\label{drag+gradP}$$ The first physical ingredient we wish to mention is rotational dynamics, whose necessity has been shown in §3. We have already mentioned in §2.3 that a geostrophic balance is established, by which Coriolis forces essentially balance the pressure force. The other physical ingredient is the background solid-to-gas drift (due to the pressure gradient), as noted in §2.2. Mathematically, a nonzero drift is required for particle density to affect the dynamics, as, in the reduced system, this can only happen through the “buoyancy force term” (proportional to the pressure gradient) in the gas continuity equation as mentioned in §2.2, which contributes to the advection term discussed in §4.2. We suggest that the physical explanation for this is that relative drift between the pressure maximum and the dust allows the former to sweep a (radial) “headwind” of particles and be an effective “trap” for the dust.

We note that the processes discussed in the previous paragraph are restricted to the $x$-$y$ plane and emphasise radial drifts and gradients. The fact that the reduced model seems to emphasise vertical gradients—although the leading-order growth rate given by equation is negatively correlated with $k_z$—may be interpreted as resulting from incompressibility, as radial velocity perturbations 