Optimal heat transport at the edge of energy stability

Abstract

Large heat flux is commonly associated with vigorous convection and turbulent mixing. Here, we show that this connection is not fundamental. Using a marginal energy-stability theory, we identify near-optimal convective heat transport with the saturation of an energy-stability constraint rather than with turbulence intensity. The theory selects mean temperature profiles whose fluxes closely approach the best available optimal transport states and rigorous upper bounds, predicting the asymptotic scaling $Nu\sim0.0245Ra^{1/2}$ at large Rayleigh number. These profiles exhibit a hierarchical structure consisting of conductive inner layers, logarithmic-like intermediate layers, and a stably stratified bulk, closely mirroring optimal transport calculations and suggesting that maximal convective heat transport emerges near marginal energy stability. More strikingly, the same profiles can be converted into exact conductive states through prescribed internal thermal forcing. Direct numerical simulations show that an initially turbulent flow then relaxes to a motionless state while maintaining a large wall heat flux. Energy-stability saturation therefore provides both a physical interpretation of transport limits and a route to high-flux heat transfer without turbulence.