Stratification-induced scale splitting in convection

Abstract

The coexistence of motions on various scales is a remarkable feature of solar convection, which should be taken into account in analyses of the dynamics of magnetic fields. Therefore, it is important to investigate the factors responsible for the observed multiscale structure of solar convection. In this study, an attempt is made to understand how the scales of convective motions are affected by the particularities of the static temperature stratification of a fluid layer. To this end, simple models are considered. The equations of two-dimensional thermal convection are solved numerically for a plane horizontal fluid layer heated from below, in an extended Boussinesq approximation that admits thermal-diffusivity variations. These variations specify the stratification of the layer. The static temperature gradient in a thin sublayer near the upper surface of the layer is assumed to be many times larger than in the remainder of the layer. In some cases, distributed heat sinks are assumed to produce a stably stratified region overlying the convective layer. Manifestations of the scale-splitting effect are noted, which depend on the boundary conditions and stratification; it becomes more pronounced with the increase of the Rayleigh number. Small-scale convection cells are advected by larger-scale flows. In particular, the phase trajectories of fluid particles indicate the presence of complex attractors, which reflect the multiscale structure of the flow. The effect of the stably stratified upper sublayer on the flow scales is also considered.