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arXiv · 2606.14138

Optimal heat transport at the edge of energy stability

Zijing Ding·Baole Wen·Hui Li
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Abstract

High heat transfer in Rayleigh--B\'enard convection is commonly associated with vigorous turbulent motion, but turbulence intensity alone does not explain how a limiting transport state is selected. We propose that such limiting states are organized by marginal energy stability. Starting from the exact perturbation-energy balance, we determine, for a prescribed mean temperature profile, the smallest neutral Rayleigh number over the balance parameter and all admissible disturbances. The corresponding marginal modes are then coupled to the exact mean-temperature equation, producing a self-consistent profile and heat flux. At large $Ra$, the selected branch gives $Nu\simeq0.0245Ra^{1/2}$ and develops conductive inner layers, logarithmic-like intermediate regions and a weakly stably stratified core. An equivalent background-field formulation yields the same governing equations and establishes uniqueness of the selected mean profile. Three-dimensional simulations at $10^6\le Ra\le10^8$ show that distributed thermal forcing based on this profile suppresses convective motion while retaining a large wall heat flux.

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Zijing Ding, Baole Wen, Hui Li. 2026-06-12. Optimal heat transport at the edge of energy stability. https://arxiv.org/abs/2606.14138

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