Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-01T15:41:43.255Z Has data issue: false hasContentIssue false
  • English
  • Français

Influence of viscous dissipation on Bénard convection

Published online by Cambridge University Press:  29 March 2006

D. L. Turcotte ,
A. T. Hsui ,
K. E. Torrance  and
G. Schubert
D. L. Turcotte
Affiliation:
Department of Geological Sciences, Cornell University, Ithaca, New York 14850
A. T. Hsui
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14850
K. E. Torrance
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14850
G. Schubert
Affiliation:
Department of Planetary and Space Sciences, University of California, Los Angeles 90024
Get access Rights & Permissions [Opens in a new window]

Abstract

The approximations implicit in Bénard convection have been modified to include viscous dissipation. It is shown that both the influence of an adiabatic temperature gradient and of viscous dissipation are governed by the same dimensionless parameter Di = αgh/cp. Numerical calculations of finite amplitude convection are given for finite values of Di. It is found that increasing Di decreases flow velocities and finally stabilizes the flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 64 , Issue 2 , 19 June 1974 , pp. 369 - 374
Copyright
© 1974 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

Batchelor, G. K. 1967 An introduction to Fluid Dynamics. Cambridge University Press.
Gebhart, B. 1962 J. Fluid Mech. 14, 225.
Gebhart, B. 1971 Heat Transfer, 2nd edn. McGraw-Hill.
Hsui, A. T., Turcotte, D. L. & Torrance, K. E. 1972 Geophys. Fluid Dyn. 3, 35.
Jeffreys, H. 1930 Proc. Camb. Phil. Soc. 26, 170.
Mihaljan, J. M. 1962 Astrophys. J. 136, 1126.
Ostrach, S. 1952 N.A.C.A. Tech. Note, no. 2863.
Ostrach, S. 1958 In Boundary Layer Research (ed. H. Gortler). pp 183–207. Springer.
Torrance, K. E. 1968 J. Res. Nat. Bur. Stand. B 72, 281.
Torrance, K. E. & Turcotte, D. L. 1971 J. Fluid Mech. 47, 113.