An idealized model for dust-gas interaction in a rotating channel

Abstract

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.