Penetrative convection in sublayer of water including density inversion

Numerical solutions of stability and convective flow in an infinite horizontal water layer, including density inversion, have been obtained using a finite element code. The evolution of the temperature field and flow pattern near the onset of convection are studied in detail. It is known that natural convection develops primarily in the lower unstably stratified layer. Of interest is the penetration of the convection rolls into the upper stably stratified layer and concurrent liquid entrainment as a function of the increasing Rayleigh number at different aspect ratios. Individual convection rolls may grow and expand before splitting up into two roll cells. It is shown that changing the aspect ratio influences critical Rayleigh number, flow symmetry, flow pattern, and transitions between flow patterns. Numerical results on heating from above or from below, agree well with available results in the literature. A correlation to predict critical Rayleigh numbers is given for the case of heating from above.