Hostname: page-component-f554764f5-fnl2l Total loading time: 0 Render date: 2025-04-10T15:30:31.495Z Has data issue: false hasContentIssue false
  • English
  • Français

Spectral approach to non-isotropic turbulence subjected to rotation

Published online by Cambridge University Press:  26 April 2006

C. Cambon  and
L. Jacquin
C. Cambon
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, UA CNRS no. 63, Ecole Centrale de Lyon, Ecully, France
L. Jacquin
Affiliation:
Office National d'Etudes et de Recherches Aérospatiales, Chatillon. France
Get access Rights & Permissions [Opens in a new window]

Abstract

The non-isotropic effects of solid-body rotation on homogeneous turbulence are investigated in this paper. A spectral formalism using eigenmodes introduces the spectral Coriolis effects more easily and leads to simpler expressions for the integral quadratic terms which come mostly from classical two-point closures. The analysis is then applied to a specific eddy damped quasi-normal Markovian model, which includes the inertial waves regime in the evaluation of triple correlations. This procedure allows for a departure from isotropy by external rotation effects. When started with rigorously isotropic initial data, the various trends observed on the Reynolds stresses and the integral lengthscales remain in accordance with the results from direct simulations; moreover they reflect a very specific spectral angular distribution. Such an angular dependence allows a drain of spectral energy from the parallel to the normal wave vectors (with respect to the rotation axis), and thus appears consistent with a trend toward two-dimensionality.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 202 , May 1989 , pp. 295 - 317
Copyright
© 1989 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.)

Article purchase

Temporarily unavailable

References

André, J. C. & Lesieur, M. 1977 Influence of helicity on the evolution of isotropic turbulence at high Reynolds number. J. Fluid Mech. 81, 187–297.Google Scholar
Aupoix, B., Cousteix, J. & Liandrat, J., 1983 Effects of rotation on isotropic turbulence. In Proc. 4th Symp. Turbulent Shear Flows, Karlsruhe (ed. L. J. S. Bradbury et al.). Springer.
Bardina, J., Ferziger, J. H. & Rogallo, R. S., 1985 Effect of rotation on isotropic turbulence. J. Fluid Mech. 154, 321–326.Google Scholar
Batchelor, G. K.: 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Bertoglio, J. P., Cambon, C., Jeandel, D. & Mathieu, J., 1979 Comparaison directe entre une modélisation directionnelle du tenseur spectral des corrélations doubles et une solution analytique dans le cas d'une turbulence homogène anisotrope. C. R. Acad. Sci. Paris 288B, 473–475.Google Scholar
Cambon, C.: 1982 Etude spectrale d'un champ turbulent incompressible soumis à des-effets couples de déformation et de rotation imposés extérieurement. Thèse d'Etat, Université Lyon I.
Cambon, C., Bertoglio, J. P. & Jeandel, D., 1981b Spectral closures for homogeneous turbulence. The 1980–81 AFOSR-HTTM-Stanford Conference on Complex Turbulent Flow, vol. III, pp. 1307–1311.Google Scholar
Cambon, C. & Jacquin, L., 1985 Non isotropic aspects in homogeneous turbulence subjected to rotation. Proc. Seventh AMS Symp. on Turbulence and Diffusion, Boulder.Google Scholar
Cambon, C. & Jacquin, L., 1987 Spectral analysis of a three-dimensional homogeneous turbulence submitted to a solid body rotation. In Advances in Turbulence (ed. G. Comte-Bellot & J. Mathieu), pp. 170–175. Springer.
Cambon, C., Jeandel, D. & Mathieu, J., 1981a Spectral modelling of homogeneous non-isotropic turbulence. J. Fluid Mech. 104, 247–262.Google Scholar
Cambon, C., Teissèdre, C. & Jeandel, D. 1985 Etude d'effets couplés de déformation et de rotation sur une turbulence homogène. J. Méc. Théor. Appl., 4, 629–657.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, 273–337.Google Scholar
Craya, A.: 1958 Contribution à l'analyse de la turbulence associée à des vitesses moyennes. Thèse dans Publications Scientifiques et Techniques, Ministère de l'Air, France.Google Scholar
Dang, K. & Roy, Ph., 1985a Numerical simulation of homogeneous turbulence. In Proc. Workshop on Macroscopic Modelling of Turbulent Flows and Fluid Mixtures. Springer.
Dang, K. & Roy, Ph., 1985b Direct and large eddy simulation of homogeneous turbulence submitted to solid body rotation. In Proc. 5th Symp. on Turbulent Shear Flows, Ithaca.
Gence, J. N. & Mathieu, J., 1979 On the application of successive plane strains to grid-generated turbulence. J. Fluid Mech. 93, 501–513.Google Scholar
Greenspan, H. P.: 1968 The Theory of Rotating Fluids. Cambridge University Press.
Herring, J. R.: 1974 Approach of axisymmetric turbulence to isotropy. Phys. Fluids 17, 859–872.Google Scholar
Holloway, G. & Hendershott, M. C., 1977 Stochastic closure for non-linear Rossby waves. J. Fluid Mech. 82, 747–765.Google Scholar
Hopfinger, E. J., Browand, F. K. & Gagne, Y., 1982 Turbulence and waves in a rotating tank. J. Fluid Mech. 125, 505–534.Google Scholar
Itsweire, E., Chabert, L. & Gence, J. N., 1979 Action d'une rotation pure sur une turbulence homogène anisotrope. C. R. Acad. Sci. Paris 289 B, 197–199.Google Scholar
Lesieur, M.: 1972 Décomposition d'un champ de vitesse non divergent en ondes d'hélicité. Revue ‘Turbulence’. Observatoire de Nice.
Orszag, S. A.: 1970 Analytical theories of turbulence. J. Fluid Mech. 41, 262–386.Google Scholar
Townsend, A. A.: 1954 The uniform distortion of homogeneous turbulence. Q. J. Mech. Appl. Maths, 2, 11000.Google Scholar
Wigeland, R. A.: 1978 Ph.D. thesis. Illinois Institute of Technology.
Supplementary material: PDF

Cambon and Jacquin supplementary material

Appendix

Download Cambon and Jacquin supplementary material(PDF)
PDF 861.2 KB