Periodic magma movement in the conduit with a barrier: A model for the volcanic tremor

We present a one‐dimensional flow model in which compressible viscous fluid runs through the dike‐like conduit with a barrier. The barrier is assumed to open or close above or under a certain threshold pressure, respectively. Constant flow rate at one end and a constant pressure at the other end are set as boundary conditions, which mimicks the fluid flow from a reservoir to an open space. The behaviour of the system depends on various parameters such as viscosity, flow rate and threshold pressure. For a set of parameters plausible for the magma flow in cracks, the system oscillates periodically even in the existence of viscous damping. Spectra of the far field displacement excited by the stress due to this oscillation show a prominent frequency peak in each case. The time interval during which the barrier is kept open (We call the ”open period”) becomes longer, as the flow rate increases. This results in the elongation of peak period expected in the spectra of far field displacement. The length of the open period is affected by both the flow rate and the interference of the pressure waves in the conduit generated by the previous opening‐closure of the barrier. This model may have an important implication for volcanic tremors whose dominant frequency and continuation time change temporarily.