SOME MEASUREMENTS OF ATMOSPHERIC TURBULENCE. 
3 
in the paper already cited (p. 13), and the conclusion is reached that such an 
occurrence would be highly improbable. 
The relation of £ to the eddy-viscosity is most easily reached via terms 3 m x /dt, 
dniy/dt in the dynamical equations. If pressure-gradient just balanced geostrophic 
wind we should have ^ 
3 ( xh) __ 3 m x />\ 
3 h ~ ~ht . K ’ 
Now by the definition of viscosity given above 
xh = /j. . dv x /dh .(7) 
Substituting (7) in (6) and inserting m x = pv x there results 
l " If} = IV. (8) 
p c/i L oh J at 
It is seen that this equation becomes identical with (l) if 
X = v x and $ = g*py, .(9) 
of which the latter is the required relation. 
On comparing equations (8) and (3), it is seen that eddy-viscosity, p, and eddy- 
conductivity, c, are of the same dimensions, and appear in their respective differential 
equations in the same way. Indeed, Taylor has suggested that they are equal.* 
This likeness would be a good argument for recording observations in terms of these 
two quantities instead of in terms of diffusivity K or turbulivity £ 
II. Shearing Stress from Pilot Balloon Observations. 
( Condensed and revised January 22, 1920.) EkmanI' in a remarkable paper 
pointed out that the total momentum of water produced by a tangential stress on 
the surface of the sea, in the steady state, is directed at right angles to the tangential 
stress, and its amount is quite independent of the value of the viscosity or of the 
variation of viscosity with depth. The same applies to the atmosphere. We may 
use this principle to find the shearing stress on the ground, provided we have a 
measure of what the momentum would be if the surface stress were zero. 
I have taken the wind at a height of l4 km. to 2|- km. as the standard of 
reference, because, by so doing, the term depending on curvature of path, and other 
small terms in the dynamical equations, are automatically allowed for to a first 
approximation. The stress at 2 km. is undoubtedly much less than that on the 
ground, and is neglected. It is best to select observations in which the momentum 
becomes nearly independent of height above U5 km. A table of results follows. 
They were computed with the help of Mrs. L. F. Kichardson. Dr. H. Jefferys 
says the selection will select abnormal lapse-rates and so abnormal viscosities. 
* ‘Phil. Trans.,’ A, vol. 215, p. 22. 
t “ On the Influence of the Earth’s Rotation on Ocean Currents,” by V. W. EKMAN, ‘ Arkiv for Matem. 
Astr. och Fysik,’ Stockholm, Bd. II., No. 11 (1905). 
B 2 
