A numerical simulation of « convection » in a cylindrical geometry

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Abstract
Rudimentary numerical simulations performed on a two-dimensional model of three-dimensional convection already give valuable informations about the process of non-linear pattern selection in convection experiments. We have considered a disc which corresponds to a cylindrical box with intermediate aspect ratio (R/h ∼ 6). Starting with low level random initial conditions we observe : 1) the linear growth of unstable modes, 2) a saturation stage during which the selection is very active, 3) a final reorganization corresponding to the slow motion of defects. Solutions which have been observed were stationary even with non-linear terms which did not derive from a potential. The structures found in these simulations are strikingly similar to those obtained experimentally with comparable aspect ratios and high Prandtl numbers. Limitations and possible improvements of the model are also discussed