Abstract
A direct numerical simulation of thermal convection between horizontal plane boundaries has been performed, at a Rayleigh number Ra=9800Ra c , where Ra c is the critical Rayleigh number for the onset of convection. The flow is found to be fully turbulent, and analysis of the probability distributions for temperature fluctuations indicates that this is within the “hard turbulence” regime, as defined by the Chicago group. Good agreement is shown to exist between their experiments and the present simulation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Antonia, R. A., Satyaprakash, B. R., and Hussain, A. K. M. F. (1982).J. Fluid Mech. 119, 55.
Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A. (1988).Spectral Methods in Fluid Dynamics, Springer-Verlag, New York.
Castaing, B., Gunaratne, G., Heslot, F., Kadanoff, L., Libchaber, A., Thomas, S., Wu, X. Z., Zaleski, S., and Zanetti, G. (1989).J. Fluid Mech. 204, 1.
Deardoff, J. W., and Willis, G. E. (1967).J. Fluid Mech. 28, 675.
Drazin, P. G., and Reid, W. H. (1985).Hydrodynamic Stability, Cambridge University Press.
Eidson, T. M. (1985).J. Fluid Mech. 158, 245.
Eidson, T. M., Hussaini, M. Y., and Zang, T. A. (1985). Proceedings of the Euromech 199 Direct and Large Eddy Simulation of Turbulent flows, Munich, Germany, September 10–October 2 (also ICASE Report 86-6, NASA Langley).
Grötzbach, G. (1983).J. Comput. Phys. 49, 241.
Herring, J. R., and Wyngaard, J. C. (1985). Fifth Symposium on Turbulent Shear Flows, Cornell University, August.
Heslot, F., Castaing, B., and Libchaber, A. (1987).Phys. Rev. A 36, 5870.
Krishnamurti, R. (1970).J. Fluid Mech. 42, 309.
Libchaber, A., Sano, M., and Wu, X. Z. (private communication).
Malkus, W. V. R. (1954).Proc. R. Soc. (London) A225, 185.
Sirovich, L. (1987).Q. Appl. Math. 45, 561.
Sirovich, L. (1989).Physica D 37, 126.
Sirovich, L., Balachandar, S., and Maxey, M. (1989)Phys. Fluids A 1, 1911.
Sirovich, L., Maxey, M., and Tarman, H. (1988). InProceedings of the Sixth Symposium on Turbulent Shear Flows, Launder, B. E. (ed.), Springer-Verlag, Berlin, p. 68.
Swarztrauber, P. (1986). Symmetric FFTs,Math. Comput. 47, 323–346.
Tarman, I. H. (1989). Analysis of Turbulent Thermal Convection, Ph.D. thesis, Brown University.
Temperton, C. (1983). Self-sorting mixed-radix fast Fourier transforms,J. Comput. Phys. 52, 1–23.
Yakhot, V. (1989).Phys. Fluids A 1, 175.
Yakhot, V. (private communication).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Balachandar, S., Maxey, M.R. & Sirovich, L. Numerical simulation of high Rayleigh number convection. J Sci Comput 4, 219–236 (1989). https://doi.org/10.1007/BF01061502
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01061502