Penetrative convection in fluid layers with internal heat sources

Abstract

The stability problem for penetrative convection in a fluid layer that is heated internally is analyzed using the methods of linear instability theory and unconditional nonlinear energy theory. Critical Rayleigh numbers in the case of a constant heat source are determined numerically from both theories. Although it is not known whether exchange of stabilities holds for this problem, a comparison between the linear and nonlinear results suggests that for top temperatures close to 4°C stationary convection is predominant when the heat source is not too large. The nonlinear results delimit a band of Rayleigh numbers where possible subcritical instabilities could arise.