  A 2D model representing the dynamical interaction of dust and gas in a
planetary channel is explored. The two components are treated as
interpenetrating fluids in which the gas is treated as a Boussinesq fluid while
the dust is treated as pressureless. The only coupling between both fluid
states is kinematic drag. The channel gas experiences a temperature gradient in
the spanwise direction and it is adverse the constant force of gravity. The
latter effects only the gas and not the dust component which is considered to
free float in the fluid. The channel is also considered on an f-plane so that
the background vorticity gradient can cause any emerging vortex structure to
drift like a Rossby wave. A linear theory analysis is explored and a nonlinear
amplitude theory is developed for disturbances of this arrangement. It is found
that the presence of the dust can help generate and shape emerging convection
patterns and dynamics in the gas so long as the state of the gas exceeds a
suitably defined Rayleigh number appropriate for describing drag effects. In
the linear stage the dust particles collect quickly onto sites in the gas where
the vorticity is minimal, i.e. where the disturbance vorticity is anticylonic
which is consistent with previous studies. The nonlinear theory shows that, in
turn, the local enhancement of dust concentration in the gas effects the vigor
of the emerging convective roll by modifying the effective local Rayleigh
number of the fluid. It is also found that without the f-plane approximation
built into the model the dynamics there is an algebraic runaway caused by
unrestrained growth in the dust concentration. The background vorticity
gradient forces the convective roll to drift like a Rossby wave and this causes
the dust concentration enhancements to not runaway.
