Penetrative Convection.

The bottom of a layer of water is maintained at 0 C and the top at a temperature greater than 4" C. Thus a gravitationally unstable layer of fluid lies below a layer which is stably stratified. When convection occurs in the lower layer, the motions will penetrate into the upper layer. This system is analyzed to determine the extent of the penetration into the stable fluid. The perturbation method employed in the present paper is a modification of the technique discussed in an earlier paper and is applicable to a system in which the infinitesimal motions can be deduced only approximately. The results indicate that the system can become unstable to a finite amplitude disturbance at values of the Rayleigh number less than the critical value of infinitesimal stability theory. A simple physical explanation is put forth to explain the occurrence of a finite amplitude instability. Experimental efforts by Furumoto and Rooth (unpublished) have not been successful in determining whether or not a finite amplitude instability occurs.