Transition to turbulent thermal convection beyond Ra = 10(10) detected in numerical simulations

We have conducted high-resolution two-dimensional calculations for a Boussinesq convection model with a Prandtl number of unity in an aspect-ratio 3 box, going from Rayleigh numbers between 10(8) to 10(14). A grid of 1024 x 3076 grid points consisting of a cosine-sine basis set has been employed for free-slip boundary conditions. We have found evidence for a transition involving the branching of plumes at a Rayleigh number of 10(10). Inside the core of these "superplumes," the structure is extremely complex. There may be another transition at Ra of 10(12), where a secondary instability may develop in regions of the local Rayleigh number which becomes supercritical inside the core of the complex "superplumes." For Ra of 10(8) to 10(10), Ra follows a 1/3 power law in the Nusselt-Rayleigh number relationship. From Ra of 10(10) to 10(12), Ra follows a 1/2 power law. Above this value the Nusselt number becomes insensitive to the variation in the global Rayleigh number and this is due to the development of small-scale convection cells vertically aligned in the interior of the extremely high Ra number flow. The global Reynolds number scales as Re approximately Ra1/4 up to Ra of 10(14). Scaling relationships based on global properties would not work in extremely high Ra situations beyond Ra of 10(12) because of the complex turbulent layered convection in the core of the flow and the severe degradation of the boundary layers.