3D Simulations of Semiconvection in Spheres: Turbulent Mixing and Layer Formation

Abstract

Semiconvection occurs in regions of stars and planets that are unstable to overturning convection according to the Schwarzschild criterion, yet stable according to the Ledoux criterion. Previous simulations in Cartesian boxes have advanced our understanding of the semiconvective instability, layer formation, and transport properties. However, much less is known about semiconvection in spherical geometry and under the influence of rotation or magnetic fields. We present 3D simulations of semiconvection in the full sphere (including $r=0$), and accounting for rotation. We find that the formation and evolution of semiconvective layers in nonrotating spheres occurs in a similar way to nonrotating Cartesian boxes, in the sense that the critical density ratio at which layers are expected to form is approximately the same in both geometries. Layers rapidly merge once they form, ultimately leading to a fully mixed convective sphere. The transport properties measured through the Nusselt numbers and the buoyancy flux ratio are also similar to results from previous studies in boxes. When rotation is added to the system, layer formation and evolution proceeds in a similar fashion to the nonrotating runs. However, rotation hampers the radial transport of heat and composition, and, as a result, the time required for the sphere to become fully mixed gets longer as the flow becomes more rotationally constrained. We also find that semiconvective layers exhibit spherical mixing in nonrotating cases, whereas in rotating cases, the mixing becomes more cylindrical. We discuss what is needed for future work to build more realistic models.