Transition to the ultimate regime in a stochastic model of radiatively driven thermal convection

Measurements of convection in a fluid whose bottom layer is radiatively heated show a transition from classical to ultimate Nu dependence on Ra for order-one Pr, with ultimate-regime Ra exponent 0.55. This transition is reproduced with the same exponent value by stochastic simulations using a formulation of one-dimensional turbulence (ODT) akin to a formulation previously applied to Rayleigh convection with fixed wall temperatures. ODT simulates viscous and conductive thermal transport along a vertical line of sight, punctuated by eddy events that instantaneously modify the flow state within sub-intervals of the line. A local energy-based event-sampling criterion endows the formulation with key attributes of turbulence phenomenology. For the radiatively driven case, the classical-to-ultimate transition is accompanied by an abrupt reduction in occurrences of small near-wall eddy events, consistent with both the conceptual picture of the ultimate regime and empirical evidence. ODT results suggest a slight dependence of the ultimate exponent on the normalized thickness of the heated layer. No other available method or evidence presently allows a statistically significant test of this prediction.