2 Q. I. TAYLOR ON EDDY MOTION IN THE ATMOSPHERE. 



to North and from West to East respectively, and if T and m represent the 

 average temperature and the average amount of water vapour per cubic centimetre 

 of air, this is equivalent to assuming that u, v, T, and m are functions of z, the 

 height, and t, the time ; and that they are independent of x and y. 



Vertical Transference of Heat by Eddy Motion. 



Let us first consider the propagation of heat in a vertical direction. The ordinary 

 conductivity of heat by molecular agitation is so small that no sensible error will 

 be introduced by leaving it out of the calculations. The only way in which 

 large quantities of heat can be conveyed upwards or downwards through the 

 atmosphere is by means of a vertical transference of air which retains its heat as 

 it passes into regions where the temperature differs from that of the layer from 

 which it started. If T' and ' represent the temperature and the vertical component 

 of the velocity of the air at any point, the rate at which heat is propagated 



across any horizontal area is j I ptrT'w' (If dij where t > and <r are the density and 

 specific heat respectively, and the integral is taken over the area in question. 



Since there is no vertical motion of the air as a whole pw' dx dy = 0. Hence, in 



order that heat may be conveyed downwards, the air at any level must be hotter 

 in a downward than in an upward current. In order that this may be the case 

 the potential temperature* of the air must increase upwards. The excess of 

 temperature in a downward current over the mean temperature at any level will 

 depend partly on the vertical distance through which the air has travelled since 

 it was at the same temperature as its surroundings, and partly on the rate of 

 change in potential temperature with height. If the hot air, after crossing the 

 horizontal area, continues on its downward course with undiminished velocity and 

 without losing heat, and if the mean potential temperature continues to decrease 

 downwards, the rate of transmission of heat across a horizontal area will continually 

 increase. On the other hand, if the air returns across the area without losing its 

 heat, there will be no resultant transmission of heat at all. The air must lose its 

 heat by mixture with surrounding air after crossing the area. 



Consider now the transference of heat across a large horizontal area A at a 

 height z. Suppose that at a time t an eddy broke away from the surrounding air 

 at height z and arrived at the point xyz at time t; z and t are then functions 

 of x, y, z, and t. Suppose that initially the eddy had the same temperature as its 

 surroundings. Let 6 (z, t) be the average potential temperature of the air in the 

 layer at height z at time t ; then since the air preserves the potential temperature 



* Potential temperature is the temperature air would assume if its volume were changed adiabatically 

 till it was "at some standard pressure, say 760 mm. 



