2 
ME. LEWIS' F. RICHARDSON ON 
It is suggested that f might be named “ the turbulivity.” Its dimensions are: 
(mass) 2 x (length) -2 x (time) -6 . 
The advantage of using f instead of K is that the former enables one to allow for 
variations of density and of turbulence in a simple and natural manner. The 
disadvantage of £ is that it has no name derivable from indoor physics. It is suited 
to the free atmosphere. We might compromise by using in place of K or f the 
“ eddy-conductivity,” c, defined by the equation 
5 (px) 
dt 
dh 
or. approximately, | =LL(oI). ... (3) 
In so doing we gain an acceptable name “ conductivity,” but we lose by the explicit 
appearance of density in the equation. Either c or f allows variations of turbulence 
with height to be treated correctly, while K does not do so, as has been pointed out 
elsewhere by the author.* The dimensions of c are (mass) x (length) -1 x (time) -1 . 
This c is of the same dimensions as the measure of turbulence discussed by 
W. Schmidt, of Vienna, under the name of “ Austausch ” in two important papers. 
(‘Sitz. Akad. Wiss.,’ Wien, 1917 and 1918.) 
However much turbulence and density may vary with height 
.(4) 
g P G = & • • 
On the contrary if there are no variations with height, 
c = pK. . . . 
(5) 
The six components of stress are denoted by xx, yy, hh, xy, yh, hx, as in the writings 
of K. Pearson. 
The convention adopted for the signs of eddy-stresses conforms to that of Love’s 
“ Theory of Elasticity.” Tractions are reckoned positive. That is to say, a direct 
stress such as xx is positive if it be a tension, negative if a pressure; and a shearing 
stress such as xh is positive when the air on that side of a level surface for which h is 
greater (i.e., above), drags the air below in the sense of x increasing. 
The definition of eddy-viscosity adopted in this paper is 
eddy shearing stress 
rate of mean shearing strain 
(A) 
in agreement with the definition used by W. Schmidt ( loc. cit., 1917, p. 5). 
The advantage of this definition is that it is simply based on the fundamental ideas 
of stress and strain, as well as being in harmony with the definition adopted in the 
theory of viscous liquids. ( cf. , Lamb, ‘Hydrodynamics,’ IV. edn., § 326). 
The question may arise as to whether the viscosity defined by (A) can ever become 
infinite by the vanishing of the denominator. The point is discussed by the author 
* Loc. cit , 
