How Much Can Theoretical Models of Compressible Convection Tell Us about Solar Granulation

Many hydrodynamic models of solar convection have been developed to study and discuss granulation and the interaction of convection and magnetic fields. They have not, however, been extensively applied to mesogranulation, supergranulation or oscillations in sunspots. In this paper both the modal expansion technique and finite difference models are examined in the application of the fully compressible equations of hydrodynamics to solar granulation. The linear theory of convective motions only gives limited information and in particular does not give the preferred spatial scales of motion that are observed. The non-linear integrations are able to reproduce the dynamic characteristics of granulation such as vertical and horizontal velocities, intensity fluctuations, energy transport and the lifetime to a good degree. This agreement is over a large range of cell sizes. Particular attention will be paid to how well each method treats each of the observed features.