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Velocity, scalar and transfer spectra in numerical turbulence

Published online by Cambridge University Press:  26 April 2006

Robert M. Kerr
Robert M. Kerr
Affiliation:
Geophysical Turbulence Program, National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307-3000, USA
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Abstract

Velocity and passive-scalar spectra for turbulent fields generated by a forced three-dimensional simulation with 1283 grid points and Taylor-microscale Reynolds numbers up to 83 are shown to have convective and diffusive spectral regimes. One-and three-dimensional spectra are compared with experiment and theory. If normalized by the Kolmogorov dissipation scales and scalar dissipation, velocity spectra and scalar spectra for given Prandtl numbers collapse to single curves in the dissipation regime with exponential tails. If multiplied by k⅗ the velocity spectra show an anomalously high Kolmogorov constant that is consistent with low Reynolds number experiments. When normalized by the Batchelor scales, the scalar spectra show a universal dissipation regime that is independent of Prandtl numbers from 0.1 to 1.0. The time development of velocity spectra is illustrated by energy-transfer spectra in which distinct pulses propagate to high wavenumbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 211 , February 1990 , pp. 309 - 332
Copyright
© 1990 Cambridge University Press

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References

Ashurst, W. T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence. Phys. Fluids 30, 2343–2353.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. 1971 The Theory of Homogeneous Turbulence (2nd edn.). Cambridge University Press.
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
Brachet, M. E., Meiron, D. I., Orszag, S. A., Nickel, B. G., Morf, R. H. & Frisch, U. 1983 Small-scale structure of the Taylor-Green vortex. J. Fluid Mech. 130, 411–452.Google Scholar
Champagne, F. H. 1978 The fine-scale structure of the turbulent velocity field. J. Fluid Mech. 86, 67–108.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
Chapman, D. R. 1979 Computational aerodynamics development and outlook. AIAAJ. 17, 1293–1313.Google Scholar
Chasnov, J., Canuto, V. M. & Rogallo, R. S. 1988 Turbulence spectrum of a passive temperature field: Results of a numerical simulation. Phys. Fluids 31, 2065–2067.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
Frisch, U. & Morf, R. 1981 Intermittency and nonlinear dynamics at complex times.. Phys. Rev. A 23, 2673.Google Scholar
Frisch, U., Sulem, P. L. & Nelkin, M. 1978 A simple model of intermittent fully developed turbulence. J. Fluid Mech. 87, 719–736.Google Scholar
Gibson, C. H. 1968a Fine structure of scalar fields mixed by turbulence. I. Zero-gradient points and minimal-gradient surfaces. Phys. Fluids 11, 2316–2327.Google Scholar
Gibson, C. H. 1968b Fine structure of scalar fields mixed by turbulence. II. Spectral theory. Phys. Fluids 11, 2316–2327.Google Scholar
Gibson, C. H., Ashurst, W. T. & Kerstein, A. R. 1988 Mixing of strongly diffusive passive scalars like temperature by turbulence. J. Fluid Mech. 194, 261–293.Google Scholar
Gibson, C. H. & Kerr, R. M. 1987 Evidence of turbulent mixing by the rate-of-strain. Preprint.
Herring, J. R. & Kraichnan, R. H. 1979 A numerical comparison of velocity-based and strain-based Lagrangian-history turbulence approximations. J. Fluid Mech. 89, 581–597.Google Scholar
Herring, J. R., Schertzer, D., Lesieur, M., Newman, G. R., Chollet, J. P. & Larcheveque, M. 1982 A comparative assessment of spectral closures as applied to passive scalar diffusion. J. Fluid Mech. 124, 411–437.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. 1985a Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence. J. Fluid Mech. 153, 31–58. (See also NASA TM 84407, 1983 .)Google Scholar
Kerr, R. M. 1985b Kolmogorov and scalar-spectral regimes in numerical turbulence. NASA Tech. Memo 86699.Google Scholar
Kerr, R. M. 1987 Histograms of helicity and strain in numerical turbulence. Phys. Rev. Lett. 59, 783.Google Scholar
Kerr, R. M. & Hussain, F. 1989 Simulation of vortex reconnection.. Physica D 37, 474–484.Google Scholar
Kerr, R. M. & Siggia, E. D. 1978 Cascade mode of fully developed turbulence. J. Statist. Phys. 19, 543–552.Google Scholar
Kida, S. & Murakami, Y. 1987 Kolmogorov similarity in freely decaying turbulence. Phys. Fluids 30, 2030–2039.Google Scholar
Kolmogorov, A. N. 1941 Local structure of turbulence in an incompressible fluid at very high Reynolds numbers. C. R. Acad. Sci. URSS 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
Kraichnan, R. H. 1959 The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5, 497–543.Google Scholar
Kraichnan, R. H. 1968 Small-scale structure of a scalar field convected by turbulence. Phys. Fluids 11, 945–953.Google Scholar
Kraichnan, R. H. 1976 Eddy viscosity in two and three dimensions. J. Atmos. Sci. 33, 1521–1536.Google Scholar
Kraichnan, R. H. 1987 Kolmogorov's constant and local interactions. Phys. Fluids 30, 1583–1585.Google Scholar
Lumley, J. L. 1965 Interpretation of time spectra measured by high-intensity shear flows. Phys. Fluids 8, 1056–1062.Google Scholar
Lundgren, T. S. 1982 Strained spiral vortex model for turbulent fine structure. Phys. Fluids 25, 2193–2203.Google Scholar
Mestayer, P., Chollet, J. P. & Lesieur, M. 1983 Inertial subrange anomalies of the velocity and scalar variance spectra in three-dimensional turbulence. Preprint.
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, vol. 2. Massachusetts Institute of Technology Press.
Oboukov, A. M. 1949 Structure of the temperature field in a turbulent flow. Izv. Akad. Nauk. SSSR, Geogr. i Geofiz. 13, 58–69.Google Scholar
Orszag, S. A. 1970 Analytical theories of turbulence. J. Fluid Mech. 41, 363–386.Google Scholar
Pao, Y.-H. 1965 Structure of turbulent velocity and scalar fields at large wavenumbers. Phys. Fluids 8, 1063–1075.Google Scholar
Pumir, A. & Kerr, R. M. 1987 Numerical simulation of interacting vortex tubes. Phys. Rev. Lett. 58, 1636–1639.Google Scholar
Siggia, E. D. 1978 Model of intermittency in three-dimensional turbulence.. Phys. Rev. A 17, 1166–1176.Google Scholar
Siggia, E. D. 1984 Collapse and amplification of a vortex filament. Phys. Fluids 28, 794.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. 1985 On the fine-scale intermittency of turbulence. J. Fluid Mech. 151, 81.Google Scholar
Van Atta, C. W. 1979 Bispectral measurements in turbulence computations. In Proc. 6th Int. Conf, on Numerical Methods in Fluid Mechanics. Lecture Notes in Physics, vol. 90 (ed. H. Cabanner, M. Bilt, V. Russnov), pp. 530–536. Springer.
Von Neuman, J. 1949 Recent theories of turbulence (A report to Office of Naval Research) In Collected Works, vol. 6 (1949–1963), p. 437.
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
Yakhot, V. & Orszag, S. 1986 Renormalization group analysis of turbulence. I. Basic Theory. J. Sci. Comput. 1, 3.Google Scholar