The scales of granulation, mesogranulation, and supergranulation

Solar granulation is described as an advection-fragmentation process in the upper layers of the convection zone. The fundamental hydrodynamic unit is the downflow plume, and from its structure the granular scale follows. Moreover, through the collective advective interaction of many small-scale and short-lived granular plumes, large spatial and long temporal mesogranular and supergranular scales naturally arise. We illustrate and examine this process of scale selection using a simplified n-body advective-interaction model. For parameters set by granulation observations and numerical plume simulations, clustering scales remarkably close to observed mesogranulation and supergranulation result.