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The mathematical model that describes the periodic spouting of a geyser induced by boiling

We have derived and modified the dynamical model of a geyser induced by gas inflow and regular or irregular spouting dynamics of geysers induced by gas inflow has been reproduced by the model. On the other hand, though we have derived the dynamical model of a geyser induced by boiling, periodic change between the spouting state and the pause state has not been adequately modeled by the model. In this connection, concerning a geyser induced by gas inflow we have proposed the model as described below. Because pressure in the spouting tube decreases obeying to the Bernoulli's theorem when the spouting state begins and water in the spouting tube begins to flow, inflow of groundwater into the spouting tube occurs. When the amount of this inflow reaches a certain amount, the spouting state transforms to the pause state. In this study, by applying this idea to the dynamical model of a geyser induced by boiling, the periodic change between the spouting state and the pause state could be reappeared. As a result, the whole picture of the spouting mechanism of a geyser induced by boiling became clear. This research results would give hints on engineering repair in order to prevent the weakening or the depletion of the geyser. And this study would be also useful for protection of geysers as tourism and environmental resources.