Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-27T16:47:50.806Z Has data issue: false hasContentIssue false
  • English
  • Français

The application of turbulence theory to the formulation of subgrid modelling procedures

Published online by Cambridge University Press:  19 April 2006

D. C. Leslie  and
G. L. Quarini
D. C. Leslie
Affiliation:
Department of Nuclear Engineering, Queen Mary College, London
G. L. Quarini
Affiliation:
H.T.F.S., Atomic Energy Research Establishment, Harwell, Oxfordshire
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem of subgrid modelling, that is, of representing energy transfers from large to small eddies in terms of the large eddies only, must arise in any large eddy simulation, whether the equations of motion are open or direct (unaveraged) or closed (averaged). Models for closed calculations are derived from classical closures, and these are used to determine the effect of filter shape, grid-scale spectrum and grid-scale anisotropy on the effective eddy viscosity: the Leonard or resolvable-scale stress is calculated separately and is found to account for 14% of the total drain in a typical high Reynolds number case.

The validity of using these eddy viscosities in an open calculation is considered. It is concluded that this is not unreasonable, but that the simulation would be much improved if the gross drain could be separated into net drain and backscatter.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 91 , Issue 1 , 9 March 1979 , pp. 65 - 91
Copyright
© 1979 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Comte-Bellot, G. & Corrsin, S. 1971 Simple Eulerian time correlation of full- and narrow- band velocity signals in grid-generated ‘isotropic’ turbulence. J. Fluid Mech. 48, 273.Google Scholar
Corrsin, S. 1961 Turbulent flow. Amer. Scientist 49, 300.Google Scholar
Crow, S. C. 1967 Visco-elastic character of fine-grained isotropic turbulence. Phys. Fluids 10, 1587.Google Scholar
Crow, S. C. 1968 Visco-elastic properties of fine-grained incompressible turbulence. J. Fluid Mech. 33, 1.Google Scholar
Deardorff, J. W. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41, 453.Google Scholar
Deardorff, J. W. 1971 On the magnitude of the subgrid scale eddy coefficient. J. Comp. Phys. 7, 120.Google Scholar
Herring, J. R. 1974 Approach of axisymmetric turbulence to isotropy. Phys. Fluids 17, 859.Google Scholar
Kraichnan, R. H. 1964 Direct interaction approximation for shear and thermally driven turbulence. Phys. Fluids 7, 1048.Google Scholar
Kraichnan, R. H. 1971 An almost-Markovian Galilean-invariant turbulence model. J. Fluid Mech. 47, 513.Google Scholar
Kraichnan, R. H. 1976 Eddy viscosity in two and three dimensions. J. Atmos. Sci. 33, 1521.Google Scholar
Kwak, D., Reynolds, W. C. & Ferziger, J. H. 1975 Three-dimensional time dependent computation of turbulent flow. Stanford Univ. Rep. TF-5.Google Scholar
Leonard, A. 1974 Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. in Geophys. A 18, 237.Google Scholar
Lesieur, M. & Schertzer, D. 1977 Amortissement autosimilaire d'une turbulence a grand nombre de Reynolds. J. Méc. 17, 609.Google Scholar
Leslie, D. C. 1973 Developments in the Theory of Turbulence. Oxford: Clarendon Press.
Lilly, D. K. 1966 On the application of the eddy viscosity concept in the inertial sub-range of turbulence. N.C.A.R. Rep. no. 123.Google Scholar
Lilly, D. K. 1967 The representation of small-scale turbulence in numerical simulation experiments. Proc. I.B.M. Sci. Comp. Symp. on Environ. Sci. p. 1866 (publ. 1967).Google Scholar
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, English edn. M.I.T. Press.
Orszag, S. A. 1970 Analytical theories of turbulence. J. Fluid Mech. 41, 363.Google Scholar
Orszag, S. A. & Patterson, G. S. 1972 Numerical simulation of three-dimensional homogeneous isotropic turbulence. Phys. Rev. Lett. 28, 76.Google Scholar
Rose, H. 1977 Eddy diffusivity, eddy noise and subgrid-scale modelling. J. Fluid Mech. 81, 719.Google Scholar
Schumann, U. 1973 Ein Verfahren zur direkten numerischen Simulation turbulenter Strömungen in Platten- und Ringspaltkanalen und über seine Anwendung zur Intersuchung von Turbulenzmodellen. Ph.D. thesis, Karlsruhe University. (Available as Rep. KFK 1854.)
Schumann, U. 1975 Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comp. Phys. 18, 376.Google Scholar
Schumann, U. & Herring, J. R. 1976 Axisymmetric homogeneous turbulence: a comparison of direct spectral simulations with the direct-interaction approximation. J. Fluid Mech. 76, 755.Google Scholar
Smagorinsky, J. S. 1963 General circulation experiments with the primitive equations. I: the basic experiment. Mon. Weath. Rev. 91, 99.2.3.CO;2>CrossRefGoogle Scholar