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

Abstract

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.

17 pages, 13 figures

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Cited by in corpus (11)

• Combined particle image velocimetry and thermometry of turbulent superstructures in thermal convection
• Convective mesoscale turbulence at very low Prandtl numbers
• Thermal boundary condition studies in large aspect ratio Rayleigh-Bénard convection
• Non-Boussinesq convection at low Prandtl numbers relevant to the Sun
• Similarities between characteristics of convective turbulence in confined and extended domains
• Effect of boundary conditions in turbulent thermal convection
• Strongly superadiabatic and stratified limits of compressible convection
• Turbulent mesoscale convection in the Boussinesq limit and beyond
• Large-scale circulations in a shear-free convective turbulence: Mean-field simulations
• Compressible turbulent convection: The role of temperature-dependent thermal conductivity and dynamic viscosity
• Molecular hints of two-step transition to convective flow via streamline percolation