Ultimate Rayleigh-Bénard turbulence

Rayleigh-B\'enard convection is the flow in a closed box heated from below and cooled from above. The ultimate regime of Rayleigh-B\'enard turbulence occurs when the dimensionless temperature difference between the bottom and top plates is large. This review gives a comprehensive overview of the theoretical approaches to the ultimate regime and of the experimental and numerical results on the transition to this regime. These are reconciled by realizing that the transition is of non-normal--nonlinear nature, as typical for the laminar to turbulent transition in shear flow. The review also suggests experimental and numerical approaches to further understand the transition to the ultimate regime.