Optimal heat transport at the edge of energy stability
Abstract
High heat transfer in Rayleigh--Bénard 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≃0.0245Ra1/2 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 106≤ Ra≤108 show that distributed thermal forcing based on this profile suppresses convective motion while retaining a large wall heat flux.
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BibTeX
@misc{ding2026optimal,
title = {{Optimal heat transport at the edge of energy stability}},
author = {Zijing Ding and Baole Wen and Hui Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.14138},
eprint = {2606.14138},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.14138},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimal heat transport at the edge of energy stability
AU - Zijing Ding
AU - Baole Wen
AU - Hui Li
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2606.14138
UR - https://arxiv.org/abs/2606.14138
AB - High heat transfer in Rayleigh--Bénard 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≃0.0245Ra^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≤ Ra≤10^8 show that distributed thermal forcing based on this profile suppresses convective motion while retaining a large wall heat flux.
ER -