The stability of cells in directional solidification

(Received 6 August 1991, revised 27 February 1992, accepted 15 May 1992)

Abstract
The stability of numerically obtained cells in the one sided model of directional solidification is investigated, using a numerical approach. In particular, the shapes of the cells corresponding to the Saffman-Taylor branch are discussed. The possibility for an oscillatory instability is investigated and the results are compared with a recent approximate analytical stability calculation. For large thermal length we find an instability which is oscillatory for some parametervalues. The results agree partially with the analytical stability calculation. The possible limit cycle arising from this instability is discussed.