G. I. TAYLOR ON EDDY MOTION IN THE ATMOSPHERE. 3 



of the layer from which it originated, the potential temperature at the point xyz 

 at time t is 8 (z , t ). 



The amount of heat which passes per second across the area A is therefore 



pa- ivQ. (z ( ) dx dy. Now 6 (z , t ) may be expressed in the form 



provided that the changes in Q in the height z z and in the time t t a are small 

 compared with 6. Hence 



wB (z , t ) dxdy = 6 (z, t) wdxdy + ^- \\--w (z -z) dxdy+ ~ \\ w (t -t) dxdy. 



JJA. JJA dZ JJA Ct JJA. 



Now t is necessarily negative, and since II wdxdy = it is evident that a 

 positive value of w occurs as often as a negative one ; hence if the eddy motion is 

 uniformly distributed w (t t) dxdy = 0. 



The rate at which heat crosses the plane is therefore 



-pa- 7T- jj w (z-z ) dxdy. 

 The rate at which heat crosses an area A at height z + <5z is 



p T ( -~-^-Sz) I w(z-z )dxdy for w(z-z (> )dxdy 



\ dz d Z /JJA JJA 



does not vary with z if the eddy motion is uniformly distributed. Hence the rate 

 at which heat enters the volume A.Sz is 



/oo-^-j <5z w (z-Zo) dxdy. 

 dz JJA 



Now since mixtures which take place within this volume merely alter the 



distribution of the heat contained in it without affecting its amount, this must be 

 o/j 



equal to pa- A.Sz. Hence we obtain the equation for the propagation of heat by 

 ct 



means of eddies in the form ^- = -,- w (z z ) dx dy. But -p w (z z ) dx dy 



ct cz A. JJA. AJJA 



is the average value of w (z z ) over a horizontal area, hence it may be expressed 

 in the form \ (wd), where d is the average height through which an eddy moves 

 from the layer at which it was at the same temperature as its surroundings, to 

 the layer with which it mixes, w is defined by the relation \ (wd) = average 

 value of w (z z ) over a horizontal plane; it roughly represents the average 



B 2 



