Transition to the ultimate regime in Rayleigh-Bénard turbulence

We will try to reconcile the various experimental observations for very large Rayleigh number Rayleigh-Bénard (RB) turbulence, where different effective scaling exponents γ in the relation Nu ~ Ra^γ between the Nusselt number Nu and the Rayleigh number Ra have been observed. Here the analogy between RB flow and parallel flow along a flat plate is illuminating. In turbulent RB convection, the core part of the flow (“bulk”) is always turbulent, while the kinetic boundary layers (BLs) can vary from scaling-wise laminar Prandtl-Blasius type boundary layer (“classical regime”, γ<1/3) to fully turbulent Prandtl-von Karman type boundary layer, leading to an enhanced heat transport (“ultimate regime”, γ>1/3). The nature of the transition may be of subcritical nature and be in analogy to the transition in parallel shear flow along a flat plate, which undergoes a transition between laminar and turbulent boundary layers that have different dependences of the skin friction coefficient on the Reynolds number. There is a similar analogy between RB flow and pipe and channel flows and Taylor-Couette flow.