  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.
