{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"9f3a6e708c1e4249c6dcb03f5c797635d1e0c8357c96b5807dc4ff9e05551e49","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["258500c4fc59f9a64e896e2e695603b95da1f16d9c9c7afb8b1b5e5861cde3d8","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"74eafe860a8815993c0d0ba6abf067d08b9cfb3fb9ca438f5252bb04b960db27","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"fluid.rb-convection.prandtl-dependence","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"How strongly heat transport depends on the fluid's ratio of viscosity to heat diffusivity, the Prandtl number, in the ultimate regime is unknown. This matters because liquid metals, stellar plasma and water have very different Prandtl numbers.","posed_since":"2024","precise":"Within the ultimate regime of Rayleigh-Benard convection, determine the exponents in Nu ~ Pr^g1 Ra^g2 (up to logarithms) for $\\mathrm{Pr} << 1$ and $\\mathrm{Pr} >> 1$. Test the 2024 model prediction $\\mathrm{Nu} \\sim \\mathrm{Pr}^{1/2}\\mathrm{Ra}^{1/2}/(\\ln \\mathrm{Ra})^2$ for $\\mathrm{Pr} <\\sim 1$ and $\\mathrm{Nu} \\sim \\mathrm{Pr}^{-1/2}\\mathrm{Ra}^{1/2}/(\\ln \\mathrm{Ra})^2$ for $\\mathrm{Pr} >\\sim 1$, and its consistency with the rigorous bound $\\mathrm{Nu} <\\sim \\mathrm{Ra}^{1/3}$ (up to logarithms) for $\\mathrm{Pr} >\\sim \\mathrm{Ra}^{1/3}$ (Choffrut, Nobili, Otto 2016).","problem_ref":"258500c4fc59f9a64e896e2e695603b95da1f16d9c9c7afb8b1b5e5861cde3d8","references":"","settled_by":"Heat-transport data at $\\mathrm{Ra} > 10^{13}$ for Pr from about 0.02 to 10 compared with the predicted exponents.","status_note":"Model proposed in 2024 (Shishkina and Lohse, arXiv:2407.16573); high-Ra data are concentrated near $\\mathrm{Pr}\\sim 1$.","title":"Prandtl-number dependence of heat transport in the ultimate 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