Volcanic Smoke, regarded as Turbulent Motion

Abstract

The gigantic column of volcanic smoke may be regarded as a free jet that gushes out into the semi-infinite atmosphere. The diameter of the vortex-ring in the smoke is nearly proportional to height (Sakurajima 1946), and this means that the average mixture-length (G. I. Taylor’s definition) is proportional to height. Velocity distribution within such a free jet should be: dz/(dt)∽1/z, or z∽t^0・5. Actual examples of rise of explosion-smokes of Asama give the empirical relation z∽t^0・6. Temperature distribution within the jet is expected to be T-T_air∽1/z, if the Prandtl number is taken as 1. Actual T-distributions, measured at several vigorous solfataras, agree well with the relation. Volcanic smokes rise higher nearly in proportion to the initial velocity of the bombs. This is also explained well by the proposed jet-model. The Wolff’s idea, in which the gas is assumed to expand “adiabatically” needs alterations. Volcanic smoke is the phenomenon which should be treated as turbulent motion. The buoyancy of gas, the effect of which was not taken into account explicitly in the present theory, should be considered too.