April 15, 1922^ 



NA TURE 



'469 



i 



Turbulence as a Meteorological Agency. 



)/« Zirkulation der Atmosphdre in den gemdsstgten 

 Breiten der Erde. Grundziige einer Theorie der 

 Klimaschwankiingen. By A. Defant. Pp. 209-266. 

 (Stockholm : Geografiska Annaler, 1921.) 



'HE study of turbulence as an agency of direct 

 numerical importance in meteorological pheno- 

 lena had its beginning before the war in the investiga- 

 tions of Akerblom Hesselberg, G. I. Taylor, Barkow 

 and W. Schmidt, and it is not surprising that it should 

 ive been developed independently on either side of 

 le front during the war : on one hand by Taylor, 

 F. Richardson, F. J. W. Whipple, D. Brunt, and 

 [. Jeffreys, and on the other hand by W. Schmidt, 

 M. Exner, and A. Defant. On both sides there has 

 ;en the recognition of a common mathematical form ■ 

 transmission upward or downward, through the 

 jency of turbulence, of various elements with numeri- 

 il coefficients that can be measured without entering 

 ito the details of the process by which the transmis- 

 |on is effected. 

 With us the study has been specially useful as 

 )plied to the eddy motion recognisable in winds and 

 )gs, which is due to the friction of the ground and 

 the consequent deviation of the surface wind from 

 "the geostrophic wind ; while on the other side the con- 

 ception has tended to the general law of " Austausch," 

 the passage upward or downward of heat or momentum 

 in consequence of the ascertained conditions of equili- 

 brium of adjacent columns. Both groups in different 

 ways have come to recognise that transference by 

 irregular turbulent motion is a principle of very general 

 application, and that turbulence may range step by 

 step, perhaps discontinuously, from the ultra-micro- 

 scopic scale of molecular turbulence which we measure 

 as viscosity to the gigantic scale of the eddy motion 

 of the great cyclonic depressions or even of the general 

 circulation of the whole atmosphere. L. F. Richardson 

 has expressed the generality in a manner which easily 

 sticks in the memory :— 



Big whirls have lesser whirls that prey on their velocity ; 

 They again have smaller whirls, and so on to viscosity. 



In course of time we may have a view of the same 

 idea of the universality of the ways of eddy motion 

 from the Japanese point of view. The present article 

 is concerned with an attempt on the part of Prof. 

 A. Defant of Innsbruck to use the turbulence of the 

 cycbnic depressions of middle latitudes to explain 

 the distribution of temperature over the earth's surface 

 and suggest explanations of climatic oscillations with- 

 out entering at all into the details of the turbulent 

 NO. 2737, VOL. 109] 



motion by which the effects are produced. It is an 

 important and suggestive chapter in a new volume 

 of meteorological theory. It deals with iurbulente 

 Strdmung grossen Stils, a greater scale than has been 

 used hitherto. Its basis is an extension of Schmidt's 

 idea of Austausch of mass, and its accompanying 

 properties in the vertical, to the Austausch of 

 mass in a horizontal surface along meridians in con- 

 sequence of the turbulent horizontal motion which is 

 expressed by the irregular barometric changes in middle 

 latitudes, between 40° N. and 70° N. These are the 

 first stages of smaller whirls on the back of the great 

 general whirl, and we read, with some curiosity as to 

 the further development of the next following stages, 

 " AUe Druckstorungen pflanzen sich mit derselben 

 Fo'-tpflanzungs Geschwindigkeit der aussertropischen 

 Zirkulation." 



With the aid of an equation, belonging to what is 

 now a recognised family, a formula is obtained for 

 the normal flow of heat across a vertical square centi- 

 metre near the ground which, with an Austausch 

 coefficient A equal to lo^ gcm.-^sec.-^ gives a flow of 

 heat northward of 100 gram calories per sq. cm. per 

 minute. The value of A is supported by the integrated 

 components of wind, north and south, at Potsdam, 

 and we are allowed to infer that the general circulation 

 of the atmosphere west to east goes on all the time 

 and is crossed by a flow alternately north and south 

 due to turbulence which on the average of the year 

 gives the numerical result specified. 



From that conclusion Defant proceeds to calculate 

 the disturbance of surface temperature for latitudes 

 north of 30° from the balance which would result 

 from radiation alone ; thence to calculate the distribu- 

 tion of temperature when the turbulence is taken into 

 account and to compare the results with Hann's normal 

 mean temperatures for successive latitudes. Finding 

 that a uniform value for the coefficient of Austausch 

 gives notable discrepancies, he adjusts the coefficient 

 to bring calculation and observation into agreement, 

 and thus arrives at the following values for A : lo® 

 at lat. 30°, 5 X lo^ from 40° to 65°, and 1-7 x 10'' at 85°, 

 with intermediate values for the intermediate latitudes ; 

 agreement being thus obtained, he claims that the 

 variation of turbulence with latitude gives a satis- 

 factory picture of the conditions so far as he knows 

 them. 



Having thus arrived at an explanation of the steady 

 state, he proceeds to discu.ss the effect of a sudden 

 permanent increase of temperature in the intertropical 

 belt, such as might be assumed to represent the effect 

 of the activityof sun-spots. He finds that the Austausch 

 would cause a corresponding change of diminished 

 amplitude with little difference of phase in more 



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