High - resolution models of solar granulation : the 2 D case

Using advanced numerical schemes and grid-re nement we present 2D high-resolution models of solar granulation with particular emphasis to down owing plumes. In the high-resolution portion of our simulation, a box measuring 1.97× 2.58 Mm (vertical × horizontal), the grid size is 1.82× 2.84 km. Calculations at the resolution usually applied in this type of simulations amount to only a few horizontal gridpoints for a down owing plume. Due to the increased number of gridpoints in our high resolution domain the simulations show the development of vigorous secondary instabilities of both the plume's head and stem. Below a depth of about 1 Mm the plume produces patches of low density, temperature, pressure and high vorticity which may last for all of our simulation time, ∼ 10 minutes, and probably considerably longer; they may be ascribed to the 2D nature of the present calculations. Centrifugal forces acting in these patches counteract the strong inward pressure. Probably most importantly, the plume's instabilities give rise to acoustic pulses created predominantly down to ∼ 1.5 Mm. The pulses proceed laterally as well as upwards and are ubiquitous. Ultimately most of them emerge into the photosphere. A considerable part of the photospheric `turbulence' in these models is due to those pulses rather than to some sort of eddies. The up ows in granules are smooth where they reach the photosphere from below even in the present calculations; however, the pulses may enter in the photosphere also in granular up ows.