Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T08:45:02.342Z Has data issue: false hasContentIssue false
  • English
  • Français

On the tendency towards hexagonal cells in steady convection

Published online by Cambridge University Press:  28 March 2006

Enok Palm
Enok Palm
Affiliation:
University of Oslo, Blindern, Norway
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper attempts to explain theoretically the observed results that (1) the cells in steady convection approach a hexagonal form, and (2) the occurrence of ascent or descent in the middle of the cell depends on how the kinematical viscosity varies with temperature. The theory is based on non-linear equations and, of course, a variable coefficient of viscosity.

It is found that, due to the variation of viscosity with temperature, the non-linear terms contain a second-order term which is destabilizing. This second-order term regulates the development and leads to a final motion composed of regular hexagons with ascent or descent in the middle of the cell according as the viscosity decreases or increases with temperature.

The influence of a variable viscosity on Rayleigh's result concerning the initiation of convection is obtained as a by-product.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 8 , Issue 2 , June 1960 , pp. 183 - 192
Copyright
© 1960 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

Bénard, M. 1901 Ann. Chim. Phys. 23, 62.
Boussinesq, J. 1903 Théorie Analytique de la Chaleur, vol. 2. Paris: Gauthier-Villars.
Christophersen, D. G. 1940 Quart. J. Mech. Appl. Math. 11, 63.
Graham, A. 1933 Phil. Trans. A, 232, 285.
Jeffreys, H. 1930 Proc. Camb. Phil. Soc. 26, 170.
Malkus, W. V. R. & Veronis, G. 1958 J. Fluid Mech. 4, 225.
Pellew, A. & Southwell, R. V. 1940 Proc. Roy. Soc. A, 176, 312.
Rayleigh, Lord 1916 Phil. Mag. 32. (Reprinted in Collected Papers, 6, 432.)
Thomson, J. 1882 Proc. Glasg. Phil. Soc. 13, 464.
Tippelskirch, H. V. 1956 Beitr. Phys. frei. Atmos. 29, 37.