Thermal instability and convection of a thin fluid layer bounded by a stably stratified region

Abstract

Results of linear stability calculations and post-stability experimental observations are reported for horizontal fluid layers with upward heat flux bounded below by a stably stratified fluid. Stability calculations were done for several families of continuous and discontinuous temperature distributions, and it was found that as a rule the flow originating in the unstable layer penetrates into the stably stratified region, resulting in increased critical cell size and correspondingly decreased critical Rayleigh number. A notable exception to this occurs for an unstable layer with a linear temperature distribution adjacent to a stable layer of very high stable density gradient. In this case energy pumped from the unstable to the stable region is sufficient to raise the critical Rayleigh number above that of a solid boundary. It is also found that, for density distributions with a more gradual transition between the stable and the unstable regions, the effect of increased cell size upon the critical Rayleigh number is sometimes masked by effects of curvature in the density profile of the unstable region, which tends to increase the critical Rayleigh number. The inadequacy of the usual definition of Rayleigh number to characterize the stability of such complex systems is discussed. Experimentally, such a temperature distribution was produced by radiant energy from above as it was absorbed by the top few centimetres of the fluid. Within an uncertainty of ± 20%, it was found that the critical experimental Rayleigh number agreed with neutral stability calculations. The supercritical convective motion consisted of vertical jets of cool surface fluid which plunged downward into the interior of the fluid. The jets were not arranged in an orderly lattice but were in a constant state of change, each jet having a tendency to merge with a close neighbour. The net loss of jets due to merging was balanced by new jets spontaneously appearing. As Rayleigh number was increased, the mean number of jets and the intermittancy increased proportionally. Temperature scans taken with a movable probe showed that cool surface fluid plunging downward in the jets was confined to a fairly restricted region, the surrounding fluid being quite isothermal.