科研之友
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摘要
Periodic variations in magma discharge rate and ground deformation have been commonly observed during lava dome eruptions. We performed a stability analysis of a conduit flow model by Barmin et al. [Barmin, A., Melnik, O., Sparks, R.S.J., 2002. Periodic behavior in lava dome eruptions. Earth and Planetary Science Letters 199 (1-2), 173-184], in which the periodic variations in magma flow rate and chamber pressure are reproduced as a result of the temporal and spatial changes of the magma viscosity controlled by the kinetics of crystallization. The model is reduced to a dynamical system where the time derivatives of the magma flow rate (dQ/dt) and the chamber pressure (dP/dt) are functions of Q and P evaluated at a shifted time t-t*. Here, the time delay t* represents the time for the viscosity of fluid particle to increase in a conduit. The dynamical system with time delay is approximated by a simple two-dimensional dynamical system of Q and P where t*. is given as a parameter. The results of our linear stability analyses for these dynamical systems indicate that the transition from steady to periodic flow depends on nonlinearities in the steady state relation between Q and P. The steady state relation shows a sigmoidal curve in Q-P phase plane; its slope has negative values at intermediate flow rates. The steady state solutions become unstable, and hence P and Q oscillate periodically, when the negative slope of the steady state relation ([dP/dQ](S)) exceeds a critical value; that is [dP/dQ](S)<t*gamma/ (2V(ch)), where V-ch is the chamber volume and gamma is an elastic constant which is related to the rigidity of chamber wall. We also found that the period and the pattern of oscillation of the conduit flow primarily depend on a quantity defined by LVch/r(4), where L is the conduit length and r is the conduit radius.
- 出版日期2008-11-30
