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Re: What keeps clouds up?



I didn't quite follow all of Leigh's post on the falling cloud problem. I
did not see Hewitt's TPT explanation so I'm not sure what you are objecting
to. Did Hewitt neglect the role of evaporation at the cloud base or what?

Whether or not the terminal velocity is entirely negligible for the physics
of cloud dynamics or not may depend on both the size of the of the droplets
involved as well as on the overall speed of the ambient air motions. By
application of Stoke's law we can find the terminal velocity of the droplets
and we find that their terminal speed is proportional to the square of their
radius. If for convienience we take the air temperature to be about 0 deg. C
so its viscosity is about 1.7 x 10^(-5) kg/(ms) then the terminal speed of
a droplet is 1.3 x 10(-6) m/s if its radius is only 100 nm, but this size is
so small that it is smaller than many/most condensation nuclei. If the
droplet radius is 1 micron then the terminal speed is 0.13 mm/s. If the
droplet radius is 10 microns then the terminal speed it 1.3 cm/s. If the
droplet radius is 100 microns then the terminal speed is 1.3 m/s. If the
droplet radius is much larger than this then Stoke's law breaks down badly
(due to the larger Reynolds number which invalidates Stoke's assumptions)
and a more sophisticated air resistance model is needed. For larger drizzle
and raindrop sizes the terminal speed becomes proportional to the square root
of the radius once the air friction is proportional to the square of the
speed rather than the first power of the speed. Once we get to big
raindrops, however, their shape is flattened out of round by the air
resistance and a sophisticated model for the drag coefficient as a function
of size and shape is then needed to predict the terminal speed.

Notice that it is possible for some of the larger droplets to fall as fast as
about 1 m/s. I would not consider this speed utterly negligible, and it may
even show up in binoculars. Admittedly, not many droplets get as big as 100
microns in radius and remain in the cloud for long. They fall so fast wrt
the surrounding droplets that they sweep up all the other droplets in their
path which makes them fall even faster. They thus grow into a drizzle or
rain drop and eventually fall out of the cloud as precipitation or virga.

David Bowman
dbowman@gtc.georgetown.ky.us