104 OCEAN CURRENTS RELATED TO THE DISTRIBUTION OF MASS 



The slope of the isobaric surfaces is small compared to the slope of the 

 boundary surface, but even the latter is very small under conditions 

 encountered in the ocean. 



As an extreme case, consider two water masses, one of salinity 

 34.00°/oo and temperature 20°, and one of salinity 35.00°/oo and tempera- 



Fig. 23. Isobaric surfaces and currents within a wedge of 

 water that extends over resting water of greater density. 



ture 10°, and assume that the velocity of the former is 0.5 m/sec. Neg- 

 lecting the effect of pressure on density, one obtains: 



p' = 1.02402, p = 1.02697, v' = 50 cm/sec, v = 0. 



In latitude 40°N, where X = 0.937 X 10-^ sec-^ and g = 980 cm/sec^, 

 formula (VI, 25) gives 



iB = 1.66 X 10-3; 



that is, the boundary surface sinks 1.66 m when x, the horizontal distance, 

 increases by 1 km (the positive z axis is directed downward). 



The slopes of the isobaric surfaces are much smaller. Inserting the 

 numerical values in (VI, 26), one obtains 



i' = -0.47 X 10-^ 



and 



ip = 0, 



meaning that within the upper layer the isobaric surfaces rise 0.47 m on a 

 horizontal distance of 100 km and that within the lower layer they are 

 horizontal. The conditions are represented schematically in the block 

 diagram in fig. 23, where the slope of the isobaric surfaces is greatly 

 exaggerated. Actually, the lighter water extends like a thin wedge over 

 the heavier water. 



As another example, consider the case where the current in the upper 

 layer is limited to a band of width L. In this case, perfect static equi- 

 librium must exist in the regions of no currents, and there the boundary 



