Non-Boussinesq low-Prandtl number convection with a temperature-dependent thermal diffusivity

In an attempt to understand the role of the strong radial dependence of thermal diffusivity on the properties of convection in sun-like stars, we mimic that effect in non-Oberbeck-Boussinesq (NOB) convection in a horizontally-extended rectangular domain (aspect ratio 16), by allowing the thermal diffusivity $\kappa$ to increase with the temperature (as in the case of stars). Direct numerical simulations (i.e., numerical solutions of the governing equations by resolving up to the smallest scales without requiring any modeling) show that, in comparison with Oberbeck-Boussinesq (OB) simulations (two of which we perform for comparison purposes), the symmetry of the temperature field about the mid-horizontal plane is broken, whereas the velocity and heat flux profiles remain essentially symmetric. Our choice of $\kappa(T)$, which resembles the variation in stars, results in the temperature field that loses its fine structures towards the hotter part of the computational domain, but the characteristic large scale of the turbulent thermal `superstructures', which are structures whose size is typically larger than the depth of the convection domain, continue to be largely independent of the depth.