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A transformation for the energy-transfer term in isotropic turbulence

Published online by Cambridge University Press:  21 April 2006

L. Crocco
Affiliation:
Via Annia 16, 00184 Roma
P. Orlandi
Affiliation:
Dipartimento di Meccanica e Aeronautica, Università di Roma, La Sapienza, Via Eudossiana, 16 00184 Roma

Abstract

The application of a particular transformation to the triadic integral results in an expression having the following advantages: (a) it satisfies global energy conservation in an evident fashion, independently of the accuracy of the energy-spectrum calculations; (b) it allows an economy of computational time; (c) it shows certain symmetries in the behaviour of non-local interactions; (d) it provides, for the non-local interactions contribution to the transfer function, an expression which is simpler and more compact than those existing, in spite of being more nearly complete; (e) finally the calculated energy-transfer distribution is in good agreement with the experimental findings through a very large range of Rλ.

Type
Research Article
Copyright
© 1985 Cambridge University Press

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References

André, J. C. & Lesieur, M. 1977 Influence of helicity on the evolution of isotropic turbulence at high Reynolds number. J. Fluid Mech. 81 187207.Google Scholar
Cambon, C., Jaendel, D. & Mathieu, J. 1981 Spectral modelling of non-isotropic turbulence. J. Fluid Mech. 104, 247262.Google Scholar
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, 273337.Google Scholar
Helland, K. N., Van Atta, C. W. & Stegen, G. R. 1977 Spectral energy transfer in high Reynolds number turbulence. J. Fluid Mech. 79, 337359.Google Scholar
Herring, J. R. & Kraichnan, R. H. 1972 Comparison of some approximations for isotropic turbulence. In Statistical Models and Turbulence (ed. M. Rosenblatt & C. Van Atta). Lecture Notes in Physics vol. 12, pp. 146194. Springer.
Kraichnan, R. H. 1976 Eddy viscosity in two and three dimensions, J. Atmos. Sci. 33, 15211536.Google Scholar
Leith, C. E. & Kraichnan, R. H. 1972 Predictability of turbulent flows. J. Atmos. Sci. 29, 10411058.Google Scholar
Lesieur, M. & Schertzer, D. 1977 Amortissement autosimilaire d'une turbulence à grand nombre de Reynolds. J. Méc. 17, 607646.Google Scholar
Newman, G. R. & Herring, J. R. 1979 A test field model study of a passive scalar in isotropic turbulence. J. Fluid Mech. 94, 169194.Google Scholar
Orszag, S. A. 1970 Analytical theories of turbulence. J. Fluid Mech. 41, 363386.Google Scholar
Orszag, S. A. & Patterson, G. S. 1972 Numerical simulation of three-dimensional homogeneous isotropic turbulence. In Statistical Models and Turbulence (ed. M. Rosenblatt & C. Van Atta). Lecture Notes in Physics vol. 12, pp. 127145. Springer.
Pouquet, A., Lesieur, M. & André, J. C. 1975 High Reynolds number simulation of two-dimensional homogeneous isotropic turbulence using a stochastic model. J. Fluid Mech. 72, 305319.Google Scholar
Yeh, T. T. & Van Atta, C. C. 1973 Spectral transfer of scalar and velocity fields in heated grid turbulence. J. Fluid Mech. 58, 233263.Google Scholar