Subgrid Scale Modeling in Solar Convection Simulations using the ASH Code
The turbulent solar convection zone has remained one of the most challenging and important subjects in physics. Understanding the complex dynamics in the solar con- vection zone is crucial for gaining insight into the solar dynamo problem. Many solar observatories have generated revealing data with great details of large scale motions in the solar convection zone. For example, a strong di erential rotation is observed: the angular rotation is observed to be faster at the equator than near the poles not only near the solar surface, but also deep in the convection zone. On the other hand, due to the wide range of dynamical scales of turbulence in the solar convection zone, both theory and simulation have limited success. Thus, cutting edge solar models and numerical simulations of the solar convection zone have focused more narrowly on a few key features of the solar convection zone, such as the time-averaged di erential rotation. For example, Brun & Toomre (2002) report computational finding of differential rotation in an anelastic model for solar convection. A critical shortcoming in this model is that the viscous dissipation is based on application of mixing length theory to stellar dynamics with some ad hoc parameter tuning. The goal of our work is to implement the subgrid scale model developed at CTR into the solar simulation code and examine how the differential rotation will be a affected as a result. Specifically, we implement a Smagorinsky-Lilly subgrid scale model into the ASH (anelastic spherical harmonic) code developed over the years by various authors. This paper is organized as follows. In x2 we briefly formulate the anelastic system that describes the solar convection. In x3 we formulate the Smagorinsky-Lilly subgrid scale model for unstably stratifed convection. We then present some preliminary results in x4, where we also provide some conclusions and future directions.