The feasibility of generating low-frequency volcano seismicity by flow through a deformable channel

Oscillations generated by flow of magmatic or hydrothermal fluids through tabular channels in elastic rocks are a possible source of low-frequency seismicity. We assess the conditions required to generate oscillations of approximately 1 Hz via hydrodynamic flow instabilities (roll waves), flow-destabilized standing waves set up on the elastic channel walls (wall modes), and unstable normal modes ringing in an adjacent fluid reservoir (clarinet modes). Stability criteria are based on physical and dimensional arguments, and discussion of destabilized elastic modes is supplemented with laboratory experiments of gas flow through a channel in a block of gelatine, and between a rigid plate and a rubber membrane. For each of the mechanisms considered, oscillations are generated if flow speeds exceed a critical value. Roll waves are waves of channel thickness variation that propagate in the direction of flow and are equivalent to traveling crack waves. The convective instability criterion is that the flow is faster than those travelling waves. Similarly, wall modes and clarinet modes require that the flow speed exceeds a critical value related to a wave speed (e.g. elastic or acoustic wave) multiplied by a geometrical factor. Flow destabilized modes offer a plausible explanation for low-frequency volcano seismicity, but there are limitations on what kind of standing waves comprises them.