PHILOSOPHICAL TRANSACTIONS. 



I. Eddy Motion in the Atmosphere. 

 By G. I. TAYLOR, M.A., Schuster Reader in Dynamical Meteorology. 



Communicated by W. N. SHAW, Sc.D., F.R.S., Director of the Meteorological 



Office. 



Received April 2, Read May 7, 1914. 



OUR knowledge of wind eddies in the atmosphere has so far been confined to the 

 observations of meteorologists and aviators. The treatment of eddy motion in 

 either incompressible or compressible fluids by means of mathematics lias always 

 been regarded as a problem of great difficulty, but this appears to be because 

 attention has chiefly been directed to the behaviour of eddies considered as indi- 

 viduals rather than to the average effect of a collection of eddies. The difference 

 between these two aspects of the question resembles the difference between the 

 consideration of the action of molecule on molecule in the dynamical theory of gases, 

 and the consideration of the average effect, on the properties of a gas, of the motion 

 of its molecules. 



It has been known for a long time that the retarding effect of the surface of 

 the earth on the velocity of the wind must be due, in some way, to eddy motion ; 

 but apparently no one has investigated the question of whether any known type 

 of eddy motion is capable of producing the distribution of wind velocity which has 

 been observed by meteorologists, and no calculations have been made to find out 

 how much eddy motion is necessary in order to. account for this distribution. The 

 present paper deals with the effect of a system of eddies on the velocity of the 

 wind and on the temperature and humidity of the atmosphere. In a future paper 

 the way in which they are produced and their stability when formed will be 

 considered. 



It is well known that wind velocity, temperature, and humidity vary much 

 more rapidly in a vertical than in any horizontal direction, and further that the 

 vertical component of wind velocity is very small compared with the horizontal 

 velocity. It has been assumed, therefore, that the average condition of the air 

 at any time is constant for a given height, over an area which is large compared 

 with the maximum height considered. If u and v represent the components of 

 undisturbed wind velocity parallel to horizontal axes, x and y, running from South 



VOL. CGXV. A 523. B [Published January 21, 1915. 



