Non-Oberbeck–Boussinesq Effects

In most numerical and theoretical investigations of Rayleigh–Bénard convection the Oberbeck–Boussinesq (OB) approximation is employed. This means all material properties are assumed to be constant, i.e., they do not vary with pressure or temperature. The only exception is the density in the buoyancy term, which varies linearly with temperature therein. As a result, the system exhibits a perfect top-bottom symmetry on time-average in the OB case.

But intuitively it is clear that if the Rayleigh–Bénard cell is too high or the temperature difference between the heating and cooling plate is too big, then the material properties are non-uniform within the cell. Hence, in nature and so to say in all experiments, one always encounters a break-up of the top-bottom symmetry. These deviations are called non-Oberbeck–Boussinesq (NOB) effects. Our objective is to examine the flow in turbulent thermal convection in different fluids considering its actual properties. Further, we also study non-Oberbeck-Boussinesq fluids under the influence of rotation.

Instantaneous temperature fields of water at Ra=108 under (a) Oberbeck–Boussinesq conditions and three different non-Oberbeck–Boussinesq conditions (b) Δ = 20 K, (c) Δ = 40 K, and (d) Δ = 60 K.

Further reading

Olga Shishkina, Stephan Weiss, Eberhard Bodenschatz. Conductive heat flux in measurements of the Nusselt number in turbulent Rayleigh–Bénard convection. Phys. Rev. Fluids 1 (2016), 062301(R).
Susanne Horn and Olga Shishkina. Rotating non-Oberbeck–Boussinesq Rayleigh–Bénard convection in water. Phys. Fluids 26 (2014), 055111.