A THEORY OF ENTRAINMENT IN CONVECTIVE CURRENTS

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Abstract
It is held that entrainment is a necessary dynamic consequence of the vertical stretching of an accelerated convective column. On this basis, equations are developed for the rate of entrainment, the vertical divergence and the lapse rate, for both unsaturated air and cloud air. It is assumed that a steady state exists, the cross section of the rising column is invariant with height, the entrained air is uniformly mixed with the rising air and the environment is at rest. The equations are integrated numerically over height in a number of selected cases. In unsaturated air, entrainment results in a lapse rate which is always greater than the dry adiabatic; if the environmental lapse-rate is superadiabatic, the lapse rate of the rising air is intermediate between the lapse rate of the environment and the dry adiabatic lapse-rate. In a cloud, entrainment results in a lapse rate intermediate between the environmental lapse-rate and the moist adiabatic lapse-rate. The lapse rate of the rising air incre... Abstract It is held that entrainment is a necessary dynamic consequence of the vertical stretching of an accelerated convective column. On this basis, equations are developed for the rate of entrainment, the vertical divergence and the lapse rate, for both unsaturated air and cloud air. It is assumed that a steady state exists, the cross section of the rising column is invariant with height, the entrained air is uniformly mixed with the rising air and the environment is at rest. The equations are integrated numerically over height in a number of selected cases. In unsaturated air, entrainment results in a lapse rate which is always greater than the dry adiabatic; if the environmental lapse-rate is superadiabatic, the lapse rate of the rising air is intermediate between the lapse rate of the environment and the dry adiabatic lapse-rate. In a cloud, entrainment results in a lapse rate intermediate between the environmental lapse-rate and the moist adiabatic lapse-rate. The lapse rate of the rising air incre...

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