar
Tavoularis, S., Bennett, S. C. & Corrsin, S. 1978 Velocity-derivative skewness in small Reynolds number, nearly isotropic turbulence. J. Fluid Mech. 88, 63–69.Google Scholar
Tennekes, H. 1968 Simple model for the small-scale structure of turbulence. Phys. Fluids 11, 669–671.Google Scholar
Van Atta, C. W. 1974 Influence of fluctuations in dissipation rates on some statistical properties of turbulent scalar fields. Izv. Atmos. Ocean Phys. 10, 712–719.Google Scholar
Van Atta, C. W. & Antonia, R. A. 1980 Reynolds-number dependence of skewness and flatness factors of turbulent velocity derivatives. Phys. Fluids 23, 252–257.Google Scholar
Vieillefosse, P. 1982 Local interaction between vorticity and shear in a perfect incompressible fluid. J. de Physique 43, 837–842.Google Scholar
Warhaft, Z. & Lumley, J. L. 1978 An experimental study of the decay of temperature fluctuation in grid-generated turbulence. J. Fluid Mech. 88, 659–684.Google Scholar
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237–255.Google Scholar
Wray, A. 1981 Very low storage time-advancement schemes. NASA Ames Research Center, private communication.
Wyngaard, J. C. 1971 The effect of velocity sensitivity on temperature derivative statistics in isotopic turbulence. J. Fluid Mech. 48, 763–769.Google Scholar
Wyngaard, J. C. & Tennekes, H. 1970 Measurements of the small-scale structure of turbulence at moderate Reynolds numbers. Phys. Fluids 13, 1962–1969.Google Scholar