Universal scaling laws in turbulent Rayleigh-Bénard convection with and without roughness
Résumé
Experimental heat-transfer measurements published in the literature seem to be contradictory, some showing a transition at $Ra \approx 10^{11}$, some showing a delayed transition at higher $Ra$, or no transition at all. New experimental and numerical heat-flux and velocity measurements, both reaching $Ra$ up to \num{e12}, are reported on a wide range of operating conditions.
In the new measurements in the rough cell which reaches Rayleigh numbers, $Ra$, up to 2.5e12, the Nusselt number show a clear $Ra^{1/2}$ scaling, hinting a fully turbulent regime. In contrast to the $Nu$ vs $Ra$ relationship, we evidence that the dimensionless heat-flux, expressed as $RaNu$, recovers a universal scaling with Reynolds number, collapses all data and highlights a universal critical Reynolds number.
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