The goal of this project is to understand convection in the Sun. Approximately 0.7 to 1 solar radius (the convective zone) is turbulent plasma driven by thermal convection. This convection is very different from the convection that has been studied extensively in laboratory and computers. Variables such as pressure, mass density, and temperature vary over several orders of magnitude within the convective zone . Intriguingly, the most significant changes happen within a very thin layer (less than 3% of solar radius) near the visible surface (photosphere) of the Sun. Within this region, convection is turbulent, dominated by radiative transport of heat out of the Sun, and the solar plasma is strongly influenced by the effects of ionization and molecular disassociation . Our goal is to understand the convection within this region. We believe to do this it is not sufficient to study convection with parameters as close to the Sun as possible but it is necessary to understand properties of turbulent radiative convection in general. In studies of turbulent Rayleigh-Benard convection (RBC) the non-dimensional temperature difference across the domain is called the Rayleigh number the non-dimensional turbulent heat flux is called the Nusselt number. Over the last three decades the central question in studies of RBS has been : how does the Nusselt number depend on the Rayleigh number ? It has now been elucidated that the answer to this question depends crucially on boundary layers near the top and bottom of the domain. In the Sun the boundary condition to the convection in the top layers is controlled by radiation. Which implies that a very different kind of boundary layer is present. Hence to understand solar convection we must understand how radiative boundary layer affects the turbulent transport of heat flux.
With this motivation we list the key questions we shall try to address :
(A) How does the Nusselt number depend on the Rayleigh number ?
(B) What are the statistical properties of the fluctuations of the heat flux ?
(C) How well can the simulations capture the pressure waves observed in the Sun ?
(D) The rapid radiative cooling typically gives rise to strongly concentrated downward flow of cold plasma and broad rising flow of the warmer plasma. This gives rise to typical granulation patterns. Our goal will be to detect and analyze such patterns at different depths and scales using Principal Component Analysis (PCA).
Our workhorse is the pencil-code (https://github.com/pencil-code) which already runs in Dardel. Radiative convection, with parameters appropriate for the Sun, has been already studied with this code by the group of Piyali Chatterjee .
The project is a preparation for a future larger project, to study magneto-convection in the Sun.
 Schumacher and Sreenivasan, Reviews of Modern Physics, 92, 2020.
 Nordlund and Stein, Living Reviews in Solar Physics, 6, 2019.
 S Dey, P Chatterjee, M OVSN, MB Korsós, J Liu, CJ Nelson, R Erdélyi
Nature Physics, 1-6, 2022.