Condensation in 'cloud is studied to
demonstrate certain general characteristics, without special assumptions about
the condensation nuclei or the vertical velocity. The equation of growth of a
droplet is constructed, taking account of ventilation due to its falling
velocity. Lifting is assumed to occur adiabatically. An approximate value is
found for the supersaturation of cloud air, which under certain conditions can
be computed from observable quantities-the cloud droplet spectrum and the
vertical velocity. Growth of drops at small sizes is very rapid : at constant
supersaturation, in a period of a few seconds, a drop in general either grows
beyond r= 1μ, or else comes so close to equilibrium at some smaller size
that growth practically ceases. When the supersaturation is moderate or large,
a threshold effect appears : the size of the condensation nucleus determines
whether or not the drop shall grow, but, if it does, has little influence on
its final size. The definition of the size of a small condensation nucleus is
reviewed and a more precise interpretation is suggested.
An attempt is made to explore the causes of the differences in microstructure between the Hawaiian orographic cloud, maritime cumuli and continental cumuli, observations on which were discussed in Part I of this series.
A model of a cumulo-nimbus updraught is presented, based on a steady-state, turbulent, condensing plume, entraining environmental air according to the simple law that the inflow velocity at any height is proportional to the upward velocity of the plume.
With this model, the shape of the cloud as well as its other properties follow from the dynamics, and cloud development is size-dependent. The virtual temperature excess at cloud base is taken as zero; this seems the only appropriate assumption for a steady-state plume model. The thermodynamical treatment is made with few approximations, and the effect of freezing on the dynamics is included in a simple fashion. Some preliminary calculations result in realistic cloud shapes and reasonable values for the internal properties.
Observations of cumuli have shown that the adiabatic model is quite inadequate, and that dry air must mix with the condensing upcurrent. Theories of the interaction between cumuli and their environment are discussed. The hypothesis that dry air enters these clouds chiefly from above is examined quantitatively. It is found that, as a result of evaporative cooling, such air could penetrate several kilometres into a growing cloud. This hypothesis accounts for the fine structure which is observed, and provides a natural and simple explanation for the fact that the lapse rate in cumuli is steeper than the wet adiabatic, and indeed approximates closely to that of the environment. Unlike alternative theories, it provides a means whereby the liquid water content may be automatically self-limiting, as the observations seem to require, for the motions which introduce dry air deep into the cloud depend for their energy supply on the presence of liquid water, and have velocities which are roughly proportional to its concentration.
A model of a cumulo-nimbus updraught is presented, based on a steady-state, turbulent, condensing plume, entraining environmental air according to the simple law that the inflow velocity at any height is proportional to the upward velocity of the plume.With this model, the shape of the cloud as well as its other properties follow from the dynamics, and cloud development is size-dependent. The virtual temperature excess at cloud base is taken as zero; this seems the only appropriate assumption for a steadystate plume model. The thermodynamical treatment is made with few approximations, and the effect of freezing on the dynamics is included in a simple fashion. Some preliminary calculations result in realistic cloud shapes and reasonable values for the internal properties.
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