148 Fluctuations 



stratification of the ocean by considering a two-layer ocean model. We 

 must now ask ourselves, what influence does the density stratification of 

 the ocean have upon its response to transient wind systems? Even very 

 crude physical arguments seem to suggest that the density stratification 

 of the ocean cannot respond rapidly to changes in the \\ind distribution. 

 Examples of such arguments are as follows : 



a) There is an immense store of available potential energy in the deep 

 warm-water mass in the Sargasso Sea, more than a thousand times the 

 kinetic energy of all the currents of the North Atlantic. We may suppose 

 that, on the average, the rate of dissipation of the kinetic energy of large- 

 scale currents in the ocean is not more than the rate of work done by the 

 stress of the wind on the ocean. (Much of the work done by the wind may 

 be dissipated in waves or in vertical shear of the surface currents.) If the 

 trade winds exert a stress of 1 djoie/cm.^ on the sea surface, and the 

 surface current there is roughly 20 cm. /sec, the rate of work done on the 

 ocean is roughly 20 ergs/cm. ^/sec, and this sets a maximum average rate 

 to dissipation of kinetic energy per unit area of the ocean currents by tur- 

 bulence. We next compute the potential energy stored in the warm central 

 core of the North Atlantic Ocean in excess of that which would exist were 

 the thermocline level ever3rvvhere. In the latter case the thermocline 

 would be at a uniform depth of about 550 m. In reality, the thermochne 

 is at a depth of 900 m. in half the ocean, and 200 m. in the remainder. If 

 the diff'erence in density of the layers above and beloAv the thermocline is 

 taken as 3 x 10~^ g./cm.^, the potential energy stored in the warm core is 

 3 X 10^ ergs/cm. 2. The potential energy stored is thus sufficient to maintain 

 the current system for at least 1700 days in the absence of the driving 

 stress of the winds. The average kinetic energy of the North Atlantic 

 Ocean is of the order of 4 x 10^ ergs/cm.^. It is no wonder, then, that the 

 density structure of the Gulf Stream System is so uniform and constant 

 a feature regardless of the vagaries of the weather. 



b) An alternative order-of-magnitude computation of the time constant 

 for the decay of the wind-driven circulation following a complete cessation 

 of the wind may be based on the time required for the volume of warm 

 water in the Central North Atlantic Ocean {3000 km. x 6500km. x 0-5 km.) 

 to drain off at the full Gulf Stream rate of discharge (70 x 10^ m.^/sec), 

 supposing all the Gulf Stream water to be lost to the Arctic seas. This 

 period turns out to be 1600 days. 



c) Another estimate of the time constant is provided by a comparison 

 of the total volume of warm water with the rate of convergence of surface 

 water due to the anti cyclonic wind system : about 1000 days. 



These quahtative considerations suggest that the density structure of 

 the ocean (and hence the current field as usually computed from hydro- 



