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The recently discovered resonant drag instability of dust settling inprotoplanetary disc is considered as the mode coupling of subsonic gas-dustmixture perturbations. This mode coupling is coalescence of two modes withnearly equal phase velocities: the first mode is inertial wave having positiveenergy, while the second mode is a settling dust wave (SDW) having negativeenergy as measured in the frame of gas environment being at rest in verticalhydrostatic equilibrium. SDW is a trivial mode produced by the bulk settling ofdust, which transports perturbations of dust density. The phase velocity of SDWis equal to the bulk settling velocity times the cosine of the angle formed bythe wave vector and the rotation axis. In this way, the bulk settling of dustmakes possible the coupling of SDW with the inertial wave and the onset of theinstability. In accordance with the concept of the mode coupling, theinstability growth rate is proportional to the square root of the dispersionequation coupling term, which itself contains the small mass fraction of dustin gas-dust mixture, the squared radial wavenumber of the modes, and thesquared bulk settling velocity. Thus, the higher is the bulk settling velocity,the heavier clumps of dust can be aggregated by the instability of the samerate.

Interpretation of the resonant drag instability of dust settling in protoplanetary disc