58 



BJ0RN HELLAND-HANSEN 



[REP. OF THE "MICHAEL SARS" NORTH 



Such a minimum would mean tiiat the conduction of heat 

 from above has stopped for some time and colder water 

 below affected the temperature. An examination of tem- 



3^T 



peratures seem to show that 



dz^ 



0. 



By — < 

 ^ Sz 



and 



0, — must, then, be r^ 

 dz 



and 



dz^ 



dz dz\ 



(Cf. section 31, case III, Fig. 6i 



The observations have not been made at so small 

 vertical intervals that a more detailed examination can 

 be performed. 



The "anomalies" of temperature at 200 metres seem 

 to show a narrow, but fairly prominent maximum of 

 temperature in July in area B. It corresponds to the 

 smaller maximum at 100 metres in the same area. The 

 course of the curve is, however, rather doubtful. Changes 

 from one year to another and not seasonal variations may 

 have asserted themselves. Apart from this special feature 

 the curves for 200 metres show an annual range of 0.3° C 

 in area B and 0.25° C in area C. 



Our examination leads to the result that the seasonal 

 variations in temperature are quite small at depths below 

 200 metres, when we disregard possible changes in the 

 velocity and direction of the currents. 



Even at 100 metres the temperature variations are so 

 small that they in most cases are of subordinate importance 

 in comparison with the local variations of temperature. 

 For smaller depths observations from different seasons 

 cannot generally be combined without a reduction to a 

 certain time of the year. As the variations in temperature 

 go nearly parallel to variations in density, the seasonal 

 changes must be taken into account by exact calculations 

 of the total pressure at certain depths or the depths from 

 the sea surface to certain isobaric surfaces. 



When the amplitude and phase of the seasonal varia- 

 tions of temperature at different levels are known, the 

 virtual coefficient of temperature conductivity may be 

 calculated. The mathematical operations are, however, 

 complicated because the coefficient of conductivity itself 

 is subjected to seasonal varitions. On my request, Dr. J. 

 E. Fjeldstad of the Geophysical Institute at Bergen has 

 performed a mathematical investigation of the problems. 

 A solution is found on the assumption that the coefficient 

 of temperature conductivity during the year varies with 

 time as a function of sine. The effect of the absorption 

 of heat radiation has been taken into account. A full 

 report on these investigations will be published in another 

 place later on, and here only the following results with 

 regard to area B may be stated: 



In the uppermost water layers the virtual coefficient 

 of temperature conductivity has an average value of about 

 20 C. G. S. units. The value decreases fairly rapidly to 

 a value which is nearly constant, at any rate down to 

 100 metres, and amounts to about 3 C. G. S. units as an 

 average for the whole year. The seasonal changes make 

 the latter value vary between about 0-5 (in summer) and 

 5-5 (in winter). 



These numerical values of the coefficient of temperature 

 conductivity are much smaller than those of the coefficient 

 of virtual friction. Many authors have tried to calculate 

 the latter. It has been found that the coefficient of fric- 

 tion is very small in discontinuity layers, but otherwise 

 it may attain very high values. Values of about 200 C. 

 G. S. units seem to be comparatively common in the sea 

 [cf. V. W. Ekman, 1927). The ratio between the virtual 

 coefficient of temperature conductivity and the coefficient 

 of friction is probably of the order of magnitude 10^ ' 

 and may perhaps sometimes be 10"^. The difference 

 between the two coefficients is understood when we assume 

 that the water particles rapidly alter their momentum 

 according to that of the surrounding particles, while the 

 variation of heat (and contents of salt etc.) inside the 

 particles takes place comparatively slowly, and is not 

 established before many of the particles in turbulent mo- 

 tion return from their new position. 



The differential equations and their solution result in 

 curves of the very same shape as those represented in 

 our figures, and verify the physical discussion given above. 

 The curves based upon the mathematical investigations 

 show a long-stretched minimum, a comparatively narrow 

 (pointed) maximum near the surface, and a relatively slow 

 rise from minimum to maximum and rapid fall from 

 maximum to minimum at 50 and 100 metres. They show 

 even a variation in the rate of the temperature rise in 

 summer at the latter depths, of a similar kind as described 

 above, though not so marked. 



The seasonal variations dealt with above are those 

 which are, so to speak, of a purely thermal character and 

 which commonly start from the surface and propagate 

 downwards. We have tried to eliminate the effect of changing 

 currents as regards their higher or lower (absolute) mean 

 temperatures, in order to obtain sufficient data for con- 

 structing the temperature curves in question. By our mode 

 of proceeding, the seasonal variations of temperature in 

 a current which is relatively warm may be juxtaposed 

 with those in water masses which are colder all the year 

 round. But even the observations from the eastern North 

 Atlantic — where the number of stations hitherto worked 

 is relatively large — do not afford sufficient material for 

 a more detailed analysis. Up to the present, we cannot 

 treat properly either the variations in the distribution of 



