Non–Oberbeck-Boussinesq effects in two-dimensional Rayleigh-Bénard convection in glycerol

We numerically analyze Non-Oberbeck-Boussinesq (NOB) effects in two-dimensional Rayleigh-Benard flow in glycerol, which shows a dramatic change in the viscosity with temperature. The results are presented both as functions of the Rayleigh number Ra up to 108 (for fixed temperature difference Delta between the top and bottom plates) and as functions of Delta ( 'nonOberbeck-Boussinesqness' or 'NOBness' ) up to 50 K (for fixed Ra). For this large NOBness the center temperature T, is more than 5 K larger than the arithmetic mean temperature T, between top and bottom plate and only weakly depends on Ra. To physically account for the NOB deviations of the Nusselt numbers from its Oberbeck-Boussinesq values, we apply the decomposition of NUNOB / NUOB into the product of two effects, namely first the change in the sum of the top and bottom thermal BL thicknesses, and second the shift of the center temperature T, as compared to Tm. While for water the origin of the Nu deviation is totally dominated by the second effect (cf. AHLERS G. et al., J. Fluid Mech., 569 (2006) 409) for glycerol the first effect is dominating, in spite of the large increase of T, as compared to Tm.