200 Density of Water Masses in Ocean, Vertical and Horizontal Density Distribution 



stratification is associated with such convection cells and is maintained by the circula- 

 tion. Rayleigh (1916) and Jeffreys (1928) investigated sucha Benard cell theoretically 

 and showed that there could be an equilibrium state with an upper layer of greater 

 density on top of a lower one with smaller density if the vertical density difference 

 between the upper and the lower layer was less than a certain limiting value given by 

 the inequality 



< 



Agli" ' 



where k is the molecular thermal conductivity coefficient, v is the kinetic viscosity co- 

 efficient and h is the thickness of the liquid layer. The unstable density difference is 

 largest in the upper part of the layer; as long as the loss of heat by evaporation tends 

 to maintain the unstable stratification the circulation will continue. It will, however, 

 cease immediately as soon as the evaporation ceases. If there is a steady current in any 

 direction in such a liquid the convection cells resolve into long bands with a corres- 

 ponding transverse circulation. 



It is not impossible that the existence and maintenance of density instability in the 

 top layer of the ocean has something to do with such phenomena. However, in order 

 to simulate conditions actually found in the ocean, the influence of radiation and 

 evaporation and especially that of the eddy conductivity and eddy viscosity must be 

 taken into account in the above inequality, instead of the molecular thermal con- 

 ductivity and the molecular viscosity. For a layer 25-50 m thick resting on top of a 

 transition layer with a stable stratification, the above inequality will give a value for 

 (p' — p) of the order of magnitude of the observed negative stabilities. By the effect 

 of the circulation a mechanical instability is thus changed into a dynamic stability. 



In more recent times the theory of convection cells has been considerably advanced 

 and has been discussed in detail in a symposium on the problems of boundary layers 

 and convection cells in the Section of Oceanography and Meteorology of the New York 

 Academy of Sciences, 1942. Stommel (1947) has presented a summary of the theory 

 of convection cells which should especially be mentioned. Neumann (1948) has paid 

 special attention to cell convection in the sea and has shown that indifferent (neutral) 

 stratification occurs only when 



^0 A"- 

 F = - ^ 



Pg h'' 



where A^'is a. dimensionless quantity of the order of M X 10^ in the ocean, A is the 

 vertical exchange coefficient and h is the thickness of the layer. This equation follows 

 directly from that given by Rayleigh if the above-mentioned change from molecular 

 into turbulent conditions is introduced. The greater the thickness of the layer h and the 

 smaller the exchange coefficient A, the smaller is the decrease in density with depth 

 that is still compatible with static equilibrium. Convection starts only when denser 

 water is situated on top of lighter and when A in the above equation exceeds the 

 critical value 1 100. 



At the "Meteor" anchor station 385 (16° 48-3' N., 46° 17-1' W.; second continua- 

 tion of the German North Atlantic Expedition, February 1938) it was found, as a 



