A general model for Mt. Ruapehu lahars |
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| Authors: | Marianne Vignaux Graham J Weir |
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| Institution: | (1) Applied Mathematics Division, Department of Scientific and Industrial Research, P.O.Box 1335, Wellington, New Zealand |
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| Abstract: | A mathematical model of the motion of lahars is presented. Lahar flows and travel speeds are calculated using a kinematic wave model which equates gravitational accelerations to frictional losses. A chezyor Manning-type law of friction is assumed, in which lahar flow rate is a simple power function of lahar depth, multiplied by another simple power of the chanel slope. Use of the model requires knowledge of essentially only one parameter which appears to be relatively insensitive for flows down a given channel. Variable channel slope effects are removed by a longitudinal scaling which applies to all flows down a given channel. For lahars generated by a single explosive event it is unnecessary to perform numerical calculations to predict lahar flow and travel time, but for lahnars produced by multiple sources in which different lahar flows are interacting, numerical calculations appear necessary. The model is applied to all recorded lahar flows from Mt. Ruapehu, and satisfactorily described all lahar flows generated by a single explosive mechanism. Such flows depend essentially only on total lahar volume. The 1968 Mt. Ruapehu lahar, generated by a series of smaller eruptive mechanisms, was modelled as the interaction of seven point sources of fluid originating from positions mathematically extrapolated up the mountain. Good agreement was obtained between the predicted times of formation of these 1968 lahars, and the times of greatest seismic amplitude. |
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