Concerning the multiscale structure of solar convection

The discrete scale spectrum of the convective flows observed on the Sun has not yet received a convincing explanation. Here, an attempt is made to find conditions for the coexistence of convective flows on various scales in a horizontal fluid layer heated from below, where the thermal diffusivity varies with temperature in such a way that the static temperature difference across a thin sublayer near the upper surface of the layer is many times larger than the temperature variation across the remainder of the layer. The equations of two-dimensional thermal convection are solved numerically in an extended Boussinesq approximation, which admits thermal-diffusivity variations. The no-slip conditions are assumed at the lower boundary of the layer; either no-slip or free-slip conditions, at the upper boundary. In the former case, stable large-scale rolls develop, which experience small deformations under the action of small structures concentrated near the horizontal boundaries. In the latter case, the flow structure is highly variable, different flow scales dominate at different heights, the number of large rolls is not constant, and a sort of intermittency occurs: the enhancement of the small-scale flow component is frequently accompanied by the weakening of the large-scale one, and vice versa. The scale-splitting effects revealed here should manifest themselves in one way or another in the structure of solar convection.