DOI: 10.1017/s0022112060000530. On the tendency towards hexagonal cells in steady convection

On the tendency towards hexagonal cells in steady convection

10.1017/s0022112060000530

Crossref journal-article

Cambridge University Press (CUP)

Journal of Fluid Mechanics (56)

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.

Bibliography

Palm, E. (1960). On the tendency towards hexagonal cells in steady convection. Journal of Fluid Mechanics, 8(2), 183â192.

Authors 1

Enok Palm (first)

References 10 Referenced 222

Tippelskirch, H. V. 1956 Beitr. Phys. frei. Atmos. 29,37.
Pellew, A. & Southwell, R. V. 1940 Proc. Roy. Soc. A,176,312.
Bénard, M. 1901 Ann. Chim. Phys. 23,62.
Jeffreys, H. 1930 Proc. Camb. Phil. Soc. 26,170. (10.1017/S0305004100015413)
Graham, A. 1933 Phil. Trans. A,232,285. (10.1098/rsta.1934.0008)
Boussinesq, J. 1903 Théorie Analytique de la Chaleur , vol. 2.Paris:Gauthier-Villars.
Malkus, W. V. R. & Veronis, G. 1958 J. Fluid Mech. 4,225. (10.1017/S0022112058000410)
Thomson, J. 1882 Proc. Glasg. Phil. Soc. 13,464.
Rayleigh, Lord 1916 Phil. Mag. 32. (Reprinted in Collected Papers, 6, 432.)
Christophersen, D. G. 1940 Quart. J. Mech. Appl. Math. 11,63.

Dates

Type	When
Created	19 years, 5 months ago (March 28, 2006, 12:30 a.m.)
Deposited	6 years, 4 months ago (April 9, 2019, 12:05 p.m.)
Indexed	2 months ago (June 27, 2025, 3:28 a.m.)
Issued	65 years, 3 months ago (June 1, 1960)
Published	65 years, 3 months ago (June 1, 1960)
Published Online	19 years, 5 months ago (March 28, 2006)
Published Print	65 years, 3 months ago (June 1, 1960)

Funders 0

None

BibTeX

@article{Palm_1960, title={On the tendency towards hexagonal cells in steady convection}, volume={8}, ISSN={1469-7645}, url={http://dx.doi.org/10.1017/s0022112060000530}, DOI={10.1017/s0022112060000530}, number={2}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Palm, Enok}, year={1960}, month=jun, pages={183–192} }

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