44 



BJ0RN HELLAND-HANSEN 



[rep. of THK "MICHAEL SARS" NORTH 



the temperature than a larger vertical motion in water 

 with smaller gradients. 



Unit variation in temperature has a much greater 

 effect upon density at high temperatures than at low. A 

 variation of 0-1° C at temperatures about 0^ C causes a 

 variation of 0-5 in the second decimal place of a,, while 



10 ^=^ 1-7 at , = 10" C, and 



2-6 at / — 20" C 



(calculated for sea-water of 35 7uu salinity). The corre- 

 sponding variations in stability are, approximately, 5, 17 

 and 26 units of lO'^ E. In other words: a variation of 

 0-1" C changes the stability 5 times as much at 20° C as 

 at zero. As variations in density act against the disordered 

 motions, these are more hampered at high temperatures 

 than at low as far as this special effect of changes in 

 temperature is concerned. But on the other hand the 

 internal friction (the molecular viscosity) decreases by in- 

 creasing temperatures. The coefficient of internal friction 

 in sea-water of 35 %u is about 0-019 (C. G. S. units) at 

 0°C, 0-014 at 10° C and 0-010 at 20° C. This means 

 that the resistance against the movement of a particle 

 amongst the other water particles is less at higher tem- 

 peratures than at lower. The problem is still more 

 complicated because the forces which generate the tur- 

 bulent motion are influenced by the internal friction. 

 Without entering further into these questions here we may 

 only state that the virtual conduction of heat depends upon 

 the absolute temperature as well as on the vertical varia- 

 tions of temperature (the first and second derivates with 

 regard to depth). 



In the sea we have also variations in salinity which 

 have a great effect upon the vertical distribution of density 

 and, consequently, upon the stability. In most parts of 

 the North Atlantic the salinity decreases from the surface 

 downwards just as the temperatures do. By the combined 

 effect of temperature and salinity we may, then, have 

 comparatively small vertical variations of density in pro- 

 portion to the variations in temperature. In Ihis case a 

 certain energy of the turbulence causes a quicker con- 

 duction of heat than in fresh water (or in sea-water of 

 constant salinity) with the same distribution of temperature. 

 In regions with Arctic water of low salinity at the surface 

 the vertical gradient of salinity is negative (reckoned down- 

 wards) and the stability correspondingly augmented. 

 The distribution of salim'ty regarded separately will here 

 counteract the virtual conduction of heat. 



When the surface layers are strongly heated in summer 

 the stability becomes very marked, notwithstanding the 

 increase of salinity on account of evaporation. The con- 

 vection of heat to lower levels is then much hindered, 

 which explains that the water-masses below the surface 



layers are so very little heated from above in the tropics. 

 Heavy wave motion at the surface causes a perfect mixing 

 only of the upper 10 to 20 metres or a little more. 



A surface current going towaids lower latitudes gene- 

 rally becomes more and more heated at the surface, 

 because the effect of the radiation from sun and sky 

 exceeds the heat lost by outward radiation and by eva- 

 poration. Then the stability becomes more and more 

 pronounced, while the virtual conduction of heat down- 

 wards is lessened. We arrive at the paradoxal result that 

 the water-masses below the surface layers are the more 

 "protected" against heating the stronger the heating at 

 the surface is. It is, then, supposed that concentration 

 by evaporation does not keep pace with the increase of 

 temperature to such a degree that the stability remains 

 constant. 



A surface current flowing towards higher latitudes 

 becomes gradually cooled, so that the stability is diminished 

 and the vertical convection facilitated. Heavy waves created 

 by a strong wind make turbulence, and, consequently, verti- 

 cal heat convection appear deeper in this case than when 

 the surface is warmer and the stability accordingly greater. 



Such variations of temperature with time that are 

 solely due to the vertical conduction of heat, may be 

 expressed by the following equation (which is analogous 

 to the equation representing the acceleration of the fric- 

 tional force in hydrodynamics): 



32 



9^2 



c'Z c'Z 



where / means temperature, / time, ;• virtual coefficient 

 of temperature conductivity, and z depth. By means of 

 this equation we may draw some general conclusions as 

 to the variations in temperature at the depth z. It makes, 

 however, a great difficulty that we know so very little 

 about the variations of r. As mentioned above, the tur- 

 bulence depends upon several factors, especially the current 



velocities 



;/ and an 



dzl 



and the stability {E). The exact 



quantitative relationship between these values and the 

 turbulence is as yet unsettled. 



To begin with, we shall assume that the temperature 

 decreases downwards as is generally the case in the sea. 

 We may then examine separately the variations in tem- 



■'- 

 perature according as "'- — - is negative, nought or positive 



(cf. Fig. 6). V is always reckoned positive. 



5 22 



