Experimental Study of the Temperature and Velocity Boundary Layers in Thermal Turbulence at Low Prandtl Number

Abstract

Despite recent progress, both from the theoretical and experimental side, the convective transport of heat in a turbulent flow is still far from being understood. For instance, the existence of an ultimate regime of convection at very high values of the Rayleigh number Ra (non-dimensional temperature difference) is only a conjecture. We report here on recent results obtained in a Rayleigh-Bénard convection experiment using mercury as a working fluid. Due to its low Prandtl number (Pr = κ/v = 0.024, κ is the thermal conductivity and v is the kinematic viscosity), it is possible to realize in well controlled experimental conditions regimes of hard turbulence that would be difficult to reach in fluids of higher Pr, such as air, water or helium. The heat transport through a fluid layer between two horizontal plates at distance L, regulated at different temperatures (T _top ≤ T _bottom ) is characterized by the Nusselt number, ratio of the total heat flux over that transported by diffusion. The hard turbulence regime of thermal convection, is characterized by a scaling of Nu versus Ra, and a stable mean circulation in the cell. It appeared recently that, in this high Nu regime, the heat transport properties are affected by boundary effects, along the plates. Our experimental set-up consist in several cylindrical cells (diameter: 10 cm, height: 5, 10, 20 cm), covering a large range of Ra (10⁵ ≤ Ra ≤ 210⁹).