Non-Oberbeck-Boussinesq effects in turbulent Rayleigh-Benard convection

Abstract

Thermally driven turbulence usually involves significant variations in the properties of the fluid, such as viscosity, thermal conductivity, thermal expansivity, and specific heat. In particular, when the fluid is strongly heated from below and cooled from above, such variations may even break the top-down symmetries of the velocity, temperature, and density profiles. To characterize non-Oberbeck-Boussinesq (NOB) effects of this nature, we have measured the temperature Tc at the center of the convection container. In this way, the top-down asymmetry between thermal boundary-layers can be conveniently described by the deviation of Tc from the mean temperature T m = (Tt+Tb)/2 between the temperatures of the bottom (Tj,) and top (Tt) plates. We have developed a theory [1, 2] for calculating the difference Tc - Tm as function of Δ= Tb - Tt that is based on boundary-layer equations with variable transport properties. Two different fluids have been considered: (i) water [1] and (ii) gaseous ethane under high pressure [2]. In the water case, we have found Tc > Tm, indicating that the top thermal-layer becomes thicker than its counterpart at the bottom plate. In contrast, Tc < Tm has been observed in gaseous ethane, since the top thermal-layer becomes thinner. In both cases, our theoretical results are in reasonable agreement with experimental measurements (cf. figure 1). Nevertheless, NOB effects on the Nusselt number are not predicted by our theory.