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



temperature. Whether this result is true when the disturbance takes place in three 

 dimensions, I have" been unable to discover. 



If it is true, there is a relation K/pv = n/p = \ (wd) between K the eddy conductivity 

 and /at the eddy viscosity ; if any method of deducing /a. from meteorological observa- 

 tions could be found, it would be possible to verify the relation numerically. 



Relation of Observed Velocity to Gradient Velocity. 



We may expect to discern the effect of eddy viscosity in cases where the wind 

 velocity changes with altitude, and where the force due to eddy viscosity prevents the 

 wind from attaining the velocity which we should expect on account of the pressure 

 distribution. These conditions arise near the surface of the earth. The velocity and 

 direction which we should expect on account of the pressure distribution, are called the 

 gradient velocity and the gradient direction. In general, the wind near the ground falls 

 short of the gradient velocity by about 40 per cent., and the direction near the ground 

 is about 20 degrees from the gradient direction. At a height which varies on land 

 from 200 to 1000 metres the wind becomes equal both in velocity and in direction to 

 the gradient wind. 



Let us consider the motion of air over the earth's surface under the action of a 

 constant pressure gradient G acting in the direction of the axis of y. The equations 

 of motions of an imcompressible* viscous fluid aret 



Dt p Sx p 



Dt p cy p 



T)W _ y 1 3 



TA . * ,-. 



Dt p Sz , 



where u, v, w are components of velocity parallel to the co-ordinates x, y, z ; p is the 

 pressure, and X, Y, Z, are the components of the external forces on unit mass of the 

 fluid. 



The forces acting are the force due to the earth's rotation and gravity. 



Hence 



X = 2wv sin \ ~] 



v . I where w is the angular velocity of the 



i Zu>u sin \ > ; 



earth s rotation and \ is the latitude. 



Z= -g J 



The pressure is given by p = constant gpz + Gy. 



* The atmosphere is not incompressible, but compressibility makes no difference in the present 

 itistance. 



t See Lamb's ' Hydrodynamics,' p. 338. 



