Journal of Fluid Mechanics

Pattern selection in single-component systems coupling Bénard convection and solidification

S. H.  Davis a1, U.  Müller a2 and C.  Dietsche a2
a1 Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60201, USA
a2 Kernforschungszentrum Karlsruhe GMBH, Institüt fur Reaktorbauelemente, Karlsruhe, West Germany

Article author query
davis sh   [Google Scholar] 
müller u   [Google Scholar] 
dietsche c   [Google Scholar] 


A horizontal layer is heated from below and cooled from above so that the enclosed single-component liquid is frozen in the upper part of the layer. When the imposed temperature difference is such that the Rayleigh number across the liquid is supercritical, there is Bénard convection coupled with the dynamics of the solidification interface. An experiment is presented which shows that the interfacial corrugations that result are two-dimensional when this solid is thin but hexagonal when the solid is thick. A weakly nonlinear convective instability theory is presented which explains this behaviour, and isolates this ‘purely thermal’ mechanism of pattern selection. Jump behaviour is seen in the liquid-layer thickness at the onset of hexagonal convection.

(Published Online April 20 2006)
(Received November 29 1983)
(Revised February 28 1984)