Ocean Currents in a Non-homogeneous Ocean 



491 



heat source, and on the other hand Q^ is that lost to the surroundings at the cold 

 source. If frictional effects are present, then the process will be irreversible. The 

 machine will give off a quantity of heat Qo, during the course of this process which is 

 greater than in the reversible case {Q'c, > Q2). The degree of efficiency of such a 

 circulation is less than Wand is given by (Qi — Q'^IQ^. In a circulation for which the 

 work done by the pressure forces is exactly sufficient to balance the loss of energy by 

 friction the degree of thermodynamic efficiency will be exactly zero. The Sandstrom 

 theorem thus states: a closed steady circulation can only be maintained in the ocean if 

 the heat source is situated at a lower level than the cold source. Sandstrom (1908) in 

 order to elucidate the content of his theorem has performed a number of very instruc- 

 tive laboratory experiments. Later on Bjerknes (1936) has presented a detailed analysis 

 of all the questions raised when dealing with thermodynamic machines of this type. 

 The two most important of the Sandstrom experiments are: 



{a) Heat source at a higher level than cold source. Here a single water type is con- 

 tained in a narrow basin but there are two sources (Fig. 225, upper picture). The heat 

 source ("warm") lies at a higher level than the cold source ("cold"). At the beginning 



Fig. 225. Upper picture: heat source situated above cold source : no circulation and vertically 

 stable stratified water layers. Lower picture: heat source situated below cold source; genera- 

 tion of a stationary circulation in the layer between the levels of the heat and cold source. 



of the experiment motions will be set up because the heated water will rise in the layers 

 above the level of the heat source and cooled water will sink in the water layers 

 below the cold source. However, when the upper water reaches the temperature of the 

 heat source and the lower water that of the cold source, these water movements will 



