Three-dimensional simulation for problem of penetrative convection near the maximum density

The problem of penetrative convection with the cubic and fifth-order equations of state proposed by Merker, Waas and Grigull is studied. Both linear instability and nonlinear stability analyses are performed to assess the suitability of linear theory to predict destabilisation of the convection. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using three-dimensional simulation. The results show that the linear threshold accurately predicts the onset of instability in the basic steady state solution.