Buoyant plumes in a moist atmosphere

Abstract

This paper describes a simple model which can be used to investigate the transport of water vapour by thermal plumes in the atmosphere. For an approximate treatment of these plumes, it is assumed (as in a previous paper) that the vertical velocity, temperature and specific humidity are constant across the ascending column, and that the inflow velocity due to mixing at the edge of the plume is proportional to the vertical velocity within the plume. The behaviour of the rising air is then investigated by means of equations representing the conservation of mass, momentum, heat and water vapour, and numerical solutions are obtained for representative cases.It is shown that in a stably stratified atmosphere the plume air will become saturated if the source is sufficiently strong, and that the height of this saturation level can be determined in terms of dimensionless parameters representative of the source and the environment. Above the saturation level the analysis is continued by taking into account both vapour and liquid phases of water, and an approximate treatment is given for the behaviour of small plume clouds. It is found that there is a critical size for these; smaller clouds remain characteristic of the plume, but larger ones extend upwards to heights which do not depend on the previous parameters.