Journal of Fluid Mechanics

Thermal convection in a vertical circular cylinder

S.  Rosenblat a1
a1 Department of Mathematics, Illinois Institute of Technology, Chicago, Il. 60616

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A theoretical investigation is made of the onset of buoyancy-driven convection in a circular cylinder. Amplitude equations are derived for the weakly nonlinear evolution of critical disturbances at moderate values of the radius-to-height ratio. It is shown that the initial form of the convective motion a t Rayleigh numbers slightly above critical is not axisymmetric. Particular attention is paid to the neighbourhoods of points where two disturbances are simultaneously critical according to linear theory; the nonlinear evolution in such neighbourhoods is studied in detail.

(Published Online April 20 2006)
(Received October 18 1981)
(Revised March 18 1982)