Strong heat transport with classical scaling in three-dimensional steady natural convection

The high-Rayleigh-number asymptotic behaviour of three-dimensional steady exact coherent states (ECS) in Rayleigh-Benard convection is studied. The square and hexagonal convection cell states, optimised to maximise Nusselt number, persist into the Rayleigh number regime where a clear asymptotic trend emerges. A detailed asymptotic analysis of the velocity and temperature fields shows that the corresponding Nusselt number follows the classical scaling at Rayleigh numbers that are otherwise computationally inaccessible. Interestingly, our analysis indicates that the Nusselt number for the ECS markedly exceeds all currently available experimental and simulation results.