  We extend the notion of a shell model to stratified systems, and propose one
that represents stratified, nonmagnetic, nonrotating convection at low Mach
number. Motivated by profiles of background stratification that support
convection in stars such as the Sun, we study numerical solutions corresponding
to a highly unstable layer above a mildly unstable layer. We find that at low
Prandtl number, convective amplitudes decrease with depth in the lower layer.
This suggests that the suppression of convection in the deeper layers of the
Sun's convection zone (the convective conundrum) can be addressed without
necessarily appealing to rotation or magnetic fields.
