5:15 PM - 7:15 PM
[SVC32-P11] Investigation of the relationship between the oscillation characteristics of harmonic tremors and fluid flow
Keywords:Volcanic earthquake, Harmonic tremor, Nonlinear oscillation, Shallow fluid system
Various types of earthquakes occur in shallow regions of active volcanoes. One phenomenon that reflects the flow of volcanic fluids in shallow fluid systems is harmonic tremors. Understanding the generation mechanism of harmonic tremors is thus important for revealing the detail of shallow hydrothermal pathways and fluid movement within them. At Mt. Azuma, located on the border between Yamagata and Fukushima prefectures, harmonic tremors suggesting the fluid movement within shallow hydrothermal system were intermittently observed in 2023. The phase portrait, depicting velocity and displacement relation, exhibits a transition in the trajectory during a single event. This suggests a non-stationary phase change of the wave, which is a characteristic of nonlinear oscillation. In addition, the value of correlation dimension of the oscillation, estimated by the Grassberger-Procaccia algorithm, saturates to a non-integer value as the reconstruction dimension of the oscillation increases. These results confirm that the harmonic tremor is not a linear phenomenon like resonance, but a nonlinear phenomenon like self-excited oscillation due to fluid flow. (Hirayama and Yamamoto, JpGU2024). In this study, as a model of the oscillation source of harmonic tremors, we consider a one-dimensional fluid flow driven by a pressure gradient in a channel with an elliptical cross section proposed by Ozaki et al. (2023) and investigate the relationship between the oscillation characteristics of harmonic tremors and model parameters such as channel geometry and pressure gradient.
In this study, we consider the fluid flow in a channel with an elliptical cross section placed in an elastic medium, and resultant oscillation of the channel wall. The fluid flow is caused by the pressure gradient between upstream and downstream sides of the channel. Here, we set model parameters assuming low viscosity and high compressibility fluid such as hydrothermal fluid, referring to the oscillation characteristics of observed waveforms at Mt. Azuma and previous studies. Next, we analyzed the dependence of the oscillatory characteristics on pressure gradient, length of the channel, and cross-sectional shape by varying each of the model parameters such as length of the channel, length of the major and minor axes of the elliptical cross section, and upstream and downstream pressures, which are related to the flow characteristics and the geometry of the channel. The fluid flow and deformation of the channel wall are obtained by numerically solving the governing equation system using predictor-corrector method.
In this channel flow model, the velocity of the fluid along the channel and the normal displacement of the channel wall mainly controls the characteristics of the resultant oscillations. Therefore, we considered following two cases: In the first case, to examine the control parameters in the flow direction, the length of the channel was varied while both cross-section and pressure gradient of the channel were kept constant; in the second case, to examine the control parameters in the perpendicular direction to the flow, the cross-sectional area of the channel was varied while aspect ratio of the cross-section was kept constant. As a result, it is found that the channel length has a larger impact on the oscillation amplitude of the flow velocity compared to the cross-sectional area. In terms of the oscillation frequency, the proportional coefficient of the fundamental frequency of the oscillation to the channel length is about six times larger than that to the change in the cross-sectional area.
Our results so far indicate that the oscillatory characteristics of the flow-induced oscillation strongly depend on the length of the flow channel, and suggest that the main characteristics of the oscillation, such as the fundamental frequency, could be modeled by adjusting the dimension of the flow channel. On the other hand, nonlinear characteristics such as changes in the phase and phase diagram of the harmonic tremors observed at Mt. Azuma, would be controlled by the deformation of the channel wall normal to the flow direction. Based on information such as dominant frequencies, characteristics of phase diagrams, and correlation dimensions, we are going to investigate and understand the hydrothermal system that generates the observed harmonic tremors.
In this study, we consider the fluid flow in a channel with an elliptical cross section placed in an elastic medium, and resultant oscillation of the channel wall. The fluid flow is caused by the pressure gradient between upstream and downstream sides of the channel. Here, we set model parameters assuming low viscosity and high compressibility fluid such as hydrothermal fluid, referring to the oscillation characteristics of observed waveforms at Mt. Azuma and previous studies. Next, we analyzed the dependence of the oscillatory characteristics on pressure gradient, length of the channel, and cross-sectional shape by varying each of the model parameters such as length of the channel, length of the major and minor axes of the elliptical cross section, and upstream and downstream pressures, which are related to the flow characteristics and the geometry of the channel. The fluid flow and deformation of the channel wall are obtained by numerically solving the governing equation system using predictor-corrector method.
In this channel flow model, the velocity of the fluid along the channel and the normal displacement of the channel wall mainly controls the characteristics of the resultant oscillations. Therefore, we considered following two cases: In the first case, to examine the control parameters in the flow direction, the length of the channel was varied while both cross-section and pressure gradient of the channel were kept constant; in the second case, to examine the control parameters in the perpendicular direction to the flow, the cross-sectional area of the channel was varied while aspect ratio of the cross-section was kept constant. As a result, it is found that the channel length has a larger impact on the oscillation amplitude of the flow velocity compared to the cross-sectional area. In terms of the oscillation frequency, the proportional coefficient of the fundamental frequency of the oscillation to the channel length is about six times larger than that to the change in the cross-sectional area.
Our results so far indicate that the oscillatory characteristics of the flow-induced oscillation strongly depend on the length of the flow channel, and suggest that the main characteristics of the oscillation, such as the fundamental frequency, could be modeled by adjusting the dimension of the flow channel. On the other hand, nonlinear characteristics such as changes in the phase and phase diagram of the harmonic tremors observed at Mt. Azuma, would be controlled by the deformation of the channel wall normal to the flow direction. Based on information such as dominant frequencies, characteristics of phase diagrams, and correlation dimensions, we are going to investigate and understand the hydrothermal system that generates the observed harmonic tremors.